maths weight problem solving

Weight Word Problem Worksheets

Related Pages Math Worksheets Lessons for Third Grade Free Printable Worksheets

Printable Measurement worksheets: Longer or Shorter Indirect Comparison for Lengths Length Word Problems Weight Word Problems Liquid Volume Word Problems

Free printable and online math worksheets to help students learn how to solve one-step word problems involving metric weights. Solving weight word problem worksheets involves understanding the information provided, identifying the key details, choosing the appropriate mathematical operation (addition, subtraction, multiplication, or division), and solving for the unknown.

• Begin by carefully reading the word problem. Identify the quantities involved, the units of measurement, and the relationships between them.
• Clearly identify what is given in the problem and what you need to find. This includes identifying the weights of objects, people, or substances.
• Pay attention to the units of measurement used in the problem. Whether it’s in kilograms, grams, or another unit, make sure you understand and convert if necessary.
• Based on the information provided, decide which mathematical operation (addition, subtraction, multiplication, or division) is needed to solve the problem.
• Translate the information into a mathematical equation or expression or use tape diagrams as a visual tool. This may involve adding weights, subtracting weights, finding the difference between two weights, or using other operations.
• Execute the plan and perform the necessary calculations. Be sure to use the correct mathematical operations and units of measurement.
• After finding a solution, check if it makes sense in the context of the problem. Ensure that the units are consistent, and the answer aligns with the information provided.
• Express the answer clearly in a sentence or statement that answers the question posed in the word problem.

Solving weight word problems requires a combination of mathematical skills, understanding of units of measurement, and critical thinking. Regular practice with a variety of problems can help students develop proficiency in solving such word problems.

Then, practice the following worksheets.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Weight Word Problem Worksheets .

More Weight Word Problem Worksheets

Printable (Answers on the second page) Weight Word Problem Worksheet #1 Weight Word Problem Worksheet #2 Weight Word Problem Worksheet #3

Online Metric Mass Word Problems

Related Worksheets

Weight Word Problems

More Printable Worksheets

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Problems Based on Average

Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

How to solve average word problems?

To solve various problems we need to follow the uses of the formula for calculating arithmetic mean.

Average = (Sums of the observations)/(Number of observations)

Worked-out problems based on average:

1. The mean weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.

Mean weight of 7 boys = 56 kg.

Total weight of 7 boys = (56 × 7) kg = 392 kg.

Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg

Weight of the 7th boy = (total weight of 7 boys) - (total weight of 6 boys)

= (392 - 338) kg

Hence, the weight of the seventh boy is 54 kg.

2 . A cricketer has a mean score of 58 runs in nine innings. Find out how many runs are to be scored by him in the tenth innings to raise the mean score to 61.

Mean score of 9 innings = 58 runs.

Total score of 9 innings = (58 x 9) runs = 522 runs.

Required mean score of 10 innings = 61 runs.

Required total score of 10 innings = (61 x 10) runs = 610 runs.

Number of runs to be scored in the 10th innings 

= (total score of 10 innings) - (total score of 9 innings)

= (610 -522) = 88. 

Hence, the number of runs to be scored in the 10th innings = 88.

3.  The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

Mean of 5 numbers = 28.

Sum of these 5 numbers = (28 x 5) = 140.

Mean of the remaining 4 numbers = (28 - 2) =26.

Sum of these remaining 4 numbers = (26 × 4) = 104.

Excluded number

= (sum of the given 5 numbers) - (sum of the remaining 4 numbers)

= (140 - 104)

= 36.  Hence, the excluded number is 36.

4 . The mean weight of a class of 35 students is 45 kg. If the weight of the teacher be included, the mean weight increases by 500 g. Find the weight of the teacher.

Mean weight of 35 students = 45 kg.

Total weight of 35 students = (45 × 35) kg = 1575 kg.

Mean weight of 35 students and the teacher (45 + 0.5) kg = 45.5 kg.

Total weight of 35 students and the teacher = (45.5 × 36) kg = 1638 kg.

Weight of the teacher = (1638 - 1575) kg = 63 kg.

Hence, the weight of the teacher is 63 kg.

5. The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.

Calculated average height of 30 boys = 150 cm.

Incorrect sum of the heights of 30 boys

= (150 × 30)cm

Correct sum of the heights of 30 boys

= (incorrect sum) - (wrongly copied item) + (actual item)

= (4500 - 135 + 165) cm

Correct mean = correct sum/number of boys

= (4530/30) cm

Hence, the correct mean height is 151 cm.

6. The mean of 16 items was found to be 30. On rechecking, it was found that two items were wrongly taken as 22 and 18 instead of 32 and 28 respectively. Find the correct mean.

Calculated mean of 16 items = 30.

Incorrect sum of these 16 items = (30 × 16) = 480.

Correct sum of these 16 items

= (incorrect sum) - (sum of incorrect items) + (sum of actual items)

= [480 - (22 + 18) + (32 + 28)]

Therefore, correct mean = 500/16 = 31.25.

Hence, the correct mean is 31.25.

7. The mean of 25 observations is 36. If the mean of the first observations is 32 and that of the last 13 observations is 39, find the 13th observation.

Mean of the first 13 observations = 32.

Sum of the first 13 observations = (32 × 13) = 416.

Mean of the last 13 observations = 39.

Sum of the last 13 observations = (39 × 13) = 507.

Mean of 25 observations = 36.

Sum of all the 25 observations = (36 × 25) = 900.

Therefore, the 13th observation = (416 + 507 - 900) = 23.

Hence, the 13th observation is 23.

8. The aggregate monthly expenditure of a family was $ 6240 during the first 3 months, $ 6780 during the next 4 months and $ 7236 during the last 5 months of a year. If the total saving during the year is $ 7080, find the average monthly income of the family.

Total expenditure during the year

= $[6240 × 3 + 6780 × 4 + 7236 × 5]

= $ [18720 + 27120 + 36180]

Total income during the year = $ (82020 + 7080) = $ 89100.

Average monthly income = (89100/12) = $7425.

Hence, the average monthly income of the family is $ 7425.

Arithmetic Mean

Word Problems on Arithmetic Mean

Properties of Arithmetic Mean

Properties Questions on Arithmetic Mean

• 9th Grade Math

From Problems Based on Average to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math . Use this Google Search to find what you need.

New! Comments

Share this page: What’s this?

• Preschool Activities
• Kindergarten Math
• 1st Grade Math
• 2nd Grade Math
• 3rd Grade Math
• 4th Grade Math
• 5th Grade Math
• 6th Grade Math
• 7th Grade Math
• 8th Grade Math
• 10th Grade Math
• 11 & 12 Grade Math
• Concepts of Sets
• Probability
• Boolean Algebra
• Math Coloring Pages
• Multiplication Table
• Cool Maths Games
• Math Flash Cards
• Online Math Quiz
• Math Puzzles
• Binary System
• Math Dictionary
• Conversion Chart
• Homework Sheets
• Math Problem Ans
• Free Math Answers
• Printable Math Sheet
• Funny Math Answers
• Employment Test
• Math Patterns
• Link Partners
• Privacy Policy

Recent Articles

5th grade geometry worksheet | angles | triangles | classification.

Aug 23, 24 02:58 PM

Worksheet on Word Problems on Percentage | Real Life Problems on Per

Aug 23, 24 10:21 AM

Data Handling | Data Analysis | Data Processing | Numerical Data | Def

Aug 23, 24 02:28 AM

Construction of Angles by using Compass, Construction of Angles

Aug 22, 24 02:01 AM

Bisecting an Angle | Bisecting an Angle by Using a Protractor | Rules

Aug 21, 24 01:22 AM

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2024.

• Solve equations and inequalities
• Simplify expressions
• Factor polynomials
• Graph equations and inequalities
• Advanced solvers
• All solvers
• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
• The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
• The calculus section will carry out differentiation as well as definite and indefinite integration.
• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions

Lesson Streak

Learn Spelling

Learn grammar, learn handwriting.

Math Solver

Geogebra math solver.

Get accurate solutions and step-by-step explanations for algebra and other math problems, while enhancing your problem-solving skills!

• Topmarks Search
• Whiteboard Resources
• Learning Games
• Topmarks Apps
• Topmarks Blog

• 11-14 Years

Play these fun Maths Games for 5-7 year olds

Choose a category:, measures games.

Coconut Ordering

Compare and order different numbers, including decimal numbers, and metric quantities involving length, mass, capacity and money.

Measuring in Cm

A measuring game which can help children to understand how to use a ruler. Children need to measure various objects against a centimetre ruler. Two levels of difficulty with whole centimetre and half centimetre examples.

Let's Compare

Let's Compare is an interactive comparison game which focuses on the comparative vocabulary of biggest, smallest, shortest, longest and tallest.

Teaching Clock

Teaching Clock is an open-ended teaching resource to help children explore telling the time in both analogue and digital formats. The digital clocks can be viewed in either 12-hour or 24-hour layout.

Telling the Time

Read the time on an analogue clock and match with digital time. Different levels of difficulty. Options include using a 24 hour clock and seeing how many correct answers you can get in a given time.

Capacity Countdown

A game by ICT games where you need to read the volumes on the scales in ml and l.

Time Tools - 12 hour to the half hour

Match each digital clock to the matching analogue time. The times are based on the 12 hour clock and are on the half hours. Two separate games are available.

Telling the Time in Words

A game where you need to tell the time in words. Use language such as 'o'clock', 'half past' and 'quarter to' and compare the analogue time to digital time. Different levels of difficulty.

Hickory Dickory Clock

A telling the time game. Choose the correct time and the mouse runs up the clock to get the cheese. Get it wrong and the cat is waiting!

Mostly Postie

Can you read scales? Then try this read the scales game which includes weights in grams and kilograms.

Reading Scales Mass

A great teaching aid for children learning to read scales involving g and kg. Generate lots of different readings. This resource works well on tablets and interactive whiteboards.

Happy Camel

Help the camel to find his toy by weighing his food on the balance scales. A good problem solving game.

Clock Splat

Match simple analogue times with digital equivalents. There are three levels of difficulty: hours, half hours and quarter hours.

An amazing resource for demonstrating the difference between two times. It is configurable so that teachers can use it at a basic level or use the questions provided.

Classroom Timer

A useful classroom timer which is configurable to countdown in either seconds or minutes.

Match the Times

A flexible matching pairs game which can help you to tell the time.

Clocking In

A telling the time game about o'clock and half past times.

Kitten Knitting - Measure lengths in cm

Move the ruler to measure granny's scarf. The scale goes from 0cm to 70cm.

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE :

• 8 Common Core math examples
• Tier 3 Interventions: A School Leaders Guide
• Tier 2 Interventions: A School Leaders Guide
• Tier 1 Interventions: A School Leaders Guide

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

Related articles

Why Student Centered Learning Is Important: A Guide For Educators

13 Effective Learning Strategies: A Guide to Using them in your Math Classroom

Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

5 Math Mastery Strategies To Incorporate Into Your 4th and 5th Grade Classrooms

Ultimate Guide to Metacognition [FREE]

Looking for a summary on metacognition in relation to math teaching and learning?

Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.

Privacy Overview

Get step-by-step solutions with MathGPT

Upload a screenshot or picture of your question and get instant help from your personal ai math tutor.

Click here to take a picture or select an image

Drag & drop or click here to upload an image of your problem

• AI Math Solver Graphing Calculator Popular Problems Worksheets Study Guides Cheat Sheets Calculators Verify Solution
• Solutions Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More...
• Graphing Line Graph Exponential Graph Quadratic Graph Sine Graph More...
• Calculators BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More...
• Geometry Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More...
• Tools Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution

• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems
• Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Coterminal Angle Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
• Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
• Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
• Linear Algebra Matrices Vectors
• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
• Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
• Physics Mechanics
• Chemistry Chemical Reactions Chemical Properties
• Finance Simple Interest Compound Interest Present Value Future Value
• Economics Point of Diminishing Return
• Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
• Pre Algebra
• One-Step Addition
• One-Step Subtraction
• One-Step Multiplication
• One-Step Division
• One-Step Decimals
• Two-Step Integers
• Two-Step Add/Subtract
• Two-Step Multiply/Divide
• Two-Step Fractions
• Two-Step Decimals
• Multi-Step Integers
• Multi-Step with Parentheses
• Multi-Step Rational
• Multi-Step Fractions
• Multi-Step Decimals
• Solve by Factoring
• Completing the Square
• Quadratic Formula
• Biquadratic
• Logarithmic
• Exponential
• Rational Roots
• Floor/Ceiling
• Equation Given Roots
• Equation Given Points
• Newton Raphson
• Substitution
• Elimination
• Cramer's Rule
• Gaussian Elimination
• System of Inequalities
• Perfect Squares
• Difference of Squares
• Difference of Cubes
• Sum of Cubes
• Polynomials
• Distributive Property
• FOIL method
• Perfect Cubes
• Binomial Expansion
• Negative Rule
• Product Rule
• Quotient Rule
• Expand Power Rule
• Fraction Exponent
• Exponent Rules
• Exponential Form
• Logarithmic Form
• Absolute Value
• Rational Number
• Powers of i
• Complex Form
• Partial Fractions
• Is Polynomial
• Leading Coefficient
• Leading Term
• Standard Form
• Complete the Square
• Synthetic Division
• Linear Factors
• Rationalize Denominator
• Rationalize Numerator
• Identify Type
• Convergence
• Interval Notation
• Pi (Product) Notation
• Boolean Algebra
• Truth Table
• Mutual Exclusive
• Cardinality
• Caretesian Product
• Age Problems
• Distance Problems
• Cost Problems
• Investment Problems
• Number Problems
• Percent Problems
• Addition/Subtraction
• Multiplication/Division
• Dice Problems
• Coin Problems
• Card Problems
• Pre Calculus
• Linear Algebra
• Trigonometry
• Conversions

Number Line

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

We want your feedback

Please add a message.

Message received. Thanks for the feedback.

Registered Nurse RN

Registered Nurse, Free Care Plans, Free NCLEX Review, Nurse Salary, and much more. Join the nursing revolution.

Weight-Based Dosage Calculations Quiz

This quiz on weight-based dosage and calculations  will test your ability to solve dosage and calculation problems of drugs that are based on a patient’s weight.

These weight-based calculation problems were designed to help you better understand how to apply basic conversions to advanced drug problems. In nursing school, you will be required to learn how to solve these types of problems, along with other drug and dosage calculations.

After you take this quiz, be sure to check out our other dosage and calculation quizzes  with video teaching tutorials  that go along with each quiz.

Demonstration on How to Solve Weight-Based Calculations

Weight-Based Calculations in Nursing

These dosage and calculation problems will test your ability on how to calculate weight-based drugs.

• B. 8.35 mL/hr
• C. 21.6 mL/hr
• D. 25 mL/hr
• A. 0.93 mL/dose
• B. 25 mL/dose
• C. 2 mL/dose
• D. 0.68 mL/dose
• A. 35.5 mL/hr
• B. 18.8 mL/hr
• C. 150 mL/hr
• D. 61 mL/hr
• A. 8.6 mL/hr
• B. 25 mL/hr
• C. 63.5 mL/hr
• D. 17.4 mL/hr
• A. 40.5 mL/hr
• B. 88.1 mL/hr
• C. 44.5 mL/hr
• D. 22.2 mL/hr
• A. 13.7 mL/hr
• B. 26.4 mL/hr
• C. 87 mL/hr
• A. 24 mL/dose
• B. 3 mL/dose
• C. 12.5 mL/dose
• D. 1.5 mL/dose
• A. 0.25 mL/dose
• B. 0.4 mL/dose
• D. 1.4 mL/dose
• A. 18.2 mL/hr
• B. 36 mL/hr
• D. 2.9 mL/hr
• A. 98 mL/hr
• B. 46.4 mL/hr
• C. 0.77 mL/hr
• D. 50 mL/hr

Weight-Based Calculation Practice Problems for Nurses

1. Doctor orders Dobutamine 4 mcg/kg/min IV infusion. The patient weighs 198 lb. You are supplied with a bag of Dobutamine that reads 250mg/250 ml. How many mL/hr will you administer?

2. Doctor orders Heparin 50 units/kg/dose subcutaneous daily. The patient weighs 93 kg. Heparin is supplied in a vial that reads 5,000 units/ml. How many mL/dose will you administer?

3. Doctor orders a Lidocaine infusion to be started at 30 mcg/kg/min. The patient weighs 298 lbs. You are supplied with a bag of Lidocaine that reads 4 mg/mL. How many mL/hr will you administer?

4. Doctor orders 20 units/kg/hr Heparin infusion to be started. The patient weighs 87 kg. You are supplied with a bag of Heparin that reads 100 units/mL. How many mL/hr will you administer?

5. Doctor orders Vancomycin 500 mg to infuse at 5 mg/kg/hr. The patient weighs 98 lbs. You are supplied with 500mg/100mL bag. How many mL/hr will you administer?

6. Doctor orders 9 units/kg/hr Heparin infusion. The patient weighs 76 kg. You’re supplied with a Heparin bag that reads 50 units/mL. How many mL/hr will you administer?

7. Doctor orders 12 mg/kg of Acyclovir. The patient weighs 115 lbs. Acyclovir is supplied as 100 mg/2mL. How many mL will you administer per dose?

8. Doctor orders 12 units/kg/hr Heparin infusion. The patient weighs 200 lbs. You’re supplied with a 30,000 units/500mL bag. What is the mL/hour rate?

9. Doctor orders 10 mcg/kg/min of a Dopamine infusion. The patient weighs 170 lbs. Dopamine is supplied as 500 mg/500mL. How many mL/hr will you administer?

10. Doctor orders 2 mg/kg of Lovenox subcutaneous daily. Patient weighs 155 lbs. You are supplied with a Lovenox syringe that reads 40 mg/0.4 mL. How many mL/dose will you administer?

Answer Key:

1. 21.6 mL/hr 2. 0.93 mL/dose 3. 61.2 mL/hr 4. 17.4 mL/hr 5. 44.5 mL/hr 6. 13.7 mL/hr 7. 12.5 mL/dose 8. 18.2 mL/hr 9. 46.4 mL/hr 10. 1.4 mL/dose

*Disclaimer: While we do our best to provide students with accurate and in-depth study quizzes, this quiz/test is for educational and entertainment purposes only. Please refer to the latest NCLEX review books for the latest updates in nursing. This quiz is copyright RegisteredNurseRn.com. Please do not copy this quiz directly; however, please feel free to share a link to this page with a friend.

Please Share:

• Click to print (Opens in new window)
• Click to share on Facebook (Opens in new window)
• Click to share on Twitter (Opens in new window)
• Click to share on Pinterest (Opens in new window)
• Click to share on Reddit (Opens in new window)
• Click to share on LinkedIn (Opens in new window)
• Click to share on WhatsApp (Opens in new window)
• Click to share on Pocket (Opens in new window)
• Click to share on Telegram (Opens in new window)

Disclosure and Privacy Policy

Important links, follow us on social media.

• Facebook Nursing
• Instagram Nursing
• TikTok Nurse
• Twitter Nursing
• YouTube Nursing

Copyright Notice

• Physics Formulas

Weight Formula

Weight is not anything but the force gravity experiences. It is represented by W and Newton is its SI unit. It is articulated as the product of mass and acceleration due to gravity. So the weight of a given object will show variation according to the gravity in that particular space. So, objects with similar mass appear in different weights across different planets.

Formula of Weight

The formula for weight is articulated as,

           W=mg

• Weight of the object is W
• Mass of the object is m
• Acceleration due to gravity is g

Solved Examples

Numerical associated to weight calculations are provided underneath:

Problem 1: Compute the weight of a body on the moon if the mass is 60Kg? g is given as 1.625 m/s 2 . Answer :

It is known that, m = 60 kg and

g = 1.625 m/s 2

Formula for weight is, W = mg W = 60×1.625 W = 97.5 N

Problem 2: Compute the weight of a body on earth whose mass is 25 kg? Answer :

It is known that, m = 25 kg and

g = 9.8 m/s 2

Formula for weight is, W = mg W = 25×9.8 W = 245 N

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Sentences & passages
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

• Word Problems
• Mass / weight

Download & Print From only $2.60

Mass word problems

Measurement word problems.

Below are our grade 5 word problems worksheets involving the measurement of mass or weight . The worksheets are in customary units (ounces, lbs), metric units (gm, kg) or mixed units. No conversions of units between the two systems are needed.

Ounces, pounds:

Grams, kilograms:

These worksheets are available to members only.

Join K5 to save time, skip ads and access more content. Learn More

More word problem worksheets

Explore all of our math word problem worksheets , from kindergarten through grade 5.

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

• Forgot Password?

The home of mathematics education in New Zealand.

• Forgot password ?
• Resource Finder

Thanks for visiting NZMaths. We have now moved over 3,500 resources to Tāhūrangi and will be closing this site on 29 August 2024  

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

This problem solving activity has a measurement focus.

Dr Martin the chemist is weighing out some pills.

He has some 5g weights and some 7g weights.

Can he weigh exactly 38g of pills?  

• Measure using grams.
• Apply addition to a measurement problem.
• Devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment).

This problem gives students the chance to do some number investigations using combinations of 5 and 7. It also builds their experience making measurement calculations. This helps extend their experience and knowledge of number, and can also extend their experience of weights and the use of balance scales.

• Copymaster of the problem (English)
• Copymaster of the problem (Māori)
• Balance scales and weights (5g and 7g) (and/or a digital representative)

The Problem

Dr Martin the chemist is weighing out some pills. He has some 5g weights and some 7g weights. Can he weigh exactly 38g of pills?

Teaching Sequence

• Ask the students to find an object that they estimate weighs 20g. Check estimates on the scales.
• Discuss students' ideas about how they made their estimates of 20g (eg, weight of small chip packet = 18g, flake bar = 30g).  What object in your desk would weigh close to 38g? How did you decide that? How do you use weights on a balance scale?  How do you use these kitchen scales? What else could we use to measure these things?
• Pose the problem.
• As the students work on the problem in pairs, ask questions that focus their understanding of the size of grams. Encourage them to write their measurements with the correct unit (g - grams).
• Focus their thinking on working systematically by asking questions about the way that they are keeping track of their work. What are you doing? How will you share what you have done with others in the class? How are you recording your measurements? How do you know that you are on the right track?
• Share solutions

Extension 

Can the chemist weigh out 52g ? Can this be done in more than one way?

38 is not exactly divisible by 5 or 7. Hence both 5g and 7g weights are needed. 38 – 7 = 31, 38 – 2 x 7 = 24, and 38 – 3 x 7 = 17 are not divisible by 5. However, 38 – 4 x 7 = 10 = 2 x 5. So Dr Martin can use four 7g weights and two 5g weights.

Solution to the Extension

(9 x 5, 1 x 7 ) or (6 x 7, 2 x 5)

Log in or register to create plans from your planning space that include this resource.

• Printer-friendly version

Choose Your Test

• Search Blogs By Category
• College Admissions
• AP and IB Exams
• GPA and Coursework

The Complete Guide to SAT Math Word Problems

A significant portion of the total digital SAT Math section will be word problems, meaning you'll need to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them.

This post will be your complete guide to SAT Math word problems. We'll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day.

Feature Image: Antonio Litterio /Wikimedia

What Are SAT Math Word Problems?

A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it.

You will be given word problems on the digital SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information.

Secondly, these types of questions allow test makers to ask questions that'd be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it'd be difficult to demonstrate and ask this with only a diagram.

Translating Math Word Problems Into Equations or Drawings

In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action.

For instance, the word "sum" means the value when two or more items are added together. So if you need to find the sum of a and b , you’ll need to set up your equation like this: a+b.

Also, note that many mathematical actions have more than one term attached, which can be used interchangeably.

Here is a chart with all the key terms and symbols you should know for SAT Math word problems:

Now, let's look at these math terms in action using a few official examples:

We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form.

We'll say that the number of salads sold = S , and the number of drinks sold = D . The problem tells us that 209 salads and drinks have been sold, which we can think of as this:

S + D = 209

Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D , but we do know how much each unit costs. Therefore, we can write this equation:

6.50 S + 2 D = 836.5

We now have two equations with the same variables ( S and D ). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S . The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S :

Now, just subtract S from both sides to get what D equals:

D = 209 − S

Finally, plug this expression in for D into our other equation, and then solve for S :

6.50 S + 2(209 − S ) = 836.5

6.50 S + 418 − 2 S = 836.5

6.50 S − 2 S = 418.5

4.5 S = 418.5

The correct answer choice is (B) 93.

This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers.

Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer.

If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer.

Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct.

Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions.

Typical SAT Word Problems

Word problems on the SAT can be grouped into three major categories:

• Word problems for which you must simply set up an equation
• Word problems for which you must solve for a specific value
• Word problems for which you must define the meaning of a value or variable

Below, we look at each world problem type and give you examples.

Word Problem Type 1: Setting Up an Equation

This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You'll also most likely see it first on the section.

For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go.

Almost always, you’ll see this type of question in the first several questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution.

It's stated that the vet recommends that, every day, the rabbit eat 25 calories per pound that it weighs, plus an additional 11 calories.

Let's put this in terms of  x. If a rabbit weighs  x  pounds, then multiplying its weight in pounds by 25 calories yields 25x calories. 

Adding the additional 11 calories gives us 25x + 11. The question states that  c  is the total number of calories that the vet recommends a rabbit eat each day.

Put this all together, and you get: c = 25x +11. This means Answer Choice D is the correct answer.

Word Problem Type 2: Solving for a Missing Value

The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.

Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics , such as averages , single-variable equations , and ratios . You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.

Let's think about this problem in terms of x . If Scott has 400 employees, randomly selected 20 employees, then found that 16 of those 20 employees are enrolled in 3 professional development courses, then we know that 16/20 employees are in three courses, or 80% because 16/20 is 0.80 or 80/100.

Because the employees were selected randomly, the best way to estimate how many of the 400 total employees are enrolled in exactly three professional development courses this year is to multiply 400 x 0.8. This gives us 320.

Answer Choice B is the correct answer.

You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram.

This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem.

Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!)

Now, because x = 56, the next angle in the triangle—2 x —must measure the following:

Let's make a rough (not to scale) sketch of what we know so far:

Now, we know that there are 180° in a triangle , so we can find the value of y by saying this:

y = 180 − 112 − 56

One possible value for y is 12. (Other possible values are 3, 6, and 9. )

Word Problem Type 3: Explaining the Meaning of a Variable or Value

This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number.

Let's break this question down.

The equation y - 5x = 6 represents the relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased, y, in yards. 

But what does the 6 represent? Let's get one of the variables by itself to see what the equation looks like then. Y is easier to isolate than x, so we'll do that.

Adding 5x to both sides of the equation gives us y = 5x + 6

Because Kaylani made x suits and used 5 yards of fabric to make each suit, 5x represents the total amount of fabric she used to make the suits. Because y represents the total length of fabric Kaylani purchased, then the equation y = 5x + 6 shows us that Kaylani purchased 5x yards of fabric to make the suits, plus an additional 6 yards of fabric.

Therefore, the best interpretation of 6 in this question is that Kaylani purchased 6  yards more fabric than she used to make the suits.

The correct answer is Choice D.

To help juggle all the various SAT word problems, let's look at the math strategies and tips at our disposal.

SAT Math Strategies for Word Problems

Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole.

#1: Draw It Out

Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you're working with. For instance, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza):

If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds.

Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer:

3 * 16 = 48 ounces (for whole pizza)

Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale):

We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale):

This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza:

48 / 6 = 8 ounces per piece

The correct answer choice is (C) 8.

As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order.

#2: Memorize Key Terms

If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it.

There are free SAT Math questions available online , so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test.

#3: Underline and/or Write Out Important Information

Even though the SAT is now digital, you're still allowed scratch paper to take notes and work out problems.

The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order.

One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question.

#4: Pay Close Attention to What's Being Asked

It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems.

Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y?

It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again.

#5: Brush Up on Any Specific Math Topic You Feel Weak In

You're likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it.

For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages!

Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good time to brush up on them—or else SAT word problems might be trickier than you were expecting!

All set? Let's go!

Test Your SAT Math Word Problem Knowledge

Finally, it's time to test your word problem know-how against real SAT Math problems:

Word Problems

Answers:  A, A, B, A

Aaaaaaaaaaand time for a nap.

Key Takeaways: Making Sense of SAT Math Word Problems

Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle.

Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work.

Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies.

What’s Next?

Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math . From polygons and slopes to probabilities and sequences , we've got you covered!

Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score .

Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan.

Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math , written by a perfect scorer.

Trending Now

How to Get Into Harvard and the Ivy League

How to Get a Perfect 4.0 GPA

How to Write an Amazing College Essay

What Exactly Are Colleges Looking For?

ACT vs. SAT: Which Test Should You Take?

When should you take the SAT or ACT?

Get Your Free

Find Your Target SAT Score

Free Complete Official SAT Practice Tests

How to Get a Perfect SAT Score, by an Expert Full Scorer

Score 800 on SAT Math

Score 800 on SAT Reading and Writing

How to Improve Your Low SAT Score

Score 600 on SAT Math

Score 600 on SAT Reading and Writing

Find Your Target ACT Score

Complete Official Free ACT Practice Tests

How to Get a Perfect ACT Score, by a 36 Full Scorer

Get a 36 on ACT English

Get a 36 on ACT Math

Get a 36 on ACT Reading

Get a 36 on ACT Science

How to Improve Your Low ACT Score

Get a 24 on ACT English

Get a 24 on ACT Math

Get a 24 on ACT Reading

Get a 24 on ACT Science

Stay Informed

Get the latest articles and test prep tips!

Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.

Ask a Question Below

Have any questions about this article or other topics? Ask below and we'll reply!

Please ensure that your password is at least 8 characters and contains each of the following:

• a special character: @$#!%*?&

10 Math Tasks for the Beginning of the Year

I have a rule about the first day of school: always do some math. No, that doesn't mean you have to start Lesson 1.1 as soon as students walk through the door, but it does mean that you should give your students a preview of the kind of thinking, reasoning, puzzling, and sense-making that they'll be doing in your class this year. Ideally, students will be so highly engaged that they barely even recognize they're doing math -- and certainly not the kind of math they're used to in school.

I also have an inordinate appreciation for what I call "interesting problems". These are tasks that use mathematical thinking and strategy, but don't require specific content knowledge like the formula for the equation of a circle or knowing what a composite function does. They are highly accessible, highly engaging, and have multiple solution strategies. The task itself can be explained in a few sentences and students can work on them for 20 minutes or 2 hours, depending on how far they want to take it. I scour the internet for tasks like these and have been collecting them for YEARS on my computer. I decided this was the year to bring them to the light and share them with the Math Medic community.

These tasks don't require formal content knowledge, but they do help students engage in the mathematical practices and develop mathematical habits of mind, such as:

Looking for and making use of structure

Representing one's thinking

Working systematically

Visualizing

Developing a convincing argument

Conjecturing and generalizing

While I've curated this list with high school students in mind, many of these tasks could be done with middle schoolers or even with adults. The inspiration for these questions came from all over this great big internet, but have been adapted and reformatted for classroom use. So, without further ado, here are my (current) top 10 "interesting problems" to do on the first day of school.

10 Interesting Problems

The Shopping Cart Task

A linear context in a LOT of disguise. Many solution strategies and great opportunities for representing one's thinking with a model or visual.

The Locker Problem

This one is set up with multiple parts providing lots of natural extensions. Thinking about a number's properties is key to this task! Make sure to print the 100s chart that is on page two on a separate sheet of paper. You can offer it to everyone or as an optional support.

A Leg to Stand On

Loads of solution strategies on this one as well. Your teacher brain might scream system of equations with 4 variables, but you'll be surprised at the intuitive solutions your students find to solve this problem.

To Run or Not to Run?

Perfect after a summer of olympics. Students deal with rates in this problem, which is an important concept for any age group and relevant for any math course.

Four 4's

This one's been famous for a long time but I'm sharing it anyway because students do great with it!

Page Turner

This one and the next two all encourage students to think systematically. There's a brute force solution but making use of structure will illuminate an easier way.

How Many 7's?

This is a good intro to thinking systematically and has a nice extension. I would use this in an Algebra 1 or Geometry course.

Oddball Numbers

This one is very difficult, so we recommend saving it for your Precalc or above courses.

This one is the most recent in my collection and I'm still thinking about the extension part!

Toothpick Challenge

I've often done this one with Geometry students because of the shapes and visual reasoning components.

Editable versions of these tasks can be found in this Google Drive folder .

How to use these in your classroom:

Pick ONE task for students to work on. We don't recommend giving multiple tasks back-to-back because it can start to feel like a worksheet, rather than a puzzle.

Solve the problem yourself first! We are purposefully not giving solutions here , so make sure you've wrestled with the problem yourself before handing it out to students.

Have students work on these in groups of 2, 3, or 4. Make sure they have enough materials available to hash out their ideas and represent their strategies. These are great to do on vertical non-permanent surfaces or poster paper.

Decide how long you will let students work. If doing this on the first day of school, we recommend about 20 minutes. If students don't have a solution by then, that is totally fine. A surprising number of them will keep thinking about the problem throughout the day or even at home.

Be ready with some extensions for groups who finish early, but make sure they understand what "done" means. Have they clearly communicated their strategy? Have they convinced themselves and others that their strategy will hold up? If giving an extension, make sure it's related to the given task, not just a different task. It's important that students are challenged in the depth of their reasoning, not in the quantity of problems.

If you're looking for more tasks like these, I highly recommend the NRICH site from the University of Cambridge.

Recent Posts

Rainbow Logic

AP Stats Lessons on a Block Schedule

AP Daily Notes for AP Precalculus

• Work & Careers
• Life & Arts

Maths and English GCSE failure rates near 40%

To read this article for free, register now.

Once registered, you can: • Read free articles • Get our Editor's Digest and other newsletters • Follow topics and set up personalised events • Access Alphaville: our popular markets and finance blog

Explore more offers.

Then $75 per month. Complete digital access to quality FT journalism. Cancel anytime during your trial.

FT Digital Edition

Today's FT newspaper for easy reading on any device. This does not include ft.com or FT App access.

• Global news & analysis
• Expert opinion

Standard Digital

Essential digital access to quality FT journalism on any device. Pay a year upfront and save 20%.

• FT App on Android & iOS
• FT Edit app
• FirstFT: the day's biggest stories
• 20+ curated newsletters
• Follow topics & set alerts with myFT
• FT Videos & Podcasts

Terms & Conditions apply

Explore our full range of subscriptions.

Why the ft.

See why over a million readers pay to read the Financial Times.

Manipulatives in Maths - A Classroom Guide for Teachers

Mathematical manipulatives are touted as essential tools for learning, but let's be honest—we've all experienced that moment of dread when we hand them out. Suddenly, your carefully planned lesson turns into chaos: One pupil starts building a fortress with the base ten blocks while another is hiding all the shiny counters.

Yet, despite these challenges, manipulatives play an important role in maths education. They bridge the gap between abstract concepts and tangible understanding, helping pupils grasp basic number sense. In fact, the National Curriculum emphasises their importance across all key stages, recognising that hands-on learning is vital for developing maths fluency, reasoning, and problem-solving skills.

So, how can we take advantage of these tools without losing control of the classroom? Let's explore the world of maths manipulatives—what they are, why they matter, and how to use them effectively in your primary school lessons.

What are manipulatives?

It can sound complicated, but manipulatives are simply hands-on tools that make abstract mathematical concepts concrete and visual . They're the building blocks, quite literally in some cases, that help pupils wrap their heads around tricky number ideas through good old-fashioned play, exploration, and modelling.

These learning aids come in all shapes and sizes, from the humble counter to the more elaborate Cuisenaire rods . Their key purpose? To give pupils something tangible to manipulate as they grapple with mathematical concepts. Whether it's using multilink cubes to understand place value or fraction circles to visualise parts of a whole, manipulatives help bridge the gap between 'maths on paper' and 'maths in real life'.

Common manipulatives you'll find in primary classrooms include:

Multilink cubes

Cuisenaire rods, base ten blocks, bead strings.

• Balance scales

Clock faces

Digit cards, hundred squares.

These tools align perfectly with the National Curriculum's aims of developing mathematical fluency, reasoning, and problem-solving skills. By allowing pupils to physically interact with mathematical ideas, manipulatives help build a strong foundation for more complex concepts down the line. They're not just toys or distractions—they're powerful learning tools that can transform how your pupils understand and engage with maths.

Why are they important?

Over the past two decades, research has consistently shown the positive impact of using manipulatives in the classroom. A 2013 report published in the Journal of Educational Psychology identified "statistically significant results" when teachers used manipulatives compared with when they only used abstract maths symbols. This highlights the role that manipulatives play in supporting conceptual understanding and facilitating the progression from concrete to abstract thinking.

Alignment with CPA approach

The NCETM agrees that physical manipulatives should play a central role in maths teaching. "Manipulatives are not just for young pupils, and also not just for those who can't understand something. They can always be of help to build or deepen understanding of a mathematical concept."

This approach aligns perfectly with the concrete-pictorial-abstract (CPA) progression. Once children are confident using manipulatives or 'concrete' resources, they can then move onto pictorial representations or the 'seeing' stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures , diagrams or models that represent the objects from the maths problem.

Enhance problem solving

But manipulatives do more than just support understanding—they're powerful tools for enhancing problem-solving skills. By allowing pupils to physically manipulate and visualise mathematical concepts, they can more easily devise strategies to tackle complex problems. This hands-on approach often leads to those 'aha!' moments we all love to see in our classrooms.

Support engagement

Moreover, manipulatives play an important role in fostering engagement and motivation. Let's face it—maths can sometimes seem dry and abstract to young learners. But introduce some colourful counters or interlocking cubes, and suddenly you've got a room full of eager mathematicians. This increased engagement is key to developing a positive attitude towards maths, which in turn supports long-term learning.

This deep understanding allows pupils to move beyond mere memorisation of facts and procedures, towards true mathematical fluency—where they can apply their knowledge flexibly and efficiently across a range of contexts.

In essence, manipulatives are not just helpful additions to our maths teaching toolkit—they're essential components in building a comprehensive, engaging, and effective mathematics education.

Types of manipulatives in primary mathematics

In this section, we'll break it common types of manipulatives into bite-sized pieces, just like we do for our pupils.

Physical manipulatives: the classics

These are the tangible, grab-them-with-your-hands resources that have been the backbone of maths classrooms for years. They're the ones that inevitably end up stuck between classroom seats and occasionally in someone's shoe.

Below is a list of common physical manipulatives in the classroom:

Ideal for teaching place value, addition, and subtraction with regrouping.

Fraction tiles

Excellent for comparing fractions and understanding equivalence.

Great for exploring 2D shapes, symmetry, and area.

Images: Wikipedia.org

Versatile tools for counting, measuring, and understanding volume.

Fantastic for developing number sense and exploring number relationships.

Essential for basic counting, sorting, and introducing simple addition and subtraction.

Useful for teaching multiplication, division, and fractions.

Image: Pinterest

Helpful for developing number sense and practicing skip counting.

Useful for probability exercises and generating random numbers for various activities.

Great for pattern recognition, matching, and basic addition facts.

Essential for teaching time-telling and understanding intervals.

Images: Pinterest & Pinterest

Useful for place value activities and forming large numbers.

Excellent for identifying number patterns and supporting multiplication and division.

Virtual manipulatives: a new kind of tool

Manipulatives have gone digital! These are interactive, online versions of our physical favourites. Think of them as the maths equivalent of e-books.

Some popular virtual manipulatives include:

Online number lines

These number lines are zoomable, clickable, and free of the uneven lines that are often result of our hand-drawn versions.

Digital base ten blocks

All the functionality without the risk of losing pieces under desks.

Interactive fraction tools

Slice and dice up pieces in any way imaginable.

Whether physical or virtual, the best manipulative is the one that helps your pupils understand the concept at hand. Whether that's a handful of multilink cubes or a fancy online simulator, if it's making those mathematical lightbulbs flicker on, you're on the right track!

Implementing manipulatives in the classroom - let them play!

Whether you have a bumper pack of manipulatives, a shared bank of resources or your very own DIY versions, it's important to teach children how to use them independently. Here are some best practices for integrating manipulatives effectively into your lessons:

• Introduce gradually : Bring in manipulatives one at a time. If you don't have enough for each child, set up a 'maths table' where pupils can take turns exploring. This works particularly well with younger years where 'choosing tables' are common.
• Allow for exploration : Give children a chance to play with and explore the manipulatives before using them for instruction. Through this exploration, they can start to imagine how the resource might be useful.
• How could you use this?
• How might this help you when adding or subtracting?
• Why do you think they're different sizes - what could that represent?
• Model usage : Once children are familiar with a resource, introduce a simple maths problem and ask them to use the manipulatives to solve it. Model the problem-solving process step-by-step, then guide children through it.
• Scaffold learning : Start with highly structured activities, then gradually reduce support as pupils gain confidence. For instance, begin with direct instruction on how to use base ten blocks for place value, then move to guided practice, and finally independent problem-solving.
• Year 1: Using counters or number lines to support addition and subtraction within 20.
• Year 2: Use fraction tiles to help pupils recognise, find, name and write fractions of a length, shape, set of objects or quantity.
• Year 3: Utilising place value charts (physical or digital) so pupils can recognise 3-digit numbers (100s, 10s and 1s).
• Integrate into lesson plans : Don't treat manipulatives as an add-on. Instead, weave them into your lessons as essential tools for understanding. Plan specific points in your lessons where manipulatives will be most beneficial.
• Support diverse learners : Manipulatives can be particularly helpful for English Language Learners (ELLs) and pupils with learning disabilities. They provide a universal language of mathematics that transcends verbal communication barriers.

Images: The Average Teacher

Manipulatives across Key Stages 1 and 2

Next, let's breakdown more examples of manipulatives in the classroom by Key Stage.

Key Stage 1 (Years 1-2): Laying the foundations

In these early years, it's all about getting hands-on with numbers and shapes.

• Number and Place Value : Introduce counters, number lines, and base ten blocks. Pupils can observe how 10 ones form a 'ten stick', helping them grasp place value concepts.
• Addition and Subtraction : Utilise multilink cubes for hands-on learning. Pupils can physically join or separate cubes to represent addition and subtraction operations.
• Fractions : Fraction tiles can be effective tools for teaching fractions. They provide a visual and tactile representation of concepts like 'half' and 'quarter'.
• Geometry : Employ geoboards for creating 2-D shapes. Pupils can then be asked to match these shapes on a 3-D surface to enhance spatial understanding.

Key Stage 2 (Years 3-6): Progressing with Purpose

As our mathematicians-in-training grow, so does the sophistication of our manipulatives. We're not ditching the basics, just building on them.

• Multiplication and Division : Array cards and Cuisenaire rods are useful for these operations. For multiplying by 6, pupils can line up 6 rods of 4 to visualise the concept.
• Fractions, Decimals, and Percentages : Fraction circles can be used alongside decimal place value charts. The 100 square is effective for teaching percentages.
• Geometry : The geoboard is a helpful tool for teaching perimeter, area, and symmetry concepts in a hands-on manner.
• Statistics : Data can be represented using multilink cube bar charts or human pictograms, making statistics more engaging for pupils.

CPA Journey: From Concrete to Pictorial to Abstract

Remember, our end goal is for pupils to solve problems without relying on physical props. Here's how we might progress:

• Concrete : Pupils physically manipulate objects to solve a problem. For example, using counters to work out 5 + 3.
• Pictorial : They draw a picture or diagram to represent the problem. Our 5 + 3 might become five circles and three circles.
• Abstract : Finally, they use mathematical symbols and numbers alone. "5 + 3 = 8."

The beauty of this approach? Pupils can always 'go back' a stage if they're struggling with a new concept. Stuck on an abstract problem? Draw a picture! Need more practise? Grab those counters!

Remember, every child's journey through these stages is unique. Some might race through, others might linger longer at certain points. The key is to ensure they have a solid understanding at each stage before moving on.

An example of moving from the concrete, to pictorial, to abstract stages.

Manipulative manners

Once you have introduced your resources, speak as a class and explain that they should come up with a set of rules for how they are treated and used. Giving children ownership over the manipulatives as well as the respect to make their own rules will make them feel accountable and lessen the likelihood of negative behaviours when using manipulatives. Write the rules up as a class and display them so they can be referred to.

Storing manipulatives

NRICH recommends children having access to manipulatives “Give open access to all the resources and allow the children free reign in choosing what to use to model any problem they may be tackling. I would make sure that children of all ages had this access from 3 to 11 years old and beyond.” While this is exactly what teachers would like to replicate in their classrooms, not all classes learn in the same way and this isn’t always achievable due to space, budgets and children’s prior experiences of manipulatives.

Once you have introduced a manipulative, decide as a class where you should store it . You know what works best for your class, so consider different options such as communal drawers, a maths table, individual packs or a collection of manipulatives for each table. Set clear rules around using and treating manipulatives to ensure they are not broken or lost. Additionally, you could create a monitor for each resource so the children can take ownership and make sure they stay tidy and accounted for.

Creating a classroom culture that uses manipulatives will aid children’s fluency and help develop their ability to solve problems, reason mathematically and share! If manipulatives are introduced in a considered and gradual way, with clear boundaries from an early age, children should see them as part of everyday learning and they will not be a novelty. They will be seen as tools instead of toys — and hopefully no more multilink towers!

For the community, by the community

Maths — No Problem! Community Event Conference, 28 November at The Royal Society, London.

Lily Lanigan

Browse by Topic

Your teaching practice.

Boost your teaching confidence with the latest musings on pedagogy, classroom management, and teacher mental health.

Maths Mastery Stories

You’re part of a growing community. Get smart implementation advice and hear inspiring maths mastery stories from teachers just like you.

Teaching Tips

Learn practical maths teaching tips and strategies you can use in your classroom right away — from teachers who’ve been there.

Classroom Assessment

Identify where your learners are at and where to take them next with expert assessment advice from seasoned educators.

Your Learners

Help every learner succeed with strategies for managing behaviour, supporting mental health, and differentiating instruction for all attainment levels.

Teaching Maths for Mastery

Interested in Singapore maths, the CPA approach, bar modelling, or number bonds? Learn essential maths mastery theory and techniques here.

Deepen your mastery knowledge with our biweekly newsletter

By clicking “Accept All” , you agree to the storing of cookies on your device to enhance site navigation, analyze site usage and assist in our marketing efforts.

Game Central

Similar problems from web search.