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Polygons - Lesson 11.1

Triangles - Lesson 11.2

Quadrilaterals - Lesson 11.3

Three Dimensional Figures - Lesson 11.5

Unit Cubes and Solid Figures - Lesson 11.6

Understanding Volume - Lesson 11.7

Estimate Volume - Lesson 11.8

Volume of a Rectangular Prism - Lesson 11.9

Apply Volume Formulas - Lesson 11.10

Finding Volume of Composite Formulas - Lesson 11.12

Find a Part of a Group - Lesson 7.1

Multiply Fractions and Whole Numbers - Lesson 7.2

Fraction and Whole Number Multiplication - Lesson 7.3

Multiply Fractions - Lesson 7.4

Compare Fraction Factor and Product - Lesson 7.5

Fraction Multiplication - Lesson 7.6

Area and Mixed Numbers - Lesson 7.7

Compare Mixed Number Factors and Products - Lesson 7.8

Multiply Mixed Numbers - Lesson 7.9

Problem Solving - Find Unknown Lengths - Lesson 7.10  

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Line Plots - Lesson 9.1

Ordered Pairs - Lesson 9.2

Graph Data - Lesson 9.3

Line Graphs - Lesson 9.4

Numerical Patterns - Lesson 9.5

Problem Solving - Find a Rule - Lesson 9.6

Graph and Analyze Relationships - Lesson 9.7

Customary Length - Lesson 10.1

Customary Capacity - Lesson 10.2

Weight - Lesson 10.3

Multistep Measurement Problems - Lesson 10.4

Metric Measures - Lesson 10.5

Problem Solving Conversions - Lesson 10.6

Elapsed Time - Lesson 10.7

Division Patterns with Decimals - Lesson 5.1

Divide Decimals by Whole Numbers - Lesson 5.2

Estimate Quotients - lesson 5.3

Division of Decimals by Whole Numbers - Lesson 5.4

Decimal Division - Lesson 5.5

Divide Decimals - Lesson 5.6

Write Zeros in the Dividend - Lesson 5.7

Problem Solving - Decimal Operations - Lesson 5.8

Divide Fractions and Whole Numbers - Lesson 8.1

Problem Solving - Use Multiplication - Lesson 8.2

Connect Fractions to Division - Lesson 8.3

Fraction and Whole Number Division - Lesson 8.4

Interpret Division with Fractions - Lesson 8.5

Addition with Unlike Denominators - Lesson 6.1

Subtraction with Unlike Denominators - Lesson 6.2

Estimate Fraction Sums and Differences - Lesson 6.3

Common Denominators and Equivalent Fractions - Lesson 6.4

Add or Subtract Fractions - Lesson 6.5

Add or Subtract Mixed Numbers - Lesson 6.6

Subtraction with Renaming - Lesson 6.7

Patterns with Fractions - Lesson 6.8

Problem Solving with Addition and Subtraction - Lesson 6.9

Use Properties of Addition - Lesson 6.10

Multiplication Patterns with Decimals - Lesson 4.1

Multiply Decimals and Whole Numbers - Lesson 4.2

Multiply Decimals and Whole Numbers - Lesson 4.3

Multiply Using Expanded Form - Lesson 4.4

Problem Solving - Multiply Money - Lesson 4.5

Decimal Multiplication - Lesson 4.6

Multiply Decimals - Lesson 4.7

Thousandths - Lesson 3.1

Place Value of Decimals - Lesson 3.2

Compare and Order Decimals - Lesson 3.3

Round Decimals - Lesson 3.4

Decimal Addition - Lesson 3.5

Decimal Subtraction - Lesson 3.6

Estimate Decimal Sums and Differences - Lesson 3.7

Add Decimals - Lesson 3.8

Subtract Decimals - Lesson 3.9

Patterns with Decimals - Lesson 3.10

Problem Solving Add and Subtract Money - Lesson 3.11

Choose a Method - Lesson 3.12

Performance Task on Chapter 3

Place the First Digit - Lesson 2.1

Divide by 1-Digit Divisors - Lesson 2.2

Division with 2-Digit Divisors - Lesson 2.3

Partial Quotients - Lesson 2.4

Estimate with 2-Digit Divisors - Lesson 2.5

Divide by 2-Digit Divisors - Lesson 2.6

Interpret the Remainder - Lesson 2.7

Adjust Quotients - Lesson 2.8

Problem Solving - Division - Lesson 2.9

Performance Task on Chapter 2

Fifth Grade 

     Math

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CHALLENGE ZONE 5th Grade Math Problems

Welcome to our 5th Grade Math Problems. Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems.

These problems are also a great way of developing perseverance and getting children to try different approaches in their math.

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5th Grade Math Problems

Here you will find a range of problem solving worksheets.

The 5th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them.

The skills the problems will help to develop include:

  • systematic working
  • logical thinking
  • number fact knowledge
  • fraction problems
  • trial and improvement strategies
  • working backwards
  • working systematically
  • searching for all possible answers.

At fifth grade, the problems are more advanced with children needing to become more systematic in their approach and experimenting using trial and improvement strategies.

Many of the problems have addition 'What if ...' questions with them to extend learning and get children looking for alternative solutions.

These sheets are great for extending learning for more able mathematicians, or using in a whole class problem solving lesson.

  • 5th Grade Math Word Problems
  • Bertie's Big Win

Bertie's Big Win is a problem involving both money and fractions which can be worked backwards. The aim of the problem is to work out how much money Bertie started with from the clue that are given.

  • PDF version
  • Fox vs Rabbit #2

Fox vs Rabbit is an activity involving mathematical modelling of a fox chasing a rabbit. The rabbit has a head-start, but the fox is faster. The aim is to find out when the fox will catch the rabbit, and whether or not the rabbit has time to reach his burrow.

  • 1..2..3..4.. Challenge

The 1..2..3..4.. Challengs is a number problem involving using the numbers 1, 2, 3 and 4 along with arithmetic operators to make the numbers from 1 to 20. It is great for practicing PEMDAS and getting children to persevere and develop their mental arithmetic skills.

There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.

  • Blank version
  • Frazer's Wall #2

Frazer's Wall #2 is a fraction problem solving activity which involves trying to work out the number of bricks that were laid in each day to find out how long it would take to make a wall. This problem is best solved by using a table or working it out one day at a time.

  • Millenary Math

Millenary Math is a time problem involving what the time will be in a thousand years/weeks/hours/minutes, etc. It is a good activity for converting units of time and knowing facts like how many days are in each month. There is no answer sheet, as the activity involves using the current time.

  • Sally's Fruit Punch #3

Sally's Fruit Punch is a money and scaling activity. The aim is to use the information to work out how much ingredients are needed. The ingredients then need to be priced to work out a total cost.

  • Sally's Fruit Punch #3 UK Version
  • Share the Treasure #5

Share the Treasure is a fraction sharing activity where the aim is to work backwards to find out how many bars of treasure the pirates had before they shared them all out. It is a good activity for developing fraction problem solving and working backwards.

  • Something Fishy #2

Something Fishy is a money problem which involves working out exactly how many of each fish were bought in order to have spent a fixed amount of money on the fish. It is a good activity for using lists and tables to find all possibilities. It is also great for perseverance!

  • Something Fishy #2 UK Version
  • The Five Primes

The Five Primes is a number activity involving finding five primes with different totals. It is a good activity for learning prime numbers up to 30, and also for working systematically.

  • The Rock Race #3

The Rock Race is a 5th grade math problem which needs some perseverance to complete. The aim of the activity is to try different routes around the 6 rocks to determine which route is the shortest.

  • Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

  • Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

  • Number Totals Investigation

Number Totals Investigation is a PEMDAS number task which involves using 3 digits and operations to make the largest or smallest possible total.

Looking for some easier math problems?

We have a range of easier word problems on our 4th grade math problems page.

The problems on this page are at a simpler level than those here.

Many of the problems, e.g. Share the Treasure, The Rock Race, Something Fishy have easier versions on this page.

  • 4th Grade Math Problems

Looking for some more fifth grade math word problems?

Here you will find our selection of free 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

  • apply their addition, subtraction, multiplication and division skills;
  • apply their knowledge of rounding and place value;
  • solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

  • 5th Grade Math Puzzles

Here you will find a range of printable 5th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

  • learn and practice their addition facts, including decimals;
  • practice their subtraction facts, including decimals;
  • practice and apply multiplication and division facts;
  • develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 5th grade.

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

All the free 5th Grade Math Worksheets in this section follow the Elementary Math Benchmarks for Grade 5.

  • Math Games 5th Grade

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  • Inspiration
 Place Value Through Millions
 Place Value Through Millions
 Compare and Order Whole Number Through Millions
 Compare and Order Whole Number Through Millions
 Hands On: Model Fractions and Decimals
 Hands On: Model Fractions and Decimals
 Represent Decimals
 Represent Decimals
 Hands On: Understanding Place Value
 Hands On: Understanding Place Value
 Place Value Through Thousandths
 Place Value Through Thousandths
 Compare Decimals
 Compare Decimals
 Order Whole Numbers and Decimals
 Order Whole Numbers and Decimals
 Problem Solving Investigation: Use the Four Step Plan
 Problem Solving Investigation: Use the Four Step Plan
 Prime Factorization
 Prime Factorization
 Hands On: Prime Factorization Patterns
 Hands On: Prime Factorization Patterns
 Powers and Exponents
 Powers and Exponents
 Multiplication Patterns
 Multiplication Patterns
 Problem Solving Investigation: Make a Table
 Problem Solving Investigation: Make a Table
 Hands On: Use Partial Products and the Distributive Property
 Hands On: Use Partial Products and the Distributive Property
 The Distributive Property
 The Distributive Property
 Estimate Products
 Estimate Products
 Multiply by One-Digit Numbers
 Multiply by One-Digit Numbers
 Multiply by Two-Digit Numbers
 Multiply by Two-Digit Numbers
 Relate Division to Multiplication
 Relate Division to Multiplication
 Hands On: Division Models
 Hands On: Division Models
 Two-Digit Dividends
 Two-Digit Dividends
 Division Patterns
 Division Patterns
 Estimate Quotients
 Estimate Quotients
 Hands On: Division Models with Greater Numbers
 Hands On: Division Models with Greater Numbers
 Hands On: Distributive Property and Partial Quotients
 Hands On: Distributive Property and Partial Quotients
 Divide Three-and Four-Digit Dividends
 Divide Three-and Four-Digit Dividends
 Place the First Digit
 Place the First Digit
 Quotients with Zeros
 Quotients with Zeros
 Hands On: Models to Interpret the Remainder
 Hands On: Models to Interpret the Remainder
 Interpret the Remainder
 Interpret the Remainder
 Problem Solving Investigation: Determine Extra or Missing Information
 Problem Solving Investigation: Determine Extra or Missing Information
 Estimate Quotients
 Estimate Quotients
 Hands On: Divide Using Base-Ten Blocks
 Hands On: Divide Using Base-Ten Blocks
 Divide by a Two-Digit Divisor
 Divide by a Two-Digit Divisor
 Adjust Quotients
 Adjust Quotients
 Divide Greater Numbers
 Divide Greater Numbers
 Problem Solving Investigation: Solve a Simpler Problem
 Problem Solving Investigation: Solve a Simpler Problem
 Round Decimals
 Round Decimals
 Estimate Sums and Differences
 Estimate Sums and Differences
 Problem Solving Investigation: Estimate or Exact Answer
 Problem Solving Investigation: Estimate or Exact Answer
 Hands On: Add Decimals Using Base-Ten Blocks
 Hands On: Add Decimals Using Base-Ten Blocks
 Hands On: Add Decimals Using Models
 Hands On: Add Decimals Using Models
 Add Decimals
 Add Decimals
 Addition Properties
 Addition Properties
 Hands On: Subtract Decimals Using Base-Ten Blocks
 Hands On: Subtract Decimals Using Base-Ten Blocks
 Hands On: Subtract Decimals Using Models
 Hands On: Subtract Decimals Using Models
 Subtract Decimals
 Subtract Decimals
 Estimate Products of Whole Numbers and Decimals
 Estimate Products of Whole Numbers and Decimals
 Hands On: Use Models to Multiply
 Hands On: Use Models to Multiply
 Multiply Decimals by Whole Numbers
 Multiply Decimals by Whole Numbers
 Hands On: Use Models to Multiply Decimals
 Hands On: Use Models to Multiply Decimals
 Multiply Decimals
 Multiply Decimals
 Multiply Decimals by Powers of Ten
 Multiply Decimals by Powers of Ten
 Problem Solving Investigation: Look for a Pattern
 Problem Solving Investigation: Look for a Pattern
 Multiplication Properties
 Multiplication Properties
 Estimate Quotients
 Estimate Quotients
 Hands On: Divide Decimals
 Hands On: Divide Decimals
 Divide Decimals by Whole Numbers
 Divide Decimals by Whole Numbers
 Hands On: Use Models to Divide Decimals
 Hands On: Use Models to Divide Decimals
 Divide Decimals
 Divide Decimals
 Divide Decimals by Powers of Ten
 Divide Decimals by Powers of Ten
 Hands On: Numerical Expressions
 Hands On: Numerical Expressions
 Order of Operations
 Order of Operations
 Write Numerical Expressions
 Write Numerical Expressions
 Problem Solving Investigation: Work Backward
 Problem Solving Investigation: Work Backward
 Hands On: Generate Patterns
 Hands On: Generate Patterns
 Patterns
 Patterns
 Hands On: Map Locations
 Hands On: Map Locations
 Ordered Pairs
 Ordered Pairs
 Graph Patterns
 Graph Patterns
 Fractions and Division
 Fractions and Division
 Greatest Common Factor
 Greatest Common Factor
 Simplest Form
 Simplest Form
 Problem Solving Investigation: Guess, Check, and Revise
 Problem Solving Investigation: Guess, Check, and Revise
 Least Common Multiple
 Least Common Multiple
 Compare Fractions
 Compare Fractions
 Hands On: Use Models to Write Fractions as Decimals
 Hands On: Use Models to Write Fractions as Decimals
 Write Fractions as Decimals
 Write Fractions as Decimals
 Rounding Fractions
 Rounding Fractions
 Add Like Fractions
 Add Like Fractions
 Subtract Like Fractions
 Subtract Like Fractions
 Hands On: Use Models to Add Unlike Fractions
 Hands On: Use Models to Add Unlike Fractions
 Add Unlike Fractions
 Add Unlike Fractions
 Hands On: Use Models to Subtract Unlike Fractions
 Hands On: Use Models to Subtract Unlike Fractions
 Subtract Unlike Fractions
 Subtract Unlike Fractions
 Problem Solving Investigation: Determine Reasonable Answers
 Problem Solving Investigation: Determine Reasonable Answers
 Estimate Sums and Differences
 Estimate Sums and Differences
 Hands On: Use Models to Add Mixed Numbers
 Hands On: Use Models to Add Mixed Numbers
 Add Mixed Numbers
 Add Mixed Numbers
 Subtract Mixed Numbers
 Subtract Mixed Numbers
 Subtract with Renaming
 Subtract with Renaming
 Hands On: Part of a Number
 Hands On: Part of a Number
 Estimate Products of Fractions
 Estimate Products of Fractions
 Hands On: Model Fraction Multiplication
 Hands On: Model Fraction Multiplication
 Multiply Whole Numbers and Fractions
 Multiply Whole Numbers and Fractions
 Hands On: Use Models to Multiply Fractions
 Hands On: Use Models to Multiply Fractions
 Multiply Fractions
 Multiply Fractions
 Multiply Mixed Numbers
 Multiply Mixed Numbers
 Hands On: Multiplication as Scaling
 Hands On: Multiplication as Scaling
 Hands On: Division and Unit Fractions
 Hands On: Division and Unit Fractions
 Divide Whole Numbers by Unit Fractions
 Divide Whole Numbers by Unit Fractions
 Divide Unit Fractions by Whole Numbers
 Divide Unit Fractions by Whole Numbers
 Problem Solving Investigation: Draw a Diagram
 Problem Solving Investigation: Draw a Diagram
 Hands On: Measure with a Ruler
 Hands On: Measure with a Ruler
 Convert Customary Units of Length
 Convert Customary Units of Length
 Problem Solving Investigation: Use Logical Reasoning
 Problem Solving Investigation: Use Logical Reasoning
 Hands On: Estimate and Measure Weight
 Hands On: Estimate and Measure Weight
 Convert Customary Units of Weight
 Convert Customary Units of Weight
 Hands On: Estimate and Measure Capacity
 Hands On: Estimate and Measure Capacity
 Convert Customary Units of Capacity
 Convert Customary Units of Capacity
 Display Measurement Data on a Line Plot
 Display Measurement Data on a Line Plot
 Hands On: Metric Rulers
 Hands On: Metric Rulers
 Convert Metric Units of Length
 Convert Metric Units of Length
 Hands On: Estimate and Measure Metric Mass
 Hands On: Estimate and Measure Metric Mass
 Convert Metric Units of Mass
 Convert Metric Units of Mass
 Convert Metric Units of Capacity
 Convert Metric Units of Capacity
 Polygons
 Polygons
 Hands On: Sides and Angles of Triangles
 Hands On: Sides and Angles of Triangles
 Classify Triangles
 Classify Triangles
 Hands On: Side and Angles of Quadrilaterals
 Hands On: Side and Angles of Quadrilaterals
 Classify Quadrilaterals
 Classify Quadrilaterals
 Hands On: Build Three-Dimensional Figures
 Hands On: Build Three-Dimensional Figures
 Three-Dimensional Figures
 Three-Dimensional Figures
 Hands On: Use Models to Find Volume
 Hands On: Use Models to Find Volume
 Volume of Prisms
 Volume of Prisms
 Hands On: Build Composite Figures
 Hands On: Build Composite Figures
 Volume of Composite Figures
 Volume of Composite Figures
 Problems Solving Investigation: Make a Model
 Problems Solving Investigation: Make a Model
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Problem-Based Tasks in Math

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Dive deeper into our Instructional Practices and methodology by taking one of our online courses.

Providing students with opportunities to grapple with math has led to amazing things happening in my class. Students are totally excited and are driven to figure out not just how to solve a problem but why it works.

– Jessica Proffitt, Fifth-Grade Teacher at Two Rivers

Watch two rivers’s teachers and students at work on problem-based tasks in math.

Problem-Based Tasks Require Students to Apply Their Knowledge in New Contexts

Problem-based tasks are math lessons built around a single, compelling problem. The problems are truly “problematic” for students — that is, they do not offer an immediate solution.

The problems provide an opportunity for students to build conceptual understanding. Problem-based tasks require students to apply their current understanding and skills to new contexts that highlight core math concepts. For example, when students solve a problem that could be solved with multiplication before they have formally been taught what multiplication is and how it works, they build an understanding that multiplication is repeated addition.

Well-designed problem-based tasks provide multiple entry points for students to engage in problem solving, ensuring that all students have access to the same concepts. When students solve the problems in different ways—including drawing pictures, acting out the problem, writing algorithms, and using manipulatives—they make connections between the variety of models that all accurately illustrate the underlying mathematics.

Problem-Based Tasks in Math Resources

problem solving lesson 9 7 5th grade

problem solving lesson 9 7 5th grade

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5th Grade Math Word Problems Worksheets

Math word problem worksheets for grade 5.

These worksheets present students with real world word problems that students can solve with grade 5 math concepts. 

We encourage students to think about the problems carefully by:

  • providing a number of mixed word problem worksheets
  • including irrelevant data  so students need to understand the context before applying a solution

The four operations

Mixed 4 operations

Estimating and rounding word problems

Grade 5 fractions and decimal word problems

Addition and subtraction of fractions

Addition and subtraction of mixed numbers

Division of numbers with fractional answers

Dividing by unit fractions

Multiplying fractions word problems

Mixed operations with fractions

More mixed fraction word problems

Decimals word problems

Measurement word problems

Mass and weight word problems

Volume and capacity word problems

Length word problems

Word problems worksheets with variables

Variables and expressions

Variables and equations

Other grade 5 word problems worksheets

Volume of rectangular prisms

GCF / LCM word problems

Mixed grade 5 word problems  

problem solving lesson 9 7 5th grade

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problem solving lesson 9 7 5th grade

35 math problems for 5th graders

Here are 35 fifth-grade math problems that will help your child stay on track!

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Author Amber Watkins

problem solving lesson 9 7 5th grade

Published September 13, 2023

problem solving lesson 9 7 5th grade

  • Key takeaways
  • 5th-grade math word problems help students apply mathematical concepts to real-world scenarios.
  • In fifth-grade math, it’s important to master fractions, decimals, and order of operations.
  • Hard problems for 5th graders can be simplified by drawing a picture or using a method that makes them easier to solve.

Table of contents

  • Word problems

Numbers & place value

  • Multiplication

If this math page has 5 sections of math problems for 5th graders with an average of 7 questions in each section, can you guess how many problems there will be in all? That’s right, there will be a total of 35 math problems for 5th graders for us to practice. Without realizing it, you just solved one of our first 5th-grade math word problems . Excellent work! Together we will review fifth-grade math problems with decimals, fractions, order of operations, and rounding. We will even consider hard math problems for 5th graders, like multiplying using square models and number lines. Don’t worry about getting the answers right the first time, each section includes math problems for 5th graders with answers if you need a sneak peek. So grab a pad and pencil and let’s begin.

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Measurement and data

Sample questions, word problems for 5th graders.

Let’s begin by covering math word problems for 5th graders.

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Mia’s water bottle can hold 24 ounces of water. She drinks two full water bottles each day. How many total cups of water does Mia drink each day? [Conversions]

problem solving lesson 9 7 5th grade

The playground is made up of four rectangular lots that are each 10 ft by 7 ft. What is the total area of the playground? [Finding area]

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 Josh lives 2.5 miles away from the park. Josh rides his bike to the park and back home four days a week. How many miles does Josh ride his bike each week? [Calculations]

Place value

In this section, we will cover math problems for 5th graders that use place values, word form to standard form, standard form to word form, and expanded form.

Which digit in the number 245 is in the hundreds place?

Which digit in the number 4,602 is in the tens place?

Which digit in the number 752 is in the ones place?

Word form to standard form

Standard form to expanded form.

4,000 + 300 + 2 = 4,302

600 + 50 + 4 = 654

20,000 + 2,000 + 300 + 60 + 5 = 22,365

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for families

In this section, we will cover fifth-grade math problems that include comparing decimals and rounding decimals to the nearest tenth, hundredth, and thousandths place. Let’s get started.

8.9 and 8.900 are the same.

Remember if the number to the right is 5 or larger, you can borrow and become one digit larger. If the number to the right is between 0 and 4, you can’t borrow and the number remains the same.

In this section, we will review math problems for fifth graders that cover the topics of adding and subtracting two and three-digit numbers using transformation, division using area models, and the order of operations .

Adding and subtracting whole numbers by transformation

A large portion of fifth-grade math problems can be made easier to solve by transformation or changing numbers to make the problem simpler. Let’s practice adding and subtracting two and three-digit numbers by transformation.

How to add numbers using transformation?

When adding or subtracting numbers, look for ways to round to make the problem simpler. Don’t forget what you do to one number, you have to do the opposite to the other. This makes sure the problem stays balanced. Let’s see how this is done. What is 48 + 52? 48 + 2 = 50

52 – 2 = 50 

50 + 50 = 100.

It may be difficult to add 48 + 52 in your head, so we round 48 to 50 by adding 2. Since we added 2 to the first number, we have to make sure to subtract 2 from the second number. So now the problem is 50 plus 50, which is much easier to calculate! 

32 – 2 = 30 68 + 2 = 70 30 + 70 = 100 The answer is 100.

208 – 8 = 200 432 + 8 = 440 200 + 440 = 640 The answer is 640.

321- 1 = 320 199 + 1 = 200 320 – 200 = 120 120 + 2 = 122 The answer is 122

Division using area models

Don’t know what an area model is? See our area model guide to help with these problems.

Using an area model find the quotient of 365 ፥ 5 =

problem solving lesson 9 7 5th grade

Using an area model find the quotient of 504 ፥ 6 =

Using the area model below, find the quotient of 872 ፥ 2 =

Order of operations

Many people remember the Order of Operations with the acronym PEMDAS- “Please Excuse My Dear Aunt Sally”, with each letter representing an operation: Parentheses, Exponents, Multiply or Divide, Add or Subtract. Solve the following equations using the order of operations.

Hard multiplication math problems

Some of the hardest math problems for fifth graders involve multiplying: multiplying using square models, multiplying fractions and whole numbers using expanded form, and multiplying fractions using number lines. Let’s practice a few of each!

Multiplying using square models

Multiplying using square models is a method to help students “see” multiplication problems in a simpler way.

Multiply 42 x 35 using the square model below.

problem solving lesson 9 7 5th grade

Multiply 55 x 76 using the square model below.

Multiply 98 x 42 using the square model below.

Multiplying fractions and whole numbers using expanded form

Multiply ½ x 5 using expanded form.

Multiply ⅔ x 6 using expanded form.

Multiply ⅙ x 7 using expanded form.

Multiplying fractions using a number line

Multiply ½ x 4/6 by using a number line.

For more math practice for 5th graders , our app for math help provides 5th-grade math help in a way that makes math fun, rewards effort over being correct, and scaffolds learning. Plus, you’ll get access to a dashboard that displays your child’s participation and progression on math topics they struggle with. Check it out today!

problem solving lesson 9 7 5th grade

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Word problem answer sheet

Mia drinks 6 cups of water each day. Explanation: There are 8 ounces in each cup. So 24 divided by 8 is equal to 3 cups each day.

280 square feet. Explanation: The area of one lot is 10 x 7 = 70 square feet. Take that area and times it by four, so 70 x 4 = 280 square feet.

problem solving lesson 9 7 5th grade

Josh rides 20 miles on his bike each week. Explanation: Each day Josh rides 5 total miles: 2.5 miles to the park and 2.5 miles back home. If we multiply that number by 4 days a week, it equals 20 miles in all.

problem solving lesson 9 7 5th grade

Writing numbers answer sheet

2 is in the hundreds place.

problem solving lesson 9 7 5th grade

0 is in the tens place.

problem solving lesson 9 7 5th grade

2 is in the ones place.

problem solving lesson 9 7 5th grade

Division using area models answer sheet

problem solving lesson 9 7 5th grade

Multiplying using square models answer sheet

problem solving lesson 9 7 5th grade

Multiplying fractions and whole numbers using expanded form answer sheet

problem solving lesson 9 7 5th grade

Multiplying fractions using a number line answer sheet

problem solving lesson 9 7 5th grade

Explanation – First divide the number line into 6 equal parts and draw up a line up to 4/6. Then find the ½ way mark of that line you drew up to 4/6. You will now see the line is divided into three parts. So the answer would be ⅓. 

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Everyday Mathematics

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Multiplication of mixed numbers; geometry; graphs.

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Multiplication of Mixed Numbers, Part 1

Home Link 7-1


Multiplication of Mixed Numbers, Part 2

Home Link 7-2


Rectangles with Fractional Side Lengths

Home Link 7-3


Using Common Denominators for Fraction Division

Home Link 7-4


A Hierarchy of Triangles

Home Link 7-5


A Hierarchy of Quadrilaterals

Home Link 7-6


Playing Property Pandemonium

Home Link 7-7


Open Response: A Hierarchy of Polygons

Home Link 7-8


Collecting and Using Fractional Data

Home Link 7-9


Identifying and Visualizing Patterns

Home Link 7-10


Rules, Tables, and Graphs, Part 1

Home Link 7-11


Rules, Tables, and Graphs, Part 2

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Old Faithful's Next Eruption

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Unit 7 Progress Check

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problem solving lesson 9 7 5th grade

Everyday Mathematics for Parents: What You Need to Know to Help Your Child Succeed

The University of Chicago School Mathematics Project

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Problem solving resources

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Preview of Behavior Reflection Think Sheet for Classroom Management

Behavior Reflection Think Sheet for Classroom Management

problem solving lesson 9 7 5th grade

Brain Teaser Higher Level Thinking Early Finisher Summer Activities Logic Puzzle

problem solving lesson 9 7 5th grade

Holidays Around the World Christmas Escape Room Printable & Digital Activity

problem solving lesson 9 7 5th grade

Interactive ZONES of Regulation Package - Name Plates, Bookmarks, & MORE!

problem solving lesson 9 7 5th grade

STEM Bins® Speed Builds STEM Activities (Morning Work, Early Finishers, Centers)

problem solving lesson 9 7 5th grade

Classroom Calm Down Corner Kit | Identifying Feelings Emotional Regulation

problem solving lesson 9 7 5th grade

STEM Bins® Hashtag Blocks Speed Builds BUNDLE - Elementary STEM Activities

Preview of Place Value Mystery Pictures

Place Value Mystery Pictures

problem solving lesson 9 7 5th grade

CUBES Math Strategy Poster Display | EDITABLE

problem solving lesson 9 7 5th grade

15 Working Memory Brain Games: Improve executive function in 5 minutes a day!

problem solving lesson 9 7 5th grade

100th Day of School Activities STEM Activities

problem solving lesson 9 7 5th grade

STEM Index Card Tower Challenge - Easy Prep Project- 2 Versions

problem solving lesson 9 7 5th grade

STEM Bins® Plastic Snowflakes / Brainflakes Speed Builds: STEM Activities SET 1

Preview of Classroom Procedure & Routine Visuals for Preschool, Pre-k and Kindergarten

Classroom Procedure & Routine Visuals for Preschool, Pre-k and Kindergarten

problem solving lesson 9 7 5th grade

Growth Mindset Escape Room Activity Game Back to School Digital & Paper

problem solving lesson 9 7 5th grade

(Educator Guide) A Little SPOT of Feelings & Emotions

problem solving lesson 9 7 5th grade

Escape Room Halloween Activity Digital or PDF Game for Parties Distance Learning

Preview of Math Logic Puzzles: 5th grade Enrichment - [Digital & Printable PDF]

Math Logic Puzzles: 5th grade Enrichment - [Digital & Printable PDF]

problem solving lesson 9 7 5th grade

Index Cards and Castles - A Design Challenge and Team Building Activity

problem solving lesson 9 7 5th grade

STEM Bins® Hashtag Blocks Speed Builds: SET 1 - STEM Activities - Fast Finishers

Preview of Quadrilateral Robots - Great Project Based Learning Math Activity (PBL)

Quadrilateral Robots - Great Project Based Learning Math Activity (PBL)

problem solving lesson 9 7 5th grade

Circle of Control Activities Inside vs. Outside of Our Control Lesson

problem solving lesson 9 7 5th grade

Cup Stacking Challenge Cards

problem solving lesson 9 7 5th grade

Math Logic Puzzles: 4th grade ENRICHMENT - [Digital & Printable PDF]

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Problem Solving     Lesson Plan

Problem Solving

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Fifth graders read and write equations. In this equation writing activity, 5th graders use real life scenarios to write equations. Students use manipulatives, draw pictures and make tables to understand how to write equations. Students work in groups and use newspapers to write equations.

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Unit 4: Add and subtract fractions

About this unit.

It's time to tackle fractions! From common denominators to unlike denominators, this unit will teach you everything you need to know to add and subtract them confidently. Get ready to show those fractions who's boss!

Strategies for adding and subtracting fractions with unlike denominators

  • Visually adding fractions: 5/6+1/4 (Opens a modal)
  • Visually subtracting fractions: 3/4-5/8 (Opens a modal)
  • Estimating adding fractions with unlike denominators (Opens a modal)
  • Visually add and subtract fractions Get 3 of 4 questions to level up!
  • Estimate to add and subtract fractions with different denominators Get 3 of 4 questions to level up!

Common denominators

  • Finding common denominators (Opens a modal)
  • Common denominators: 1/4 and 5/6 (Opens a modal)
  • Common denominators: 3/5 and 7/2 (Opens a modal)
  • Common denominators review (Opens a modal)
  • Common denominators Get 3 of 4 questions to level up!
  • Equivalent expressions with common denominators Get 3 of 4 questions to level up!

Adding and subtracting fractions with unlike denominators

  • Adding fractions with unlike denominators introduction (Opens a modal)
  • Adding fractions with unlike denominators (Opens a modal)
  • Subtracting fractions with unlike denominators introduction (Opens a modal)
  • Subtracting fractions with unlike denominators (Opens a modal)
  • Adding and subtracting 3 fractions (Opens a modal)
  • Solving for the missing fraction (Opens a modal)
  • Add fractions with unlike denominators Get 5 of 7 questions to level up!
  • Subtracting fractions with unlike denominators Get 5 of 7 questions to level up!
  • Add and subtract fractions Get 3 of 4 questions to level up!

Adding and subtracting mixed numbers with unlike denominators

  • Adding mixed numbers: 19 3/18 + 18 2/3 (Opens a modal)
  • Subtracting mixed numbers: 7 6/9 - 3 2/5 (Opens a modal)
  • Adding mixed numbers with regrouping (Opens a modal)
  • Subtracting mixed numbers with regrouping (unlike denominators) (Opens a modal)
  • Add and subtract mixed numbers with unlike denominators (no regrouping) Get 3 of 4 questions to level up!
  • Add and subtract mixed numbers with unlike denominators (regrouping) Get 3 of 4 questions to level up!

Adding and subtracting fractions with unlike denominators word problems

  • Adding fractions word problem: paint (Opens a modal)
  • Subtracting fractions word problem: tomatoes (Opens a modal)
  • Add and subtract fractions: FAQ (Opens a modal)
  • Add and subtract fractions word problems Get 3 of 4 questions to level up!

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National mathematics program lesson scripts

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What is the National Mathematics Program?

The National Mathematics Program by the Department of Education is a systematic approach to teaching mathematics in schools. It aims to provide students with a solid foundation in mathematics, enabling them to develop critical thinking and problem-solving skills. The program is designed to align with global standards, ensuring that students receive a quality education that prepares them for future academic and career opportunities.

Understanding the Budget of Work

The Budget of Work is a detailed outline that breaks down the mathematics curriculum into manageable segments over a specified period, usually an academic year. It serves as a roadmap for educators, helping them to plan and allocate time efficiently across different topics and skills. Here’s what it typically includes:

  • Objectives: Clear goals for what students should achieve by the end of each period.
  • Topics: A list of topics to be covered, arranged in a logical sequence.
  • Time Allocation: Specific time frames assigned to each topic, ensuring balanced coverage throughout the year.
  • Assessment Plans: Scheduled evaluations to monitor student progress and understanding.

Exploring Lesson Scripts

Lesson Scripts are detailed guides that outline the step-by-step process of delivering a lesson. They include instructions, activities, and resources needed to teach a particular topic effectively. Here’s what you’ll typically find in a lesson script:

  • Lesson Objectives: What the students should learn and be able to do by the end of the lesson.
  • Materials Needed: List of materials and resources required for the lesson.
  • Step-by-Step Instructions: Detailed instructions on how to conduct the lesson, including explanations, demonstrations, and activities.
  • Assessment Strategies: Methods to evaluate student understanding and progress during and after the lesson.

Download Free Budget of Work and Lesson Scripts

We understand the importance of having access to quality educational resources. That’s why we are offering free downloads of the Budget of Work and Lesson Scripts for the National Mathematics Program by the Department of Education. These resources are meticulously crafted to support both teachers and students in achieving their educational goals.

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Grade 1 Budget of Work and Lesson Scripts                                                                                                       Grade 2 Budget of Work and Lesson Scripts                                                                                                       Grade 3 Budget of Work and Lesson Scripts

Grade 4 Budget of Work and Lesson Scripts                                                                                                       Grade 5 Budget of Work and Lesson Scripts                                                                                                       Grade 6 Budget of Work and Lesson Scripts

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  1. 180 Days of Problem Solving for Fifth Grade

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  3. Problem Solving with Volume, 5th Grade Volume Lesson & Quiz (5.MD.5

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  20. Problem Solving Lesson Plan for 5th Grade

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