problem solving task grade 5

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These incredibly powerful, flexible activities can be used with a variety of content and contexts.

These games are chosen for their simplicity and depth.

Problems that resist easy solutions while encouraging perseverance and deeper understanding.

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Every student deserves to have the opportunity to problem-solve and engage in genuine mathematical thinking. Rich tasks are designed to make these rich learning experiences possible. We’ve written these tasks to launch quickly, engage students, and promote the habits of mind mathematicians need: perseverance & pattern-seeking, courage & curiosity, organization & communication.

This free video PD series will help you get the most out of the tasks below.

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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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Grade 5 Performance Tasks

Students will be asked to solve constructed response questions involving multiplication of fractions and whole numbers. Students will also write a letter that explains mathematically how many cookies a boy will be bringing to the bake sale.

Source: CORE, California Education Partners (CAED)

Students will be asked to solve constructed response questions involving multiplication and division of whole numbers and/or fractions in part one of the task. Students will also critique a student work sample and explain why the problem was solved incorrectly.

Students must add and subtract fractions with unlike denominators. Students will also estimate whether or not John has enough gas to reach a destination and explain their reasoning. Lastly, students will decide how to divide their time (represented as fractions) between the different attractions at Disneyland.

Students will solve a series of problems regarding supplies needed for classrooms using the four operations with whole numbers and decimals to hundredths. They will then be asked to look at two ads for local stores and advise the principal of the best way/place to purchase the supplies.

Students will be asked to expand upon number patterns, graph points on a coordinate plane, compare and analyze data, and draw conclusions.

Students will be asked to solve some constructed response questions involving division of unit fractions and whole numbers. Students will also write a letter that explains mathematically why purchasing one snack product is more economical than the purchasing the other.

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Fifth Grade Math Worksheets

Free & printable grade 5 math worksheets.

Our grade 5 math worksheets cover the 4 operations, fractions and decimals at a greater level of difficulty than previous grades. We also introduce variables and expressions into our word problem worksheets .  

Choose your grade 5 topic:

4 operations.

Place Value & Rounding

Add & Subtract

Multiply & Divide

Order of Operations

Add & Subtract Fractions

Multiply & Divide Fractions

Converting Fractions

Fractions to / from Decimals

Add & Subtract Decimals

Multiply Decimals

Divide Decimals

Data & Graphing

Word Problems

Sample Grade 5 Math Worksheet

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• Inside Mathematics
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• common core resources

5th Grade Common Core Resources

Here you will find all fifth grade resources to guide and support mathematics teaching and learning.

These resources are organized by mathematical strand and refer to specific Common Core math content standards.

Quick reference: What are these tools?

Performance Assessment Tasks      Hexagons in a Row (5.OA.3)

Inside Problem Solving      Digging Dinosaurs (5.NBT.B.7) Performance Assessment Tasks      Decimals (5.NBT.3, 5.NBT.4)      Fractions (5.NBT.3, 5.NBT.4)      Fruits and Vegetables (5.NBT.5, 5.NBT.6)

Inside Problem Solving      Movin ‘n Groovin (5.NF.B.4) Performance Assessment Tasks      Cindy's Cats (5.NF.1, 5.NF.2, 5.NF.4, 5.NF.6)      Fractions (5.NF.2, 5.NF.3)

Performance Assessment Tasks      Fruits and Vegetables (5.MD.1)      How Many Cubes (5.MD.3 - 5.MD.5)

Performance Assessment Tasks      Granny's Balloon Trip (5.G.1 - 5.G.2)      Sorting Shapes (5.G.3 - 5.G.4)

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5th grade math - fraction multiplication situations.

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Daily Math Word Problems - Grade 5 (Worksheets)

Updated:  20 Jul 2019

A set of 20 problem solving questions suited to grade 5 students.

Non-Editable:  PDF

Pages:  6 Pages

• Curriculum Curriculum:  CCSS, TEKS
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This set of problem solving questions has been designed to support teachers when teaching students about problem solving in mathematics.

It provides students with the opportunity to work through 20 math word problems , identifying the important information and how they can work it out using a variety of methods.

An answer sheet has been included.

teaching resource

Daily math problems - grade 5.

A 44 slide editable PowerPoint Template for problem solving in mathematics.

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Percy's Place Value Puzzle

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Identifying and Naming Angles – 4th Grade Math Worksheet

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Acute, Right and Obtuse Angles – 4th Grade Math Worksheet

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Location Math Investigation - Blackbeard's Bounty

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Multiplying and Dividing By 1,000 Poster

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Dividing by 1,000 Worksheet

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2-D Shape Bingo

Engage your students while consolidate learning about 2D shapes, their names and properties with 2D Shape Bingo!

Multiplication Facts PowerPoint - One Times Tables

A 28-slide PowerPoint to use when learning about multiplication.

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6 Free Math Performance Tasks for Grades K-5

Innovative performance tasks to differentiate and extend math learning for all students!

Marshall Cavendish’s Primary Mathematics program empowers all students to develop critical-thinking skills, master concepts, and build the confidence needed to set the stage for long-term math achievement.

Struggling to find math resources that resonate with your students and align with your curriculum goals? Discover how Marshall Cavendish’s Primary Mathematics can transform your math instruction. Try out these free performance tasks with the corresponding teacher guides to experience how students can demonstrate mastery through real-life application of mathematics. The newly launched curriculum is a print/digital core math program for elementary students. Get the performance tasks for grades K-5 and see just how many ways these resources will enhance your students’ math skills.

Let’s explore the performance task for each grade level topic below.

Kindergarten: Cultivate a love for numbers with Ande’s Nature Walk

A captivating performance task designed to immerse young learners in the fundamentals of composing and decomposing numbers up to 10. Through this real-world adventure, students are not just learning, they are connecting, exploring, and finding joy in the world of mathematics.

1st Grade: Explore addition and subtraction with Balloon Adventures

Math becomes an adventure in this performance task filled with narrative-rich word problems in addition and subtraction. Join characters Aki, Brooke, and Isabel as they navigate through balloon-related challenges, turning abstract mathematical concepts into relatable and engaging experiences.

2nd Grade: Enhance problem-solving skills with Shopping Math Adventures

A thoughtfully crafted performance task focusing on the essential skills of addition and subtraction using bar models. In this real-world shopping scenario, students employ bar models as a visual tool to solve both two-step and one-step word problems, strengthening their understanding and application of mathematical concepts.

3rd Grade: Discovering the World of Multiplication and Division

Embark on a mathematical adventure with your students as they delve into the complexities of multiplication and division with numbers 6 through 9. This performance task masterfully balances previous knowledge and introduces new challenges, guiding students through a progressive journey of understanding and skill acquisition.

4th Grade: The Mysteries of Multiplication and Division

This task is a journey of numerical exploration, building on previous knowledge while introducing new challenges and concepts related to numbers 6 through 9.

5th Grade: Mastering fractions through pizza-purchase scenarios

Engage students in a captivating and relatable performance task centered around adding and subtracting fractions in real-life pizza-purchase scenarios. This task boosts critical thinking and problem-solving skills while solidifying students’ understanding of fractions.

What sets Primary Mathematics apart?

The newly launched Primary Mathematics is a comprehensive K-5 math curriculum that uniquely combines U.S. standards with the renowned Singapore Math pedagogy. This program is meticulously designed to cater to every student, promoting equity and differentiation in the classroom. Here’s why it stands out:

• Print/Digital Format: Integrated print/digital resources and interactive tools provide detailed teacher support to plan, develop, and deliver each lesson with confidence and effectiveness.
• Singapore Math Pedagogy: This renowned approach ensures a deep understanding and the development of strong critical thinking and problem-solving skills through the use of rich tasks, visual models, productive struggle, and mathematical discourse. 
• Equity and Differentiation: Every student is given the opportunity to succeed, regardless of their starting point, with just-in-time differentiation resources for each lesson that help teachers meet students’ needs whether reteaching or extending math concepts.
• Performance Tasks Aligned With Chapter Goals: Practical application and explanation of mathematical knowledge reinforce learning objectives.
• Progression to Mastery: Skill integration from previous chapters and even grade levels builds a comprehensive understanding. Mastery is achieved through intentional sequencing and variation of concepts developing from the basic to the complex. Students learn to think mathematically, use the depth of knowledge from previous lessons, and apply the concepts and strategies in new ways.
• Student and Teacher Rubrics: Tools for self-reflection, assessment, and targeted feedback ensure personalized learning.
• Point-of-Use Teaching Support: Teacher resources provide support throughout the learning process with question prompts, lesson and chapter planning, teacher tips, and differentiation tools to address the needs of all learners.

Embrace the transformative power of Primary Mathematics and join a community of educators dedicated to nurturing mathematical excellence.

Download these free math performance tasks today to get a sneak peek at the engaging resources primary mathematics offers., you might also like.

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Free Printable Performance Tasks Worksheets for 5th Grade

Math Performance Tasks: Discover a collection of free printable worksheets for Grade 5 students, designed to enhance their mathematical skills and understanding through interactive problem-solving activities.

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Explore printable Performance Tasks worksheets for 5th Grade

Performance Tasks worksheets for Grade 5 are essential tools for teachers to effectively engage their students in learning and mastering mathematical concepts. These worksheets cover a wide range of topics, including arithmetic, fractions, decimals, geometry, and more. They are designed to help students develop critical thinking and problem-solving skills through various types of exercises, such as Math Word Problems. These problems require students to apply their knowledge of math concepts to real-world situations, thereby enhancing their understanding and retention of the material. Teachers can use these worksheets to supplement their lesson plans, assess students' progress, and provide additional practice opportunities to ensure that their Grade 5 students are well-prepared for the challenges of higher-level math courses.

In addition to Performance Tasks worksheets for Grade 5, teachers can also utilize Quizizz, an online platform that offers a variety of interactive quizzes and learning games to reinforce math concepts. This platform allows teachers to create customized quizzes that align with their lesson objectives, making it an excellent resource for assessing students' understanding of Math Word Problems and other topics. Furthermore, Quizizz offers a vast library of pre-made quizzes and learning games, covering a wide range of Grade 5 math topics. This enables teachers to easily integrate these resources into their lesson plans, providing students with engaging and interactive learning experiences. With the combination of Performance Tasks worksheets and Quizizz, teachers can effectively support their Grade 5 students in achieving math proficiency and success.

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Grade 5 Math Samples

Non-common core, common core, teks (for texas), decimal place value unit.

• Unit Description

Crab Walk Relay Race

Students determine the best combinations of students for three crab walk relay teams so that the teams are as equally matched as possible.

Phoning New Friends

Students determine which calling plan is the most cost effective for Sarah to keep in touch with her friends from soccer camp.

The Decimal Place Value Unit involves understanding and representing the relative position, magnitude and relationships within the numeration system in order to answer questions such as:

• How can you use the additive property of place value (expanded notation) to decompose the number 0.123?  
• How can you use the multiplicative property of place value to describe the meaning of each digit in the number 0.123?  
• How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5.555?
• Standard Description

Popsicle Party

Students determine the number of cartons of Popsicles the Franklin School needs for its 950 students.

A Border for Mr. Gomez's Kitchen

Students determine how many tiles Mr. Gomez needs to make a tile border along his kitchen walls.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Football Players

Students round the weights of 12 football players to the nearest hundred and the nearest tenth to determine if they will earn a dinner at Pete's Restaurant.

Bamboo and the Botanist

Given scientific data that shows how much two bamboo plants have grown over seven days, student make observations and record their thinking using equality and inequality symbols.

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TEKS standards covered: 5.2A, 5.2B, 5.2C

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Problem-solving skills are necessary in all areas of life, and classroom problem solving activities can be a great way to get students prepped and ready to solve real problems in real life scenarios. Whether in school, work or in their social relationships, the ability to critically analyze a problem, map out all its elements and then prepare a workable solution is one of the most valuable skills one can acquire in life.

Educating your students about problem solving skills from an early age in school can be facilitated through classroom problem solving activities. Such endeavors encourage cognitive as well as social development, and can equip students with the tools they’ll need to address and solve problems throughout the rest of their lives. Here are five classroom problem solving activities your students are sure to benefit from as well as enjoy doing:

1. Brainstorm bonanza

Having your students create lists related to whatever you are currently studying can be a great way to help them to enrich their understanding of a topic while learning to problem-solve. For example, if you are studying a historical, current or fictional event that did not turn out favorably, have your students brainstorm ways that the protagonist or participants could have created a different, more positive outcome. They can brainstorm on paper individually or on a chalkboard or white board in front of the class.

2. Problem-solving as a group

Have your students create and decorate a medium-sized box with a slot in the top. Label the box “The Problem-Solving Box.” Invite students to anonymously write down and submit any problem or issue they might be having at school or at home, ones that they can’t seem to figure out on their own. Once or twice a week, have a student draw one of the items from the box and read it aloud. Then have the class as a group figure out the ideal way the student can address the issue and hopefully solve it.

3. Clue me in

This fun detective game encourages problem-solving, critical thinking and cognitive development. Collect a number of items that are associated with a specific profession, social trend, place, public figure, historical event, animal, etc. Assemble actual items (or pictures of items) that are commonly associated with the target answer. Place them all in a bag (five-10 clues should be sufficient.) Then have a student reach into the bag and one by one pull out clues. Choose a minimum number of clues they must draw out before making their first guess (two- three). After this, the student must venture a guess after each clue pulled until they guess correctly. See how quickly the student is able to solve the riddle.

4. Survivor scenarios

Create a pretend scenario for students that requires them to think creatively to make it through. An example might be getting stranded on an island, knowing that help will not arrive for three days. The group has a limited amount of food and water and must create shelter from items around the island. Encourage working together as a group and hearing out every child that has an idea about how to make it through the three days as safely and comfortably as possible.

5. Moral dilemma

Create a number of possible moral dilemmas your students might encounter in life, write them down, and place each item folded up in a bowl or bag. Some of the items might include things like, “I saw a good friend of mine shoplifting. What should I do?” or “The cashier gave me an extra $1.50 in change after I bought candy at the store. What should I do?” Have each student draw an item from the bag one by one, read it aloud, then tell the class their answer on the spot as to how they would handle the situation.

Classroom problem solving activities need not be dull and routine. Ideally, the problem solving activities you give your students will engage their senses and be genuinely fun to do. The activities and lessons learned will leave an impression on each child, increasing the likelihood that they will take the lesson forward into their everyday lives.

You may also like to read

• Classroom Activities for Introverted Students
• Activities for Teaching Tolerance in the Classroom
• 5 Problem-Solving Activities for Elementary Classrooms
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• Motivating Introverted Students to Excel in the Classroom
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Tagged as: Assessment Tools ,  Engaging Activities

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Fun teaching resources & tips to help you teach math with confidence

Engaging & Rich Math Tasks to Reach Every Student

Looking for deep and meaningful ways to challenge your students? Think rich tasks are only for your advanced students? Think again!

All students learn more and retain more when they are given opportunities to engage with meaningful math problems through inquiry. All students benefit from being pushed just beyond their capabilities and engage in a little productive struggle.

What Does Teaching Through Problem Solving Look Like?

Typically in a math classroom, the structure and routine looks like this: the teacher gives examples and works out math problems. The class then works together on some additional examples through guided practice. Finally, students are given a set of problems to try on their own. They’re finally ready for independent work!

What’s the problem with this method?

For one, to be perfectly honest, it’s boring. Watching the teacher work out problem after problem is tedious and just not fun .

And I know you might be thinking, “Ok, but not everything can be fun. Cleaning the bathroom is not fun, but it still has to be done.”

And I hear you! Certainly, there are times when we just have to suck it up and do the hard work, even if it’s not all fun and games.

But if we want kids excited and engaged in the learning process, we have to actually give them a chance to engage in the learning process. 

So what does this look like? Take that earlier example of a day in the typical math classroom and turn it on it’s head.

Meaning rather than moving from I do to we do and then finally you do , you start with you do . This means you start the lesson by giving students a rich math task that is just a little beyond their comfort zone.

Ready to dive right in? Check out my complete online training course on teaching through problem solving & inquiry:

>>> Problem Solved: How to Teach Math Through Problem Solving & Inquiry

What constitutes a rich math task.

Though this might sound complicated or like you’ll have to completely re-invent the wheel, it’s definitely not! It simply means you start by challenging kids with a problem that has not yet been explicitly taught . (Notice I said not yet taught. Please know that direct teacher instruction is still important and still has it’s place. I just believe it should come later in your lesson).

This could be as simple as a word problem from the next section of your fraction unit.

It could be a visual math task or puzzle.

It could be a more involved, ongoing project that allows kids to use and apply what they know and build on it over time.

It could simply be a question that forces your kids to think, such as “Which is greater, 2/4 or 3/8?”

For more ideas about what makes a math task rich, consider these questions:

• Is it new content that is related to something my students already know?
• Is it a low-floor, high-ceiling task that every single student can engage with?
• Can the problem be solved in multiple ways , using multiple strategies ?
• Is it, or does it allow for visualization using pictures and models?
• Does it relate to students interests or everyday life in some way?

Please note that any given task is not going to check off every single one of these boxes. These questions are simply meant to guide you as you think about and prepare math lessons using meaningful, rich math tasks for your students.

What if a Math Task is Total Flop?

What do you do when you have a problem that you’re excited about and you present it to your students only to find that it doesn’t engage them at all, or it’s completely beyond their abilities?

First, don’t stress! Not every task is going to be a winner or be the perfect fit for where your kids are mathematically.

Instead, consider why it did not go well:

• Was the math just a little too far beyond what your students were ready for? If so, adjust the task to include simpler numbers or try again with a little more guidance from you as the teacher.
• Was the topic of the task of no interest to them? Maybe you picked a work problem that you thought would relate to their lives, but it just didn’t. Try asking them what their interests are to see if you can tweak the problem to relate to something they are excited about!
• Was it too closed, with only one solution and method? Try opening it up by removing some of the parameters. This will turn it into a problem with multiple possible solutions. Or consider a task that covers the same math skill, but can be solved using multiple methods or visual tools. This will allow students more room to explore and think through the task.

Ready to Engage Your Students with Rich Math Tasks? Try These!

Below you will find an ever-growing list of meaningful and engaging tasks to help your students make sense of math. Click on any of the graphics to learn more about the task or activity and grab your FREE download!

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Introducing operations with fractions in mathematics can sometimes be confusing for students and frustrating for teachers.

Providing some context within which students can conceptualise fractions can really help solidify these abstract concepts in students’ minds, especially when adding and subtracting fractions to amounts that are greater than a whole.

In this ‘low threshold, high ceiling’ task, students take the role of the owner of a cake wholesaler, baking and supplying cakes to local café businesses. As café owners order their weekly cakes by the slice, students are required to add unit fractions together to calculate total cake orders. They then solve problems associated with subtracting fractional remainders, using equivalent fractions and converting between improper fractions and mixed numerals.

This downloadable ‘rich task’ lesson resource is designed for teachers and students in Years 5 to 7. It is mapped against Australian Curriculum (Mathematics), with an emphasis on problem solving and reasoning in operating with fractions .

The task comes with a comprehensive grading rubric to assist teachers who wish to use the project for formal assessment purposes.

This task was developed in consultation with Greta Public School (NSW), a CHOOSE MATHS Schools Outreach partner school.

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