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Interactive math manipulatives, printables, questions, and videos.

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Teaching Math | Classroom Resources | Class Playground

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Printables, videos, & interactive activities to help teachers use edtech in their classrooms. Math topics include area, perimeter, time, & more--100% free!

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Online manipulatives bring all of the learning and fun without the mess. Our math virtual manipulatives help students grasp abstract concepts through modeling. Literacy virtual manipulatives create a fun space for practicing spelling, rhyming, and more!

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Virtual Manipulatives | Mathematical Modelling | Toy Theater

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Original teaching tools aimed at supporting teachers in the elementary school classroom. Two color counters, 3D dice, probability spinners, graph builders, fraction bars, base ten blocks, and more!

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Need some ideas on coding? Check out this blog.

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Deanna Pecaski McLennan, Ph.D., is an educator in Southern Ontario who is greatly influenced by the Reggio Emilia approach to Early Childhood Education. She believes in a play-based, exploratory, democratic learning environment and has spent much time reading, researching, and writing about these various issues. Contact her at deannapecaskimclennan@yahoo.ca.

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I am a Reggio Emilia inspired Full Day Kindergarten teacher and mother to three young children. This blog is meant as a communication tool for the families of our children and as a learning tool for the many educators who follow us. Please feel free to comment on posts and participate in our collective understanding of emergent curriculum.

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Images to encourage discussion about real life examples of items and how they are grouped.
It swirls but it goes where it needs to!

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Flexible activities, games, rich tasks, resources (to purchase at a discount) and don't forget to check out their blog under Resources, to see what websites they recommend and links to puzzles. Well worth it!

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Transform the first 5 - 10 minutes of math class into a pedagogical powerhouse.
These openers promote rigorous thinking and discourse, and shift classroom culture toward student engagement and meaningful work.
A perfect prerequisite for using rich tasks, and fantastic for every age.

NEW! How to Use Mathematical Openers PD mini workshop is now live!
It's available at Grassroots Workshop for $39. Check it out here!

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Transform the first 5 - 10 minutes of math class into a pedagogical powerhouse. These openers promote rigorous thinking and discourse, and shift classroom culture toward student engagement and meaningful work. A perfect prerequisite for using rich tasks, and fantastic for every age. NEW! How to Use Mathematical Openers PD mini workshop is now live!

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10 Nonfiction Children's Books That Humanize Mathematics

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10 Nonfiction Children's Books That Humanize Mathematics

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Need I say more?

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Hidden Figures
by Margot Lee Shetterly

High school students who enjoyed the 2016 blockbuster "Hidden Figures" can dive deeper into the true story of African-American women whose calculations helped launch NASA astronauts into space through Margot Lee Shetterly's book of the same name. For younger students, there's a young readers' edition and a picture book version .
More books about Katherine Johnson
In addition to "Hidden Figures," NASA mathematician and Presidential Medal of Freedom recipient Katherine Johnson is at the center of several other recent books. Those titles include her middle-grade autobiography, " Reaching for the Moon ," and two picture books, " Counting on Katherine " by Helaine Becker and Dow Phumiruk and " Counting the Stars " by Lesa Cline-Ransome and Raúl Colón.

Rote learning can make math feel like it's all about rules. Zaha Hadid's life shows otherwise. The Iraqi-British architect designed opera houses, museums and bridges whose swirling structures and irregular shapes defied convention. Teachers and students can extend the learning by checking out real photos of Hadid's work and mapping their locations around the world.

A winner of the 2019 Mathical Book Prize , this picture book captures the life of Sophie Germain, a girl who grew up amid the French Revolution and found order and sense in math. Sophie dedicated her adult life to tackling big math problems, such as Fermat's Last Theorem. McClintock's marker, gouache and collage illustrations infuse the space around Sophie with vibrant numbers and equations, making the dynamic activity of her mind visible for readers.
Ada Lovelace biographies
As coding increasingly makes its way into curricula , it's important for students to see names beyond Steve Jobs and Bill Gates connected to the development of information technology. Ada Lovelace, for example, is credited with writing the first computer program. A recent spate of picture books celebrate that legacy. Titles include " Ada's Ideas " by Fiona Robinson, " Ada Byron Lovelace and the Thinking Machine " by Laurie Wallmark and April Chu and " Ada Lovelace, Poet of Science " by Diane Stanley and Jessie Hartland.

The Boy Who Loved Math: The Improbable Life of Paul Erdos
by Deborah Heiligman and LeUyen Pham

Young readers don't need to understand Paul Erdos' mathematical proofs to relate to his dislike for adult rules and his zeal for his favorite subject. Born in Hungary, Paul spent his life exploring and adoring numbers with friends all over the world . With equations, graphs, and number groups peppered throughout the artwork, this book's illustration note provides avenues for extended learning about concepts such as harmonic primes and amicable numbers.

This biography spotlights Grace Hopper - another forgotten female pioneer of computer science . You've heard of a software "bug," but did you know the origin of the term? When one of the U.S. Navy's early computers stopped working, Grace used a pocket mirror and her penchant for problem-solving to find the root of the trouble: a trapped moth, blocking a switch. She also developed a computer language that simplified programming and retired from the Navy as an admiral.

Growing up in the segregated south, Raye Montague navigated racial and gender discrimination as she steered toward her dream of designing ships. Rhyming text shares Montagues early interest in math and how she taught herself engineering while working as a U.S. Navy typist. When a president ordered a ship design in an expedited time frame, Montague surprised her white male colleagues by completing the world's first ship design by computer. She eventually became a registered engineer and the Navy's first female program manager of ships.

A collective biography for middle grade readers, this illustrated volume includes profiles on mathematicians Wang Zhenyi, Ada Lovelace and Grace Hopper. According to Marcie Flinchum Atkins , who is a school librarian in Fairfax County, Virginia, this book is ideal "for students who want to read just a small bit of information about a person" and for teachers who "want to do a short read aloud about one particular person that is featured." Flinchum Atkins also recommends Harrison's other collective biography, "Little Leaders: Bold Women in Black History," which features Katherine Johnson among its 40 profiles.

As a traveling merchant in the 12th and 13th centuries, Leonardo Fibonacci learned and promoted mathematical ideas from across cultures, such as the Hindu-Arabic numeral system. With little known about his life, this biography crafts a fictional narrative around the facts about the number pattern that orders the natural world - now called the Fibonacci sequence. The final page includes prompts for children to explore the pattern in the book's illustrations and with familiar objects.

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10 Nonfiction Children's Books That Humanize Mathematics - MindShift

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Math is often seen as a subject removed from everyday feelings and experiences. These ten books reveal the people who loved math and made it an important part of their identities.

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Website with activities and lessons for students at home, her blog, math video clips for teaching math at home or at school, podcasts.

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Construction Flagging Shapes

Construction flagging tape is used by construction workers to, for example, rope off a new slab of concrete in the sidewalk. It costs only a few dollars per roll and can be found in home improvement stores and online. It isn't sticky (though the name implies this), does not tangle like yarn does, and because it must be seen from a distance, flagging tape comes in fun fluorescent colors. You can use it to learn geometry by tying the ends together to make a loop about 40 feet long. Find a wide-open space and have 4 or 5 kids grab on to the flagging (you might have to get in on the action or invite the neighbor kids over). Can you make 2D and, gulp, 3D shapes? Talking together about the attributes of the shapes and working cooperatively to create them supports purposeful math-positive vocabulary development. Most of all, it's fun mathematics education for even the most math-panicked parents!

Materials: playdough, activity sheet (download here)

Instructions: Have children roll out and place a worm on each of the worm drawings on the activity sheet. Then have children order the worms from shortest to longest. They can place the worms on a blank sheet of paper and trace around them for a permanent record of their work, if desired.

Have children write the digits 1 through 9 on a paper. Take turns rolling two dice. On each turn, the player may cover either the sum rolled on the dice or any two numbers that are still uncovered and that add to the sum rolled. For example, if a sum of 8 is rolled first, the player may cover: 8, or 1 and 7, or 2 and 6, or 3 and 5. Later in the game, if the sum of 8 is rolled again and the 5 is already covered, then the player cannot use the 3 and 5 combination and must play one of the other open possibilities. When a player cannot play, they are out and have a score of the sum of the uncovered numbers. Play continues for remaining players until everyone is out. The last person to go out will not necessarily win; the person with the lowest score wins. (Stenmark, Thompson, and Cossey 1986)

Scaled drawings can be fun ways to integrate art with math and think about multiplication as scaling (resizing). Each person draws a simple design with straight-ish lines (pine trees, sail boats, and flags work well) on a piece of centimeter grid paper. Trade papers and "blow up" the picture by making all the lines 2 times longer. For example, if drawing a pine tree, the trunk on the original might be 6 centimeters long and 2 centimeters wide, but on the scale drawing the trunk is drawn 12 centimeters long and 4 centimeters wide. Children might have to tape together several sheets of centimeter paper to have enough space for their double-sized drawing. Now make a scale drawing that is half as big as the original. This time the pine tree's trunk is 3 centimeters long and one centimeter wide. Display all three masterpieces together and show off how multiplication by a whole number or a fraction resizes the drawings. This is an art and math project worthy of hanging on the fridge!

Remove the face cards from a deck of playing cards. Each player gets seven cards. The rest of the cards are the fishing pond. Players look in their hand for two cards with a sum of 10 (number bonds for 10--examples shown here). If they find a number bond, they set it aside. Take turns asking other players for the card needed to complete a number bond. For example, if you have a 5 in your hand, ask another player for a 5. If they don't have a 5, you "Go Fish" by picking up a card from the fishing pond. The winner is the player with the most number bonds for 10 when all the cards have been used.

Wrapping Paper Sets
Materials: wrapping paper scraps, markers

Instructions: Have children circle sets of two objects, such as two teddy bears, two presents, or two balloons-whatever pattern is found on the wrapping paper. Next time, have students circle sets of three, four, or five.

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20-Minute Math Ideas | MathPositiveMindsets

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Construction Flagging Shapes Construction flagging tape is used by construction workers to, for example, rope off a new slab of concrete in the sidewalk. It costs only a few dollars per roll and can be found in home improvement stores and online.

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Still under construction, but there are some articles talking about using particular strategies in the classroom such as concept circles and math think alouds.

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Cathy Marks Krpan - Exploring and learning about math education together

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As teachers we continually strive to explain to our students how they will use the mathematics they are learning in their daily lives. Many resources provide examples of laying tile for area, building fences for perimeter, and eating pizzas for the division of fractions as real-life applications of mathematical concepts.

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Trent Math Education Research Collaborative 

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Trent Math Education Research Collaborative 

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Scroll to the bottom to investigate the Quick Links. It is well worth a look.

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The Trent Math Education Research Collaborative (TMERC) is a team led by Dr. Catherine D. Bruce, Professor and Dean of Education, Teaching and Learning. The goal of this team is to share the products and findings of research with a wide audience, and this website is one of its main vehicles for doing so. Some key members of the team include: Tara Flynn (Director of Research), Rich McPherson (Videographer, Resource Developer and Webmaster), as well as several research assistants.

Key areas of research include teacher and student efficacy, the effectiveness of alternative models of professional learning for teachers, the use of technology in the mathematics classroom, as well as teaching and learning in the difficult-to-learn areas of fractions and algebra. Another exciting area of research is Math for Young Children, which investigates early mathematics (JK - Grade 2) with a particular focus on young children's spatial reasoning.

We call ourselves a "collaborative" because collaboration with educators is at the heart of all of these research initiatives. The knowledge being developed in these research areas is a direct result of meaningful and productive partnerships with teachers, early childhood educators, consultants, school boards, independent schools, and the Ontario Ministry of Education. We want to gratefully acknowledge the contributions that these dedicated, inquiring educators continue to make to the ongoing research conducted by Cathy and her team.

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The Trent Math Education Research Collaborative (TMERC) is a team led by Dr. Catherine D. Bruce, Professor and Dean of Education, Teaching and Learning. The goal of this team is to share the products and findings of research with a wide audience, and this website is one of its main vehicles for doing so.

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Resources for classroom teachers which includes posters, rich tasks, research articles, videos, courses....

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The term "growth mindset" comes from the groundbreaking work of Carol Dweck. She identified everyone holds ideas about their own potential. Some people believe that their intelligence is more or less fixed and in math - that you can do math or you can't. About 40% of students have these damaging "fixed mindset" ideas. Another 40% have a "growth mindset" - they believe that they can learn anything and that their intelligence can grow. The other 20% waver between the two mindsets.

Students with a fixed mindset are those who are more likely to give up easily, whereas students with a growth mindset are those who keep going even when work is hard, and who are persistent. The two mindsets are associated with different achievement pathways as the papers on this page show. It is possible to change mindsets - my student online class which can be accessed under courses - has been shown to shift students' mindsets from fixed to growth and cause higher mathematics achievement. There are a range of resources on this page - a poster of math norms, a strategizer card with lots of teaching ideas, a short video to boost students' mindset, and some interesting short papers.

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The term "growth mindset" comes from the groundbreaking work of Carol Dweck. She identified everyone holds ideas about their own potential. Some people believe that their intelligence is more or less fixed and in math - that you can do math or you can't. About 40% of students have these damaging "fixed mindset" ideas.

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Play or build increasingly challenging puzzles to balance the mobiles. Sign up for free to track your progress.

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Continue Anyway

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Past presentations from Marian Small which have many open questions and parallel tasks. She's our home-grown math guru!

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He's on a learning mission and sharing resources he's created for free. Need subitizing slides? He's got them. Estimation mysteries? He's got those, too! Did I mention that they're free?

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Steve Wyborney's Blog: I'm on a Learning Mission

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Steve Wyborney is on a learning mission to spread math joy to classrooms everywhere! On this blog you'll find math resources for teachers and for kids of all ages.

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Thought provoking puzzles for math teachers and students. There are many different, but correct ways of choosing which one doesn't belong.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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A way to engage students in math-based conversations and to justify their thinking. Make sure you scroll down to access the free google form that students can use. Make a copy? Why thank you, I will!

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Would You Rather Math – ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT WITH MATH

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don’t go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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Videos provocations from @DrCarriecutler and her teacher candidates.

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We created these 3 Act Tasks for our Houston-area students, but we want to share them with the world. Enjoy our creativity and math-positive mindsets! For mo...

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Series of books listed in chart format, highlighting the grade they are applicable to and the topic in math. The books with the lessons can be ordered online and are available for fiction and non-fiction books.

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Lessons and games

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Teaching multiplication of fractions is, in one way, simple-the rule of multiplying across the numerators and the denominators is easy for teachers to teach and for students to learn. However, teaching so that students also develop understanding is more demanding, and Marilyn Burns tackles this in her new book Teaching Arithmetic: Lessons for Multiplying and Dividing Fractions, Grades 5-6 (Math Solutions Publications, 2003). In the following excerpt from Chapter 2, Marilyn builds on what students know about multiplying whole numbers to begin developing understanding of what occurs when we multiply fractions.

I began the lesson by posting the chart of "true" statements about multiplying whole numbers that I had previously generated with the class:

1. Multiplication is the same as repeated addition when you add the same number again and again.

2. Times means "groups of."

3. A multiplication problem can be shown as a rectangle.

4. You can reverse the order of the factors and the product stays the same.

5. You can break numbers apart to make multiplying easier.

6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one.

I planned to use these statements as a base for helping the students think about multiplying fractions. To begin, I pointed to the first statement:
1. Multiplication is the same as repeated addition when you add the same number again and again.
"Do you think this is true when we think about fractions?" I asked. I wrote on the board:

"Talk with your neighbor about how you might make sense of this problem with repeated addition," I continued.

After a few minutes, I called on Juanita. She said, "I think you can do it by adding one-half over and over again. I did one-half plus one-half, like that, six times. I think the answer is three." I wrote on the board:

"How did you get the answer of three?" I asked.

Juanita responded, "One-half plus one-half is one whole, and you can do that three times, and you get three." I wrote:

Eddie added, "It's like if you had six times something else, you could add the something else six times, and that's what Juanita did with the one-halves."

"So, does this first statement work for multiplying with a fraction?" I asked. The students nodded their agreement, and I wrote OK next to the first statement.

I then pointed to the second statement:
2. Times means "groups of."
"Does it make sense to read 'six times one-half' as 'six groups of one-half'?" Most of the students nodded.

Saul added, "The answer is still three." I wrote OK next to the second statement and then pointed to the third statement:
3. A multiplication problem can be shown as a rectangle.
I asked, "Can we draw a rectangle to show six times one-half?" The students weren't sure.

"Suppose the problem were six times one," I said, writing 6 x 1 on the board. The students were familiar with using rectangles for whole number multiplication. I sketched a rectangle, saying as I did so, "One side of the rectangle is six units long and the other side of the rectangle is one unit long." I labeled the sides 6 and 1 and then divided the rectangle into six small squares.

"See if this rectangle helps you think about how I might draw a rectangle to show six times one-half," I said.

Kayla said, "Just cut it in half."

"Which way should I cut the rectangle?" I asked.

"Sideways," Kayla said. I split the rectangle as Kayla suggested, then erased the 1 and replaced it with 1 written twice. Also, I shaded in the bottom half to indicate that it wasn't part of the problem.

"The top half of the rectangle is six units by one-half unit and shows the problem six times one-half. The bottom shaded half shows the same problem again, but we don't need to consider both. How many squares are there in the unshaded rectangle? Does this still give an answer of three?"

Damien explained, "Two halves make a whole, and you do that three times, so the six halves make three whole squares. Three is still the answer."

"But what about if both the numbers are fractions?" Julio challenged.

"Let's try one," I said. I wrote on the board:

I decided to show the students a way to think about representing the problem with a rectangle. "When I draw a rectangle for a multiplication problem with fractions, I find it easier first to draw a rectangle with whole number sides. So, for this problem, I think about a rectangle that is one by one," I said. I drew a square on the board, labeled each side with a 1, and continued, "This rectangle is a square because both factors are the same. It shows that one times one is one. Now watch as I draw a rectangle inside this one with sides that each measure one-half." I divided the square, shaded in the part we didn't need to consider to show the 1/2-by-1/2 portion in the upper left corner, and labeled each side 1/2.

I said, "The part that isn't shaded has sides that are each one-half of a unit. How much of the one-by-one square isn't shaded?"

"One-fourth," several students responded.

Saul was skeptical. He asked, "You mean that one-half times one-half is one-fourth?" I nodded.

"I don't get it," he said.

"But do you agree that the unshaded rectangle has sides that are each one-half?" I asked. Saul nodded.

"But you're not sure that the answer of one-fourth is correct?" I asked. Again, Saul nodded.

"Let's see if the other statements can help you see why," I said. I knew that if the students thought of the problem as "one-half of one-half," they would agree with the answer of one-fourth. I planned to develop this idea, and I used the next statement to do so.

I pointed to the next statement:
4. You can reverse the order of the factors and the product stays the same.
Craig commented, "That should work." Others agreed.

"But it doesn't matter for one-half times one-half," Brendan said. "If you switch them, you still have the same problem."

I said, "Right, so let's think about this statement for the first problem we solved-six times one-half. What about if we think about the problem as one-half times six?" I wrote on the board:

I continued, "If we think about the times sign as 'groups of,' then one-half times six should be 'one-half groups of six.' But that doesn't sound right. It does make sense, however, to say 'one half of a group of six,' or 'one-half of six,' and leave off the 'groups' part. Both sound better, and they're still the same idea. What do you think 'one-half of six' could mean?"

"It's the same," Sabrina said. "One-half of six is three, so one-half times six is three, and that's the same as six times one-half."

I said, "Let's think about one-half times one-half the same way. What is one-half of one-half?"

I heard several answers. "A fourth." "A quarter." "One-fourth."

"So what do you think about reversing the order of the factors when the factors are fractions?" I asked.

The students agreed that it would work, so I wrote OK next to Statements 3 and 4.

"Let's look at the fifth statement," I said, pointing to it:
5. You can break numbers apart to make multiplying easier.
"Talk with your neighbor about how you could apply this statement to the problem six times one-half."

After a few moments, I called on Brendan. He said, "It works. You could break the six into twos, and then you do two times one-half three times. Two times one-half is one. One plus one plus one is three. So it works." I wrote on the board:

Anita said, "We split the six into four and two. Half of four is two and half of two is one and two plus one is three. It works." I recorded:

I wrote OK next to the statement. "We have one statement left," I said, pointing to it:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one.
I asked, "Does this statement hold true for six times one-half?"

"It doesn't work," Sachi said. "Three is smaller than six, so it doesn't work."

"Could we change the statement so that it does work?" I asked.

Julio said, "It should say at the end 'unless the factors are zero or one or a fraction.'" I edited the statement as Julio suggested:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one or a fraction.
I thought about how to respond. If one of the factors is a fraction less than one, then Julio's idea works. But if the fraction is more than one, Julio's idea might not work. I wanted to acknowledge Julio's idea but also give him the chance to refine it. I posed a problem that had a fraction as one of the factors for which the answer was greater than both of the factors. I said, "That's a good idea, but I think it needs a little more information. Think about this problem-six times three-halves. That's the same as six groups of three-halves." I wrote on the board:

"Talk with your neighbor about what the answer would be to this problem," I said. After a couple of minutes, I called on Craig.

"We got nine," he said. "We knew that three-halves is the same as one and a half, and one and a half plus one and a half is three, and three plus three plus three is nine, so the answer is nine." I recorded Craig's idea on the board:

Craig continued, "And nine is bigger than six or three-halves. So the statement doesn't work. It works the way it used to be, but it doesn't work the way you changed it."

"I think I can fix what I said," Julio said. "The fraction has to be smaller than one. So any number that is zero or one or in between makes an answer that is smaller than the factors."

"So what should I write to change the statement?" I asked.

Julio said, "At the end, write 'zero or one or a fraction that's smaller than one.'" I wrote on the board:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one or a fraction smaller than one.
Julio and others nodded. I wrote OK next to the revised statement.

This was just the first lesson I planned to teach about multiplying fractions. In later lessons, I further developed the students' understanding and skills.

From Online Newsletter Issue Number 12, Winter 2003-2004

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Teaching multiplication of fractions is, in one way, simple-the rule of multiplying across the numerators and the denominators is easy for teachers to teach and for students to learn. However, teaching so that students also develop understanding is more demanding, and Marilyn Burns tackles this in her new book Teaching Arithmetic: Lessons for Multiplying and Dividing Fractions, Grades 5-6 (Math Solutions Publications, 2003).

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Includes problems, book lessons, games etc.

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Games, lessons, challenges and enrichment for grades 7 to 10 students, teachers, parents and tutors.

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WiredMath.ca is a free math website with games, lessons, challenges and enrichment. It is created for middle or junior high school grade 7, grade 8, grade 9, and grade 10 students, teachers, parents and tutors. Many of the exercises increase enjoyment, confidence and ability in mathematics and are good for homework and test preparation. The exercises can also be used for enrichment with students in grades 4, 5 and 6.

Mathematics teachers everywhere will find similar core topics that are covered in each required course. The expectations for each lesson are taken from the grade 7, 8, 9, and 10 Ontario Mathematics Curriculum.

The ' Did You Know' and ' A Slice of History ' boxes in each exercise add knowledge, variety and interest for the student.

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Wired Math - Games, Lessons, and Resources for Grades 7, 8, 9, and 10

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WiredMath.ca is a free math website with games, lessons, challenges and enrichment. It is created for middle or junior high school grade 7, grade 8, grade 9, and grade 10 students, teachers, parents and tutors. Many of the exercises increase enjoyment, confidence and ability in mathematics and are good for homework and test preparation.

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Want real world problems for grades 7 and beyond? Find it here.

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High school students often ask about mathematics "When will we ever use this in the real world?".

In fact, researchers in mathematics and computer science are making new discoveries all the time. These discoveries are being applied in some surprising contexts - in industry, finance, medicine, the environment, and the justice system, to name just a few. Modern mathematicians don't just work in isolation - they collaborate with doctors, environmental scientists, lawyers, engineers and experts in many other fields on applications that are changing the world in powerful ways.

Examples

Explore some real-world problems being solved by mathematicians. For each real-world problem, try your hand at a related mathematical problem. These problems are designed to be accessible to students in grades 7-8 and later. Solutions are provided.

Images from Wikimedia Commons

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Design - Graphics, University of Waterloo

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CEMC - Web Resources - Real World Problems - Uses of Math

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High school students often ask about mathematics "When will we ever use this in the real world?". In fact, researchers in mathematics and computer science are making new discoveries all the time. These discoveries are being applied in some surprising contexts - in industry, finance, medicine, the environment, and the justice system, to name just a few.

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Problems of the week for grades 3-12 and solutions. Also includes additional problems from 2017-2018, 2018-2019

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The Problem of the Week is designed to provide students with an ongoing opportunity to solve mathematical problems. Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up.

Subscribe Now!

Information for Teachers

Problems are organized into themes. A problem may have more than one theme.

These problems may be used in a variety of different ways including:

posting the problems in a classroom,

discussing the problems with students, and

integrating the problems into the curriculum.

We know that teachers will use these problems in many creative ways!

Solutions to the problems will be sent out to teachers one week after the problems are e-mailed.

Problem and Solution Archive

The following table has links to booklets containing all the problems and solutions from particular years. The problems are organized into themes, grouping problems into various areas of the curriculum. A problem often appears in multiple themes.

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Design - Graphics, University of Waterloo

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The CEMC has become Canada's largest and most recognized outreach organization for promoting and creating activities and materials in mathematics and computer science.

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Free resources, lessons and activity sheets from the U of W

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Free resources, lessons, and exercises to assist Grades 4, 5, and 6 students, mathematics teachers, and parents, integrating online math games and tools. Topics include geometry, spatial sense, number sense, numeration, measurement, patterning, algebra, data management, and probability.

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Free Math Apps

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Demonstrate key math concepts in your classroom using our new virtual manipulatives!

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Free Math APPs

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Integrated Financial Literacy Resources from CODE (Council of Ontario Drama and Dance Educators)

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Integrated Financial Literacy Resources from CODE (Council of Ontario Drama and Dance Educators)

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Some resources are available only when logged-in as an active member.

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Subject Division Elementary Resources for Financial Literacy 

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Subject Division Elementary Resources for Financial Literacy 

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(Lessons from CODE, ELAM, ERGO etc.)

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Subject and Division Associations have developed learning resources to demonstrate connections between financial literacy knowledge and skills and various curriculum expectations. The links below will take you directly to the financial literacy resources posted on the subject/division association websites. As new material is released, links will be posted on this page.

To support the development of further resources, the Council of Ontario Drama and Dance Educators have developed A Guide to Curriculum Resource Writing Projects.

Catholic Curriculum Corporation
A resource document has been created to embed financial literacy concepts in elementary Family Life Education (grades 4 to 8). This resource includes a comprehensive introduction, three lesson plans per grade, and a Scope and Sequence of Expectations showing connections between financial literacy education and the Family Life Education and the Religious Education Ontario Catholic Curriculum Policy Documents.

Council of Ontario Drama and Dance Educators (CODE)
CODE developed resources to support financial literacy through the Dance and Drama curriculum from grades 4-12. Elementary lessons integrate other curriculum areas such as Language, Social Studies and Mathematics.

English Language Arts Network (ELAN)
ELAN has developed a series of lessons which make connections between the Language and English curricula and financial literacy skills and knowledge from Grades 4-12. The lessons address a range of topics such as poverty, charity, the global village, and needs and wants.

ESL/ELD Resource Group of Ontario (ERGO)
The Making Good Choices Financial Literacy Series was created by a project team comprised of ESL/ELD Teachers in Ontario and lead by the ESL/ELD Resource Group of Ontario (ERGO) subject association. The series includes several levelled texts created for English Language Learners in ELD Programs. The texts are intended to teach both emergent literacy skills and foundational numeracy skills. Each levelled text is accompanied by a guided reading lesson plan, running record, and other supporting resources.

International Language Educators' Association (ILEA)
ILEA developed a resource package which can act as a springboard for teachers of any language program who want to incorporate financial literacy within the language skills and knowledge as students develop listening, speaking, reading and writing skills. All lesson plans are written in English and student resources are translated into French, Spanish, German, Arabic, and Simplified Chinese.

Ontario Association for Mathematics Education (OAME)
Ontario Association for Mathematics Education OAME has developed lessons to support financial literacy that encompass mathematics curriculum expectations for Grades 4-12. Also available for selected grades are:

SMART Notebook files and

Professional Learning Series and Adobe Presenters to provide an orientation to the resources

Ontario Elementary Social Studies Teachers' Association (OESSTA)
Ontario Association of Junior Educators (OAJE)
In partnership, OESSTA and OAJE have developed resources to support the integration of financial literacy concepts in the Social Studies, History and Geography curriculum for grades 4-8.
Ontario Modern Language Teachers' Association (OMLTA)
OMLTA has developed several lessons that integrate financial literacy knowledge, skills, and vocabulary in Core French courses for Grades 4-12. The lessons address a range of topics related to financial literacy including needs and wants, budgeting, and planning for the future. Supports for International Languages Levels 1, 2, 3 and 4 are also provided.

Ontario Music Educators' Association (OMEA)
OMEA has developed a series of lessons which make connections between the Grade 7-10 Music curriculum and financial literacy skills and knowledge. The lessons address a range of issues including careers in the recording industry, music event planning, and the cost of buying and repairing instruments.

Ontario Physical and Health Educators' Association (OPHEA)
Click here to view OPHEA's webinar Making Cents of the Elementary Health and Physical Education Curriculum. In this webinar participants explored ways to integrate financial literacy skills and knowledge within the elementary Health and Physical Education curriculum, grades 4-8. Financial literacy skills are integrated with the living skills and Healthy Living strand in the Health and Physical Education curriculum.

Ontario School Library Association (OSLA)
This website, developed by OSLA, features interactive lesson plans which can be used in a variety of curriculum areas from grades 7 to 12 including: Business Studies (Finance, Digital Literacy, Productivity Software), Mathematics (Linear Relations), Social Sciences & Humanities (Research and Inquiry Skills), and English (Media Studies).

Science Teachers' Association of Ontario (STAO)
STAO has developed a 3 lesson series connecting Science expectations to financial literacy. The lessons focus on the following strands: Grade 6: Matter and Energy - Electricity and Electrical Devices, Grade 7: Earth and Space Systems - Heat in the Environment and Grade 9 (Applied/Academic): Physics - The Characteristics and Applications of Electricity.

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Subject and Division Associations have developed learning resources to demonstrate connections between financial literacy knowledge and skills and various curriculum expectations. The links below will take you directly to the financial literacy resources posted on the subject/division association websites. As new material is released, links will be posted on this page.

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The resources below are organized by grade, but the videos, teaching and learning examples and other resources found within can be useful in numerous teaching and learning situations across different subjects. Many of the teaching strategies used in the resources are applicable across a range of subjects and disciplines and can be adapted for different grades. In addition to discipline-specific resources, highlights videos are available that provide general information about financial literacy education in Ontario. An elementary Scope and Sequence document is available to highlight curriculum expectations related to financial literacy education in the current Ontario curriculum.

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The resources below are organized by grade, but the videos, teaching and learning examples and other resources found within can be useful in numerous teaching and learning situations across different subjects. Many of the teaching strategies used in the resources are applicable across a range of subjects and disciplines and can be adapted for different grades.