Embedded Files
We are hopeful that these activities will help create connection and give parents, students and teachers opportunities to do their at-home learning in a way that minimizes stress and encourages engagement. We will add more tasks periodically.
Below is a menu of suggestions to choose and pick from. We have provided ideas for each strand to provide more choice. For each task we indicate the KEY CONCEPT within that strand, for example, COUNTING in Number. We have also indicated one or two curricular competencies. Many competencies could emerge through a math experience - we have chosen ones which we think are more likely to emerge. Teachers may decide to choose different ones.
Note that there is also a routine provided.
As this is for Grades 3-5, you may wish to adapt the task for your learners as appropriate.
Number: Number represents and describes quantity (how many or how much)
Number: Number represents and describes quantity (how many or how much)
COUNTING
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Ask students gather up a collection of small objects (e.g., toy cars, buttons, Cheerios, etc.) -- no more than 100.
Invite students to count their collections.
Encourage students to make equal-sized groups or form arrays to help them count.
How can you use multiplication to count your collection? Can you count your collection another way? Which way of counting is your favourite? Why?
ESTIMATING
Estimate reasonably
Use mathematical vocabulary and language to contribute to mathematical discussions
Have students gather a container (water glass, vase, bowl) and a collection of items that will fit in the container (jellybeans, marbles, dried beans)
Without counting, place a handful of items in the container
Have students make a high/low estimate: What number are you sure is too little?
What number are you sure is too much? What number is just right?Students may write down their answers or give them orally
Ask: What strategy did you use to estimate how many?
Count the items in the container. Ask: How close was your estimate?
Add or take out some of the items and repeat the activity
Encourage students to use previous rounds to refine their estimates
Other types of estimation can involve using lengths of string, rolling a ball, etc.
This activity can also be done using Steve Wyborney’s Estimation Clipboard slide decks
DECOMPOSING (PARTS-WHOLE)
Represent mathematical ideas in pictorial and symbolic forms
Develop and use multiple strategies to engage in problem solving
In April Pulley Sayre’s One Is a Snail, Ten is a Crab numbers are represented by the number of animal "feet" on each page.
One is a snail, two is a person, four is a dog, six is an insect, eight is a spider, and ten is a crab. Share this information through the image on the right.
Other numbers are made up--or composed--of these numbers (or animals). For example,
Seven is an insect (6) and a snail (1). But 7 could also be a dog (4) and a person (2) and a snail (1).
Thirty is three crabs (3 * 10) or ten people (10 * 2) and a crab.
Invite students to think about and record (using pictures and symbols) what other numbers might be. For example,
36 might be three crabs and an insect or eighteen people or …
43 might be seven insects and a snail or five spiders and a person and a snail or …
120 might be twelve crabs or twenty insects or ten crabs and five dogs or …
Encourage students to write multiplication equations where appropriate.
Ask "What strategies can you use?" (place-value, doubling, skip-counting, etc.) "What do you notice?" (four 6s is the same as six 4s) "What patterns can you see?" (the odd numbers have to have at least one snail)
REPRESENTING NUMBER (PLACE VALUE)
Represent mathematical ideas in pictorial and symbolic forms
"Using 8 base ten blocks (small cubes, rods, flats, or large cubes), what numbers could you make? Record these possibilities using pictures and numbers."
Drawings work for this task but virtual base ten blocks are an alternative.
Students may start by using blocks of the same kind (8 small cubes are 8, 8 rods are 80, …) before combining different kinds of blocks (5 rods and 3 small cubes is 53, 7 flats and 1 rod is 710, …).
Ask "What patterns do you see?"
Students may also be flexible in deciding which type of block represents a unit ("Which one is 1?").
If a flat is one, then a rod is one-tenth, a small cube is one-hundredth, and a large cube is ten so 6 rods and 2 small cubes is 0.62.
Extend the task by asking "What if you used 13 base ten blocks?"
This brings in the possibility of solutions that involve regrouping (e.g., 2 flats and 11 rods is 310).
NUMBER OPERATIONS (meanings)
Develop mental math strategies and abilities to make sense of quantities
Develop and use multiple strategies to engage in problem solving
This image shows some bars of chocolate (or maybe pieces of one bar). The focus of this activity is the meanings of the operations in context.
What story problems can you write about the chocolate?
Can you write a question for your problem that you would use addition to solve? What about subtraction?
Can you write a question for your problem that you would use multiplication to solve? What about division?
How do you decide which operation to use when you have a problem to solve?
NUMBER OPERATIONS
Develop mental math strategies and abilities to make sense of quantities
Develop and use multiple strategies to engage in problem solving
Show Image A and ask: How many? How do you know?
Show Image B and ask: How many now? How do you know?
Ask other questions such as:
How does A help you to solve B?
What is the same and different about A and B?
Explain your strategy for multiplying? Why did you choose it? Is there another way you can do it?
Can you create your own A and B pair of images?
Note: These images are taken from Berkeley Everett's Math Flip decks. More can be found here. Digital decks are also available here.
Fractions (representing)
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Use reasoning to explore and make connections
Show students this image. Ask questions such as:
Which of these images show a fraction and which do not? Explain your reasons.
What fractions can you see represented?
Choose one of the images. What would that fraction look like in a different shape?
Adaptation: For students who have not yet been introduced to the concept of fractions, this activity may be done by introducing a single image one at a time.
Image from Fraction Talks
Patterns: We use patterns to represent identified regularities and to make generalizations
Patterns: We use patterns to represent identified regularities and to make generalizations
IDENTIFYING PATTERNS
Communicate mathematical thinking in many ways
Explain and justify mathematical ideas and decisions
Share the following patterns with your students. Ask:
Which of the following are patterns?
How do you know?
How would you describe the pattern rule?
3, 6, 9, 12, …
2, 6, 10, 14, …
2, 4, 8, 12, ...
21, 19, 17, ...
EXTENDING PATTERNS
Use reasoning to explore
Communicate mathematical thinking in many ways
Share the following patterns with your students. Ask:
What repeats? How would you describe the pattern rule?
What comes next? What comes before?
What will be the 10th number in the pattern?
How do you know?
BUILDING PATTERNS
Model mathematics in contextualized experiences
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Have students gather materials (small objects, stickers, markers, etc.).
Ask questions such as:
What increasing (growing) and decreasing (shrinking) patterns can you build using your materials?
How do you know it is a pattern? What comes next? What comes before?
What increasing (growing) and decreasing (shrinking) patterns can you make using numbers?
Ask open questions such as:
A pattern contains the number 11. What could the pattern be?
Sample Responses: 9, 10, 11, 12, ... 5, 8, 11, 14, 17, ...
A pattern contains the numbers 7 and 15. What could the pattern be?
Sample Responses: 7, 9, 11, 13, 15, ... 3, 7, 11, 15, ...
Extension idea: Students can share their patterns and play "Guess my Rule"
PATTERNS WITH INDIGENOUS CONNECTIONS
Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts
Represent mathematical ideas in concrete and pictorial forms
Ask students to watch the video on the right. Tell your students to pause the video each time they're asked a question. Here's a direct link to the video.
The questions in the video are:
What natural elements connect you to your land and place?
Where do you think the inspiration for these shapes came from?
Why do you think water would be an important inspiration for Coast Salish First Nations?
What designs and patterns can you create?
See if you can find other styles of First Nation art from different parts of Canada. What shapes and patterns are important in each of the pieces you find? What other mathematical connections do you notice?
Ask your students to look at the shapes on the right (circles, crescents, trigons) and ask:
What increasing or decreasing patterns can you create with these shapes? Sketch your ideas.
The images suggest not only using the shape as an attribute, but also the size. Students may consider other attributes like colour and orientation.
Alternatively you can provide this handout so they can cut out the shapes to build their patterns concretely.
For more indigenous math ideas, check out the Surrey School District First Peoples Elementary Math page.
FN Shapes Intro.mp4
PATTERNS IN CHARTS AND TABLES
Explore and analyze mathematical ideas using reason.
Share the record of a "Choral Count" on the right.
Ask students to mark up this record, finding and describing as many patterns as they can. For example:
a repeating pattern of 3, 5, 3, 5, ... in the ones place
a pattern of 1, 1, 2, 2, 3, 3, ... in the tens place
increasing by 5 going down each column (or 10 if you skip over every 2nd number)
increasing by 25 going left to right in each row
increasing by 30 on a diagonal
Ask questions to encourage students to make predictions such as:
Can the number 165 be in the count? What about 163? Why or why not?
If this number is in the count, in which row and column will it be? How do you know?
PATTERNS WITH INDIGENOUS CONNECTIONS
Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities
Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts
Please read this blog post to learn about respectfully connecting cultural practices and perspectives of First Peoples to increasing patterns.
Cultural context as well as a detailed description of the math task is provided there.
Phyllis Atkins at blessing ceremony for We Are All Connected to This Land
Shape & Space: We can describe, measure, and compare spatial relationships
Shape & Space: We can describe, measure, and compare spatial relationships
ATTRIBUTES
Use reasoning to explore and make connections
Use mathematical vocabulary and language
Provide pictures/printables containing 3D shapes (prisms and pyramids) or polygons.
Ask: How are 2D and 3D shapes the same? How are they different?
Provide students with a template for a Venn Diagram or ask them to draw one.
Sort the shapes in different ways using the Venn Diagram
Ask: What attributes can we use for 3D shapes, but not for 2D shapes?
If students struggle to identify attributes, provide vocabulary (prism, pyramid, vertex, face, edges, symmetry) as needed.
Game Extension: “Guess My Shape” One person makes a riddle using several attributes of a shape, ending in “What shape am I?”
Reveal the whole riddle or one line at a time until the other person guesses the shape.
IDENTIFYING/BUILDING
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Use mathematical vocabulary and language
Provide the tangram image on the right and ask:
What shapes do you see?
How do you know what to call each shape?
Provide a set of trangrams (also see note below), or they can draw. Ask:
Using some of the tangram pieces, can you make a triangle, a square, a rectangle, a trapezoid? What polygons can you make?
Using all of the tangram pieces, what other shapes can you make?
Can you make a picture of something?
Note: Alternatively students can use the free tangram tool from the Mathigon
LINEAR MEASUREMENT: non-standard and standard units
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Explain and justify mathematical ideas and decisions
Ask students to gather some rectangular objects (containers, books, packages, etc.)
Ask them to use their hand or a small object (eg. paper clip) to measure the length or perimeter of each object. Ask: "What makes a good unit for measuring?"
Ask them to measure the object again using a ruler (in centimeters if their ruler has them). Ask questions such as:
Compare your 2 different measurements of the objects.
How is using the ruler (standard units) different from measuring with non-standard units? How are they the same?
How does having standard units of measure help us compare and talk about measurements?
Alternatively you can provide this handout that they could use. For a non-standard unit they could use a smaller object like a paperclip.
SHAPES WITH INDIGENOUS CONNECTIONS
Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts
Represent mathematical ideas in concrete and pictorial forms
First refer to the video and questions in the PATTERNS WITH INDIGENOUS CONNECTIONS task above.
Ask your students to look at the shapes on the right (circles, crescents, trigons) and ask questions such as:
How are these shapes similar or different from other shapes you know?
Identify lines of symmetry in these shapes.
Use these shapes to create a design that has symmetry.
Alternatively you can provide this handout so they can cut out the shapes to build their design concretely.
AREA MEASUREMENT
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Provide students with an image like the one shown. Students can use grid paper or cut out paper squares.
Ask students to experiment with creating other shapes that have the same area as the rectangle (triangles, trapezoid, other rectangles).
Is it possible to create a square with this area?
What other shapes can you create with the same area?
LINE SYMMETRY WITH INDIGENOUS CONNECTIONS
Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities
Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts
Please read this blog post to learn about respectfully connecting cultural practices and perspectives of First Peoples to line symmetry.
Cultural context as well as a detailed description of the math task is provided there.
Data & Statistics: Analyzing data & graphs enables us to compare and to interpret
Data & Statistics: Analyzing data & graphs enables us to compare and to interpret
SORTING/ATTRIBUTES: This activity can be an extension of the Geometry (Attributes) task or done at a different time.
Use reasoning to explore and make connections
Explain and justify mathematical ideas and decisions
Using pictures or a small collection (prisms and pyramids, polygons or other objects) have students sort in a variety of ways
Provide students with organizational templates (Venn Diagram, Carroll Diagram, Bar Graph)
Ask: What do we need to think about when we are collecting data? How could we keep track of the data for our collection?
If students find this challenging, prompt them to think about attributes/labels and encourage them to use templates to sort in different ways.
COLLECTING: How can we keep track?
Connect mathematical concepts to each other and to other areas and personal interests
Represent mathematical ideas in concrete and symbolic forms
Instructions to students:
Do some exercises (jumping jacks, sit ups, push ups, stairs, etc.)
Keep track of how many you did after each set: use a tally, write the number, etc.
Record how many of each exercise you do each day this week.
Keep your data in a safe place. You will need it for next week’s activity.
Ask:
How can we collect our data, so it will show us what we did?
What other ways of recording/displaying data have you seen? (This could involve a ‘scavenger hunt’ activity.)
REPRESENTING
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Use reasoning to make connections
Instructions to students:
Use your data from the COLLECTING activity.
Create a table and a bar graph to show your exercise data.
Be sure to label each exercise in your table/graph and include a title.
Ask:
What do you notice about your exercise program when you look at your graph?
Why is it helpful to have different ways of recording information?
ANALYZING DATA
Use reasoning to explore and make connections
Explain and justify mathematical ideas and decisions
Provide students with a bar graph and/or double-bar graph. Examples are shown below.
Ask questions such as:
What do you notice? What do you wonder?
Which has the most? Which has the least?
What other questions does this graph answer for you?
Other suggested questions are below each graph.
Which of these types of graph do you know? You may wish to look up the ones you do not know.
How many more people like line graphs compared to bar charts?
Which favourite graph is half the number of another favourite graph?
How many people do you think were surveyed for this graph?
What is your favourite type of graph?
How many more minutes does Mrs. Williams give on Wednesday compared to Thursday?
Which teacher assigns the most homework?
Overall, does a student have more homework on Wednesday or Thursday?
On which day does a teacher assign half as much homework as another teacher?
EXPERIMENTAL PROBABILITY
Use mathematical vocabulary and language to contribute to mathematical discussions
Use reasoning to explore and make connections
Students can use a die or a coin for this activity
Ask students to predict how many times each number will come up if they roll the die 20 times or how many times they should get heads/tails if using a coin.
Ask: " How did you make your prediction?"
Record predictions.
Now do the experiment and keep a tally of the results.
Ask questions such as:
How does this experiment help you understand chance?
What things in your life do you leave to chance?
What things do you want to be certain about?
Routines
Routines
NUMBER TALK IMAGES
Visualize to explore mathematical concepts
Communicate mathematical thinking in many ways
Share a dot arrangement or photo from ntimages.weebly.com. An example is shown.
Ask how many do you see? How do you see them? How many different ways of seeing them can you come up with?
For example,
“I see 3 boxes with 5 containers of gum in each and one with 4 boxes of gum. So, 5, 10, 15… 19. 19 boxes of gum.”
“I see 5 missing spaces from 24, so 19.”
Recording Template (optional)
To read a more in-depth explanation of this routine, see the blog posts referenced on the home page of the Number Talk Images site.
ESTI-MYSTERY: Estimation Meets Math Math Mysteries
Use reasoning to explore and make connections
Estimate reasonably
Each Esti-mystery provides an image and invites students to wonder what number is represented by the image. As you go through each page of the Esti-Mystery, clues will appear that will allow the students to use math concepts to narrow the set of possibilities to a small set of numbers. In the end, the students will need to call upon their estimation skills to solve the mystery and find the missing number.
Ask students to solve this Esti-mystery (pdf).
Students can use these charts to help with tracking their eliminations when refining their estimates. (optional)
For more information, and to find more Esti-mystery tasks, go to this blog post by Steve Wyborney on Esti-mysteries.
SPLAT!
Develop mental math strategies and abilities to make sense of quantities
Visualize to explore mathematical concepts
Splat! shows a collection of dots and then covers some with a splats. In this Multi-Splat version, each splat covers the same number of dots. The problem is to figure out how many dots that is.
For digital slide decks and instructions for Splat, please see this page from Steve Wyborney.
Splat can also be played with a number of small objects and a “splat” cut out of paper or fabric or combined with story mats to encourage computational number stories.
WAYS TO MAKE A NUMBER
Represent mathematical ideas in pictorial and symbolic forms
Communicate mathematical thinking in many ways
Ways to Make a Number is a "Playing With Quantities" routine shared by Jessica Shumway in her Number Sense Routines books.
Invite students to record as many ways as they can think of to make a given number--say 37, 0.37, or 370 000.
Look for and encourage:
decomposing (200 000 + 170 000 = 370 000)
place value (3 tenths and 7 hundredths make 37 hundredths)
benchmarks (0.37 = 0.25 + 0.12)
visual ways of thinking about numbers (pictures, number lines, base ten blocks, etc.)
using patterns (30 + 7 = 37, 29 + 8 = 37, 28 + 9 = 37, …)
Push student thinking by adding constraints (Think of ways to make 370 000 using subtraction; Think of ways to make 37 using multiplication.)
WHICH ONE DOESN'T BELONG?
A Which One Doesn't Belong? set is made up of four objects (numbers, shapes, graphs, etc.), each of which has at least one reason not to belong. There is not one right answer; if a claim is true, then it is correct.
Share a Which One Doesn't Belong? set, like the one on the right and challenge your students to find reasons why each object is different than the rest.
Provide some helpful prompts for students to share their ideas:
_____ does not belong because...
All _______ have ______ except _______
What makes _________ different from the others is…
Only _______ has _______
Note: Students often notice properties they don't know names for (yet). Use these noticings as opportunities to introduce vocabulary.
For more information and possible sets see the Which One Doesn't Belong? website.
Sample responses:
16 doesn't belong because it's even.
9 is the only number that is less than 10.
What makes 25 different from the others is that it's the value of a coin.
43 is the only number that you can't get by multiplying a whole number by itself.
ESTIMATION 180
Use reasoning to explore and make connections
Estimate reasonably
Estimation 180 is designed to be a daily warmup to encourage students to explore strategies for estimation in a variety of different contexts. Students should be encouraged to use strategies other than guessing, such as using background knowledge, benchmarking and comparison. A collection of images can be found on this website.
Ask students to record their estimates on their sheets using too high, too low and just right numbers.
Encourage students to share their estimation strategies. If possible, they may refine their estimates after listening to the strategies of others.
A digital version of this task can be found here.
Show students this image.
Encourage students to discuss/consider the effectiveness of their chosen strategy and how they might refine their estimates next time.
More Estimation 180 ideas can be found here.
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