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Tasks for K to Grade 2, organized by strand, and also routines.
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 pictorial and symbolic forms
Reflect on mathematical thinking
Ask parents to gather up to 10, 20, or 100 small objects (e.g., toy cars, buttons, Cheerios, etc.) for their child.
Invite students to count their collections.
Encourage students to make groups or use tools like cupcake liners, ice cube trays, ten frames to help them count.
Ask:
How did you 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 small container (water glass, vase, bowl) and a collection of items that will fit in the container (jellybeans, marbles, dried beans)
Without counting, place a small 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).
Invite students to think about and record (using pictures and symbols) what another number, might be. For example,
9 might be a spider (8) and a snail (1) or two dogs (4 and 4) and a snail (1) or …
16 might be a crab (10) and an insect (6) or two spiders (8 and 8) or …
36 might be three crabs and an insect or eighteen people or …
Ask "What strategies can you use?" (place-value, doubling, skip-counting, etc.) "What do you notice?" "What patterns can you see?"
DECOMPOSING (PARTS-WHOLE)
Develop, demonstrate, and apply mathematical understanding through play
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Have students play a backyard version of "Shake and Spill" using a stick and a number of rocks.
10 and 20 are good numbers to work with as they help build students knowledge of "Partners to 10".
Toss the rocks at the stick, which acts as a divider for the two parts.
Source: Royal Heights teacher Parbee Brar (link to tweet)
NUMBER OPERATIONS
Develop mental math strategies and abilities to make sense of quantities
Develop and use multiple strategies to engage in problem solving
Provide this image and ask questions such as:
How many dinosaurs are there in the picture? How do you see them?
How many if one more dinosaur arrived? If one went away?
How many more dinosaurs need to arrive for there to be 15?
How many dinosaurs need to jump in the water for there to be 10 dinosaurs swimming?
How many dinosaurs would there be if 5 dinosaurs left?
What equations can you write to show what is happening with the dinosaurs?
Note: Numbers can be adjusted to fit class/student needs.
Students can make their own stories with their own toys, and drawing their own mat.
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 subtracting? 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.
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?
EXTENDING PATTERNS
Use reasoning to explore
Communicate mathematical thinking in many ways
Share the following patterns with your students. Ask:
What repeats? What's the pattern core?
What comes next?
What comes before?
How do you know?
BUILDING PATTERNS
Model mathematics in contextualized experiences
Represent mathematical ideas in concrete and pictorial forms
Have students gather materials (small objects, stickers, markers, toys, etc.). Ask questions such as:
What kinds of patterns can you build? (You can use colours, sounds, toys, movements, or other ideas.)
How do you know it is a pattern? What comes next? What comes before?
Can you make more than one pattern that follows the same rule? For example, if the rule is AAB:
red red blue, red red blue
clap clap stomp, clap clap stomp
short short tall, short short tall
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?
For the pattern question above, you can ask your students to look at the shapes on the right (circles, crescents, trigons) and ask:
Select all or some of these shapes. What patterns can you create? 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
ANALYZING PATTERNS
Develop, demonstrate, and apply mathematical understanding through problem solving.
Explain and justify mathematical ideas and decisions.
Each of the images on the right is a "pattern" that has been messed with in some way. Perhaps an element has been added or removed, or one or more attributes of an element has been changed, or two neighbouring elements have swapped positions.
Have students choose one of the sequences to fix so that it is a pattern. Ask:
What repeats? What's the pattern core?
What's the mistake?
How did you fix it?
Invite students to create their own pattern, mess it up in a small way, and challenge you, their parents, or their classmates to fix it.
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 repeating 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
Explain and justify mathematical ideas and decisions
Have students (parents) gather 6 shapes or provide a picture/printable sheet.
Ask: How could you sort these shapes? What other ways could you sort them?
Encourage students to explain their rules for sorting. They can do this orally and/or record the different attributes that they used to sort.
If students find thinking about how to sort difficult, ask: What makes these shapes similar? What makes them different? Encourage thinking about colour, size, number of sides, symmetry, etc.
This activity can be repeated with different collections (toys, foods, clothing).
Game Extension: Play “Guess My Rule” One player sorts and the other tries to guess what sorting rule was used.
IDENTIFYING/BUILDING
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Use mathematical vocabulary and language
Provide the image on the right and ask:
What shapes do you see?
How do you know what to call each shape?
Provide tiles (page 1) or shapes (page 2), or ask students to draw them. Ask:
Using 4 tiles/shapes, can you make one triangle, a square, a rectangle? What other shapes can you make?
Using more tiles/shapes, what other shapes can you make?
Note: Alternatively students can use the free Pattern Shapes tool from the Math Learning Center.
LINEAR MEASUREMENT (non-standard units)
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Explain and justify mathematical ideas and decisions
Ask students to find some things around their home to measure (furniture, containers, toys, etc.).
Ask them to use their hands to measure how long or tall the objects are.
Ask questions such as:
How can you use your hands to compare the objects? Which object is the longest or tallest? Which object is the shortest?
What other things can you use to measure? What makes a good measuring tool?
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 that you know?
What designs can you make?
AREA MEASUREMENT (non-standard units)
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Provide students with the images of the frame and the coloured shapes or provide them with the link to the printout sheet (see below). Students can also do this activity with small items found in the home (coins, dried beans, counters).
How many blue squares will fit into the white frame?
How many of the green circles will fit before they have to overlap?
Which shape is the best choice if we want to cover the most area inside the frame?
Why do we need to use the same shape if we are measuring how many will fit in the frame?
Source: NRICH Templates can be printed from this link.
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
Have students(parents) gather a small collection of objects (shapes, toys, books) or provide a picture/printable sheet.
Ask students: What attribute could we use to sort the collection?
Once students sort their collection, ask: How could we organize the groups so we can see which has more or less?
If students find organizing their groups challenging, prompt them to try grouping vs lining up the objects.
Ask: Why might we group objects? How does lining them up help?Students can be asked to colour in grid paper or draw pictograms to represent their sorts on paper.
Ask: How does sorting and organizing help us understand our collections?
COLLECTING DATA: How can we keep track?
Connect mathematical concepts to each other and to other areas and personal interests
Represent mathematical ideas in concrete, pictorial, 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 DATA
Represent mathematical ideas in concrete and pictorial forms
Reflect on mathematical thinking
Instructions to students:
Use your data from the COLLECTING activity.
Colour in a chart, grid paper or other option to show how many of each exercise you did altogether last week.
Use a picture or a word to label each exercise
Ask:
Why is it helpful to have different ways of recording information?
What do you notice about your exercise when you look at your graph?
ANALYZING DATA
Use reasoning to make connections
Explain and justify mathematical ideas
Provide students with a pictograph. Examples are shown on the right.
Ask questions such as:
What do you notice?
What do you wonder?
Which has the most? least?
What other questions does this graph answer for you?
Other suggested questions are below each graph.
What is a good title for this graph?
How many more buses are there than teddy bears?
How many Golden Delicious apples are there?
How many more Red Rome apples are there than McIntosh?
PROBABILITY (K-2)
Use mathematical vocabulary and language to contribute to mathematical discussions
Provide students with a picture of a spinner like the one shown.
Ask questions such as:Which colour is the spinner most likely to land on?
Which colour is the least likely?
How often will the spinner land on red, green or blue?
How often will the spinner land on purple?
What can you say about the spinner that is certain?
What can you say about the spinner that is uncertain?
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 8 peaches – 3 on top, 5 on the bottom”
“I see 3 peaches on each side and 2 in the middle, so 8 altogether.”
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 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 small number 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 splat. The problem is to figure out how many dots are covered.
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 7, 17, or 37.
Look for and encourage:
decomposing (4 and 3 make 7)
place value (3 tens and 7 ones make 37)
friendly numbers (17 is 3 less than 20)
visual ways of thinking about numbers (pictures, tallies, ten frames, base ten blocks, etc.)
using patterns (30 + 7 = 37, 29 + 8 = 37, 28 + 9 = 37, …)
Push student thinking by adding constraints (Write ways to make 7 using three addends; Think of ways to make 17 using subtraction.)
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 one digit number.
What makes 25 different from the others is that I say it when I skip count by 5s.
43 is the only number that is close to 50.
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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