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 6-7, 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? How can you use your collection to think about factors and multiples?
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
Apply multiple strategies to solve problems
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 …
Ask "How did thinking about factors and multiples help you build these numbers?" "Which numbers can be represented using only one of the six animals?"
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).
In Math 6 & 7, students explore larger numbers (i.e., to billions).
"If the small cube is 1 (making the large cube 1000), what would 10 000, 100 000, … 100 000 000 000 look like? What patterns do you see?" (repeating pattern of cube, rod, flat in the "periods").
DECIMAL 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 the price of a litre of gas. In the past year, the price of gas has changed a lot! The focus of this activity is the meaning of the operations in context
What story problems can you write about gas prices?
Can you write a question for your problem that you would use multiplication to solve? What about division?
Can you write a problem that requires more than one operation?
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 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.
Fractions (representations)
Represent mathematical ideas in concrete, pictorial, and symbolic forms
Use reasoning to explore and make connections
Present the image to students. Ask questions such as:
What fractions do you see in this picture?
If the white rectangle is 1 1/2, how much is the whole square?
If the red square is 1 whole, how much are each of the other shapes?
How is the 'whole' related to the fraction? What do the numbers in a fraction represent? What do the numbers in a mixed number represent?
Image from Trish Kepler via Twitter
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 with your students. Ask:
Which of the following are patterns?
How do you know?
How would you describe the pattern rule?
EXTENDING PATTERNS
Represent mathematical ideas in pictorial and symbolic forms
Communicate mathematical thinking in many ways
Share the following with your students. Ask:
What repeats?
What comes next?
What will the 10th number in the pattern be? What about the 100th?
How do you know?
How would you describe the pattern rule?
Nudge students' thinking by asking questions such as:
Can the number 36 be in the pattern? What about 37?
Why or why not? For example:
"36 cannot be in the first/second pattern because 36 is a multiple of 3 and each number in the pattern is one less/one more than a multiple of 3."
"36 can be in the 3rd pattern because it's a multiple of 6. I can skip count by 6s to say the numbers in the output."
"36 cannot be in the fourth pattern because it's even and the output is all odd."
BUILDING PATTERNS
Use reasoning to explore and make connections
Represent mathematical ideas in pictorial and symbolic forms
Ask students to create two patterns (increasing and/or decreasing) by filling in two tables, one in which the inputs are provided, and one in which they choose their own inputs.
Ask questions such as:
How do you know it is a pattern? What comes next? What comes before?
Use materials or draw a picture to make a visual pattern for each table.
Ask open questions such as:
Represent a pattern in a table of values such that:
one of the outputs is 12.
two of the outputs are 5 and 14.
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 patterns can you create with these shapes? Can you create a visual pattern? Sketch your ideas.
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
INCREASING PATTERNS FROM GRAPHS
Explain mathematical ideas.
Show students two graphs of linear patterns (one at a time) like the ones shown.
Ask "What are some possible patterns that this graph might represent? Explain your thinking."
Looking at both graphs ask, "How are these linear graphs similar? How are they different?"
Adapted from: Marian Small
Grade 7 teachers you may wish to use graphs that use all four quadrants.
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 mathematical vocabulary and language
Use reasoning and logic to explore and analyze mathematical ideas
Provide pictures/printables of angles, triangles or quadrilaterals.
Ask: How are these shapes the same? How are they different? How are they related to each other?
Provide students with vocabulary for identifying angles/triangles (acute, obtuse, right, reflex, isosceles, equilateral).
Game Extension: “Guess My Shape” One person makes a riddle using several attributes of a triangle or quadrilateral, 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 pattern block image on the right and ask: "What shapes do you see?"
Provide a set of pattern blocks (also see note below), or they can draw on the grid provided. Ask:
Using several of the pattern blocks pieces, can you make a triangle? a rhombus? a trapezoid? a parallelogram? a hexagon?
Using several of the pattern block pieces, can you make a regular hexagon? an irregular hexagon? What other polygons can you make?
Note: Alternatively students can use the free Pattern Shapes tool from the Math Learning Center.
Note: Grade 7 geometry and measurement is about circles and prisms. These will come up in other tasks. In the meantime these tasks are still meaningful for them to think about.
LINEAR MEASUREMENT
Use reasoning and logic to explore and analyze mathematical ideas
Explain and justify mathematical ideas and decisions
Grade 6 instructions (perimeter):
Draw different rectangles that have a perimeter of 36 cm. You can use grid paper, or blank paper.
Draw other polygons that have perimeters of 36cm.
Also try composite shapes.
Are some shapes easier to determine perimeter than others? Explain your thinking.
Grade 7 instructions (circumference):
Find some circular objects around the house (bowls, containers).
Use string to measure the circumference of each object. Measure the length of the string with a ruler to find the measure of the circumference in centimeters.
Use the same string to compare the measurements of the diameter and the circumference. Record the measurements (in cm) in a table.
What is the relationship between a circle’s circumference and it’s diameter? How can this relationship help us make predictions?
Measure the diameter of another circular object and then predict it’s circumference. Measure the circumference to confirm your prediction.
Alternatively you can provide this handout of circles.
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:
What properties of a shape can change without changing the name of the shape? What needs to stay the same?
Use transformations (slides, turns, reflections, dilatations) of these shapes to create a design.
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
Grade 6:
Provide students with the image on the right. Explain that the image contains three rows. For each row, ask the questions:
What is the area of the shape (solid line only) on the right?
How does the image on the right help you to figure out the area of the shape on the left?
The purpose of this activity is for students to notice the relationship between the areas of:
parallelograms and rectangles
triangles and parallelograms
trapezoids and parallelograms
Students can practice by drawing more parallelograms, triangles, and trapezoids on grid paper, and figuring out their areas.
Grade 7:
Provide students with the image on the right or a printout of different sized circles. Students may also draw/trace their own circles.
Tell them to use small objects (coins, dried beans, counters) to measure the diameter of the circle. Then cover the area of the circle with the same units.
Ask: "What is the relationship between a circle's diameter and its area?"
Draw or find another circle. Measure its diameter using your object. Estimate the area based upon the relationship you discovered. Measure the area using your objects. Ask, "How close was your estimate?"
TRANSFORMATIONS OF 2-D SHAPES 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 logic and reasoning to explore and apply mathematical ideas
Explain and justify mathematical ideas and decisions
Provide pictures/printables of quadrilaterals, prisms and pyramids or triangles.
Ask students to choose (or prompt) 2 attributes of their shapes (# of sides and # of angles, area and perimeter, length and width).
Have students create a table to represent the shapes in their collection using the 2 attributes.
Ask: What is the relationship between the 2 attributes? How does the table help us?
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
Have students choose 3-5 activities to track every day this week. Some useful choices might be exercise, schoolwork, screentime, sleeping, relaxing.
Tell them to keep their data in a safe place. They will need it for next week’s activity.
Ask:
How can you organize your tracking so it will be useful later?
What categories can we use, so that we are tracking most of the time in the day?
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 logic and reasoning to make connections
Grade 6 instructions:
Choose one of the categories of data you collected last week, like how many minutes you spent doing exercise or sleeping.
Create a table and line graph to show how much of the activity you did each day. Be sure to label your table and graph and include a title. Remember to include a scale (hours or minutes) on the y axis.
Ask:
What does the graph tell you about your activity last week?
Are there any patterns?
Grade 7 instructions:
You will be using all the categories of data that you tracked last week.
Create a circle graph that shows the ratio/percent of the week that you spent doing each activity.
Be sure to include a title and a legend to show what the sections of your graph mean.
Ask:
What does the graph tell you about your activity last week?
Does the graph tell you everything about your week? How could you improve it?
ANALYZING DATA
Use reasoning and logic to explore, analyze, and apply mathematical ideas
Explain and justify mathematical ideas and decisions
Provide students with a line graph (Grade 6) or a circle graph/pie chart (Grade 7). 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.
What would be a good title for this graph?
How many times is a teenager reminded 4 times?
Which number of times being reminded has a frequency of 5?
How many more times is a teenager reminded 3 times compared to 5 times?
What does the graph say about the frequency that a teenager is reminded 6 times?
Is this a good graph? What would make it better?
What percent of the time is spent doing homework and research combined?
What combination of activities make up 50% of the computer use time?
If the total amount of time spent is 3 hours:
How much time is spent playing games?
How much more time is spent on social activities compared to games?
What activities could the "Other" represent?
What would your circle graph look like?
PROBABILITY
Use mathematical vocabulary and language to contribute to mathematical discussions
Use reasoning to explore and make connections
Students can use dice or coins for this activity.
Ask students to record all possible numerical outcomes (sums) of rolling two dice.
The activity can be adapted by using only one die, or more than two.Ask questions such as:
What is the theoretical probability of rolling a 7? 12? 1?
Which number would you choose if you wanted the highest probability of winning?
Which number has the least probability of being rolled?
Have students roll the dice 20 times and record their results.
Ask students to compare the theoretical probability to the experimental probability results.
Ask:
What affects the outcome of the experiment?
Why are the results different each time?
How is knowing the theoretical probability of an event helpful?
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 4 diagonals of 14 because 7 and 7 make 14. Four times 14 is 56.”
“I see eight 3s and eight 4s and 24 plus 32 is 56.”
“I see 16 dice – 4 rows of 4 or 8 blue and 8 pink.”
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 splats. In the 2-colour Splat! shown below, the problem is to figure out how many dots are covered under each splat. Different coloured splats have a different number of dots covered.
There are several pairs of numbers that work. How are they related?
For digital slide decks and instructions for Splat, please see this page from Steve Wyborney.
There are also Fraction Splats! available!
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 370 000 000.
Look for and encourage:
decomposing (200 000 000 + 150 000 000 + 20 000 000 = 370 000 000)
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 (0.30 + 0.07 = 37, 0.29 + 0.08 = 0.37, 0.28 + 0.09 = 0.37, …)
Push student thinking by adding constraints (Think of ways to make 0.37 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:
Only 16 is even.
9 is the only number whose digits don't add to 7.
What makes 25 different from the others is that it's a multiple of 5.
43 is the only number that is prime.
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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