Minds On

Counting ahead

Use your notebook to solve the word problem.

River's Auntie is teaching River how to weave bracelets. Indigenous people use weaving and braiding to make many things. For example, the Haida use cedar bark to make hats and Inuit or First Nations snowshoes are made from weaving too. River is planning to give their friends the bracelets on National Aboriginal Day. It happens on June 21st, the summer solstice, every year. On this day all Canadians recognize and celebrate the culture, heritage, and contributions of First Nations, Inuit, and Metis peoples.

Let's practice!

River is having fun learning. River would like to make bracelets for each of her friends. River needs two pieces of embroidery string for each bracelet. River is making one bracelet for each of her seven friends.

Auntie has given River 15 pieces of embroidery string. Will River have enough string to give each friend a bracelet?

Use a variety of representations to show your thinking.

Ways to solve

There are many strategies for solving a math problem. Let’s focus on three strategies now.

Skip counting

There are seven bracelets. Each bracelet needs two pieces of string. We can skip count by two’s to solve this math problem.

7 skips of 2 = 14

2 + 2 + 2 + 2 + 2 + 2 + 2 = 14

River needs 14 pieces of string in order to have enough string to make seven bracelets for their friends.

Multiplication

We can use a multiplication sentence to solve a math problem.

River has seven bracelets. Each circle represents one bracelet. River needs two pieces of string to make each bracelet. We can make seven groups of two.

7 groups of 2 strings.

The multiplication sentence says 7 groups of 2 is 14.

River needs 14 pieces of string, so she will have enough string to make seven bracelets for her friends.

Division

We can use division to solve a math problem.

Auntie gave River 15 pieces of embroidery string. Each bracelet needs two pieces of string. River is making seven bracelets.

To divide, we make equal groups of two from 15. We need to make seven equal groups of two for the bracelets.

7 groups of 2 strings. 1 string is leftover.

We have made 7 groups of 2 from 15, so we know River has enough string to make seven bracelets.

14 divided by 7 equals 2. 14 is the dividend, the large number being put into smaller groups. 7 is the divisor, the number of groups there are and 2 is the quotient, the answer or the number of items in each group.

In this learning activity, we are going to explore different ways of counting to 1,000 and different ways to represent multiplication and division facts.

Action

Counting to 100

When we skip count, we add the same number each time.

We can skip count by 5s to 100. Let’s start at 45 and count by 5s to 100. 

We can skip count by 10s to 100. Let’s start at 50 and count by 10s to 100.

We can skip count by 20s to 100. Let’s start at 40 and count by 20s to 100. 

Do you notice anything when the skip count is a bigger number? Write down your ideas in your notebook.

Skip counting to 1,000

We can count to 100 by 5s, 10s and 20s, and we can count to 1,000 by 50s, 100s and 200s.

Counting by 50s

Count the objects.

Violeta made trays of five cookies. Each tray contains five cookies. Count in 5s to find out how many cookies Violeta made.

How is counting by 5 and counting by 50 the same? Record your answer in a video clip.

Counting by 100s

When skip counting by 100s, we add 100 to get to the next number, and the digit in the hundreds column changes by one.

Let’s explore the following example.

Daniel is skip counting to 1,000.

Which skip count is he using? Which digit changes each time? What will the next three numbers be?

Count by 200s

We can count by 200s using what we know about counting by 100s.

Try counting by 200s to 1,000. Start at zero.

Let's share as a class.

When we count by 200s, the hundred digit changes. Instead of changing by one, it changes by two.

0, 200, 400, 600, 800, 1,000

100, 300, 500, 700, 900

250, 450, 650, 850, 1,050

Let's practice!

Show your work and solve for one of the following word problems using skip counting strategies. Use a variety of representations to show your thinking.

Task A: School field trip

We are going on a trip to the museum. We will ride on a bus to get there. Each bus seats 50 students. There are 425 students in our school. How many buses will we need?

Task B: Butterfly garden

We are planting butterfly bushes to attract butterflies in our butterfly garden. Each butterfly bush attracts at least 100 butterflies. If we plant seven bushes, about how many butterflies will we attract?

Multiplication and division

When we count by the same number, we call it repeated addition.

Example: 3 + 3 + 3 + 3 = 12

Another term we use to describe repeated addition is multiplication. When we multiply, we combine equal groups.

The opposite of multiplication is division. When we divide, we break up a number into equal groups.

There are many ways to represent multiplication and division.

Skip counting to multiply and divide

When we count by the same number, we call it repeated addition.

When we subtract by the same number, we call it repeated subtraction.

We can use repeated addition and repeated subtraction to recall multiplication and division facts.



Student Tips

Math sentences

Multiplication and division tell the story of repeated groups of equal size.

The multiplication sentence says: "There are 7 equal groups of 2 for a total of 14."

The division sentence says: "In a total of 14, there are 7 equal groups of 2."

Multiplication and division are opposites operations.

Let's practice!

How does knowing a multiplication fact help to solve a division fact?

Solve the following problems and show your work.

  • 30 ÷ 5 = ?
  • Ask yourself: ? × 5 = 30
  • 27 ÷ 9 = ?
  • Ask yourself: ? × 9 = 27
  • 56 ÷ 7 = ?
  • Ask yourself: ? × 7 = 56
  • 16 ÷ 8 = ?
  • Ask yourself: ? × 8 = 16

Equal groups

Equal groups are groups with the same number of objects in each group. We can show multiplication and division using equal groups.

Student success

Think-Pair-Share

Solve the problem and then share your ideas in your notebook.

Rania has 36 coins that Rania would like to share with their friends. Rania wants to make sure everyone receives an equal share of coins.

How many ways can Rania create equal groups of 36 coins?

Write a multiplication or division statement for each solution.

Use counters to help solve the question. Use a variety of representations to show your thinking.

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Arrays

An array is a way to group objects by arranging them in rows and columns.

Access the following Homework Zone: Mathematics segment entitled “Arrays” to learn more about how to visualize multiplication using an array.


Array model for multiplication and division

Number lines

You can show multiplication using a number line.

Two stacked number lines numbered from 0 to 30 in counts of 5. The first number line shows how to solve the multiplication statement 3 times 5 using arrows. The first arrow jumps from 0 to 5. The second arrow jumps from 5 to 10 and the third arrow jumps from 10 to 15. It takes three jumps of five to equal fifteen. The second number line shows how to solve the division statement 15 divided by 5 using arrows. The first arrow starts at 15 and jumps back to 10, the second arrow starts at 10 and jumps back to 5 and the third arrow starts at 5 and jumps back to 0. 15 is split into three different jumps, with five numbers in each jump.

Let's practice!

Let's work together to solve the first problem.

Describe how you would get to 14 using multiplication and division facts.

Solve the next two problems. Share your ideas in your notebook.

Describe how you would get to 16 using multiplication and division facts.

Describe how you would get to 9 using multiplication and division facts.

Solve the last problem. Share your ideas in your notebook.

Describe how you would get to 7 using multiplication and division facts.

Consolidation

Around the classroom

River's friend Juna explains how to solve the following problem:

River gave the bracelets made to their friends on National Aboriginal Day. The bracelets were a success, and now River's Auntie is teaching traditional weaving and braiding to all the children in the community. They are honouring their culture as they make traditional sashes, hats and baskets.

River is posting flyers in the community about the weaving classes. River has 20 posters and wants to post 4 posters in different buildings in her community including the library and school. In how many buildings will she be able to hang posters?

Juna's explanation:

There are 20 posters. River needs 4 posters in each school. We divide to figure out how many equal groups of 4 we can make from 20. We start with 20 counters and put 4 counters in each group. The answer is 5.

Student Success

Think-Pair-Share

Create three word problems:

How can you improve on Juna's explanation?

Can you represent or communicate Juna's thinking another way?

Create three-word problems:

  • one counting word problem using skip counting of 50s, 100s or 200s to 1,000
  • one multiplication word problem
  • one division word problem

Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.

Sharing school supplies

Seven students have a pack of pencil crayons. If there are 100 pencil crayons in each pack, how many pencil crayons are there all together? Use a method of your choice to show your thinking.

Press the “Solution” button to reveal the answer.

Words: We can count by 100s to find the answer. 7 groups of 100 is 700.

Number sentence: 100 + 100 + 100 + 100 + 100 + 100 + 100 = 700

Picture:

An array of 7 boxes of pencil crayons. There are 100 crayons in each box.

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel…

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.