Minds On

Multiplication review

Let’s brainstorm: how might we solve the question 13 × 10? What strategies could we use?

In your notebook or using another method, try to use objects, images, numbers, diagrams or words to show your thinking.

Press ’Hint’ to access a suggestion for one strategy that could be used to solve this question.

A rectangle with 12 rows and 3 columns. The number 36 points to the centre of the rectangle to show that the whole rectangle is made up of 36 smaller squares.

An array is a rectangular arrangement of objects into rows and columns. It is used to represent multiplication.

For example, 12 × 3 can be represented by 36 objects arranged in 12 rows and 3 columns. Arrays can also be used to represent the area of a rectangle.

Action

Patterns in multiplication

Our number system is full of many patterns that can help us learn how numbers work. Multiplication especially has many patterns!

In this learning activity, we are going to explore some patterns when multiplying numbers by 10, 100 and 1000 to help us build our mental math skills!

Multiplying by 10

Examine the following chart that shows whole numbers multiplied by 10. Can you identify any patterns?

Question Representation Answer
4 × 10 A rectangle with 10 rows and 4 columns of squares. = 40
10 × 10 A rectangle with 10 rows and 10 columns of squares. = 100
12 × 10 A rectangle with 10 rows and 12 columns of squares. The squares in the two farthest right columns are coloured red. = 120
25 × 10 A rectangle with 10 rows and 25 columns.

A rectangle with 10 rows and 25 columns of squares. There is a dark line marking the midpoint between the first twenty columns, and the five farthest-right columns are coloured red.

 = 250
86 × 10 A rectangle with 10 rows and 86 columns of squares. The ten farthest right columns are coloured red. = 860
112 × 10 A rectangle with 10 rows and 112 columns of squares. The ten farthest right columns are coloured red. = 1120

Now let’s examine the same questions but using a place value chart. Is the pattern any easier to identify?

Student Success

What’s the pattern?

When we multiply a whole number by 10, the place value shifts one position to the left. This happens because when we multiply by 10, we are increasing the value by a factor of 10.

Multiplying by 100

Next, let’s examine what happens when we multiply whole numbers by 100. In a notebook or using another method of your choice, find the missing values:

5 × 100 = 500

17 × 100 = 1700

43 × 100 = ?

61 × 100 = 6100

123 × 100 = ?

456 × 100 = 45,600

Brainstorm

Brainstorm

Explain the strategy you used to solve for the missing answers. Do you notice a pattern when numbers are multiplied by 100?

When you’re ready, press ’Solution’ to access an explanation of the pattern.

What’s the pattern?

When we multiply a whole number by 100, each place value shifts two positions to the left.

Multiplying by 1000

Choose 4 different two- or three-digit numbers and using a strategy of your choice, multiply them by 1000. Compare the answers. What do you notice? Is there a pattern?

Press ’Hint’ to access some information to help you with your work.

Consider using a place value table, like the one modelled in the multiplying by 10 and multiplying by 100 sections, to help you compare your answers and identify any patterns.

Practice

Independently or with a partner if able, take turns making up two- or three-digit numbers. You can decide by rolling a die, pulling cards, or using paper numbers from 1 to 9.

If you choose an odd number (1, 3, 5, 7, 9), make up a 3-digit number. If you choose an even number (2, 4, 6, 8), make up a 2-digit number.

Once you have your number:

  • multiply it by 10 and record the answer
  • multiply it by 100 and record the answer
  • multiply it by 1,000 and record the answer

Practice this a few times until you feel comfortable multiplying 2-or 3-digit numbers by 10, 100, and 1,000.

Consolidation

Multiplying rabbits

Did you know? Rabbits can have several litters of babies each year? This is because rabbits have a short gestation period of about 25 to 28 days.

Consider the following scenarios. Record your thinking in a notebook or using another method of your choice. Be sure to record a math sentence for each question. Represent your calculations using an array or another method of your choice.

  1. If 10 rabbits each give birth to 12 babies, how many babies are born in total?
  2. If 100 rabbits each give birth to 11 babies, how many babies are born in total?
  3. If 1000 rabbits each give birth to 14 babies, how many babies are born in total?

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

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