Minds On
Representing numbers
There are many ways to represent numbers. Let’s use the number seven as an example. What numbers can we add, subtract, multiple or divide to equal seven?
See what combinations you can create, then click the ‘Hint’ button to access some suggested answers.
Examples: 7 = 4 + 3, 7 × 1, 8 − 1, 10 − 3, …
For each of the following numbers, represent the number in as many different ways as you can. You may use: addition, subtraction, division, multiplication, words, pictures, on a hundreds chart, on a number line, etc.
Record your ideas using a method of your choice.
|
First Number |
Second Number |
Third Number |
|---|---|---|
|
10 |
55 |
72 |
Action
Equivalence
When we say 5 + 2 = 4 + 3, we are saying the expression 5 + 2 and 4 + 3 are equivalent or equal. Both expressions equal seven. In an equation both sides must always be equal.
Examine the following photo to understand how expressions can be represented on a balance scale, using both numbers and images.
On one side of the scale there is the expression 4 + 3. On the other side there are 4 triangles plus 3 inverted triangles. The equation 4 + 3 = 7 is below the scale.
Balancing the scales
We will now attempt to balance the following scales. Determine the missing number in the box. Complete the following fillable and printable document Balancing Scales. You can also complete this activity in your notebook or using a method of your choice.
You may use the following Hundred Chart or another tool, such as a number line, counters, or any material of choice, to help support your understanding.
Press the ‘Activity’ button to access Balancing Scales.
Not Equal
If two sides of an equation are not balanced, it means that they are not equal. To demonstrate that an equation is not equal we use the not equals symbol, which is represented as ≠.
Complete the following, demonstrating that the sides of the equations are not equal. You may use the following fillable and printable document Balancing Scales. You can also complete this activity in your notebook or using a method of your choice.
Press the ‘Activity’ button to access Balancing Scales.
Press the ‘Answer’ button to reveal the answers and check your work.
Balance 1 : 20 + 10 ≠ 50, the sum of 20 and 10 is less than 50.
Balance 2 : 15 + 25 ≠ (any number less than 40), the sum of 15 and 25 is greater than (any number greater than 40)
Greater than and lesser than in equalities
When two sides of an equation are not equal it is called an inequality. One side is greater than the other. We use symbols to show this inequality, the greater than (>) and less than (<) symbol.
Complete the following, demonstrating if the sides of the equations are greater than or lesser than.
You may use the following fillable and printable document Greater Than or Lesser Than Scales. You can also complete this activity in your notebook or using a method of your choice.
Press the ‘Activity’ button to access the Greater Than or Lesser Than Scales.
Press the ‘Answer’ button to reveal the answers and check your work.
Solutions may vary. These are a few sample solutions.
Balance 1 : 10 + 20 > 25 (the sum of 10 and 20 is greater than 25)
Balance 2 : 25 + 50 > 35 (the sum of 25 and 50 is greater than 35)
Balance 3 : 50 + 16 > 36 (the sum of 50 and 16 is greater than 36)
In the following questions the numbers are not given. You can choose any number that makes the inequality true. You may wish to use a hundred chart, number line, or any other method to support your understanding and to display your thinking.
- 12 + (Blank) > 20
- 3 + (Blank)< 20
- (Blank) > 7 + 8
- 15 < 12 + (Blank)
- (Blank) + (Blank) > 16
- (Blank) + (Blank)< 19
Press the ‘Answer’ button to reveal the answers and check your work.
- any number greater than 8
- any number less than 17
- any number greater than 15
- any number greater than 3
- any two numbers that have a sum greater than 16
- any two numbers that have a sum less than 19
Consolidation
Balancing a budget
Two artists are recording the total they spend on supplies each week.
They are working with a budget of $20 altogether. Find the sum of both artists’ costs for the week.
You may use the following fillable and printable document Total Budget Chart. You can also complete this activity in your notebook or using a method of your choice.
Press the 'Activity' button to access Total Budget Chart.
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.