Minds On

True or false?

You are presented with the following four statements. Your task is to decide which statements are true and which are false. Some may be both! Be prepared to justify your response.

  • 12 = 6 + 6
  • Three students are the same as one student and two more students.
  • One old tree is much bigger than one young tree.
  • Three pounds of rocks is the same as three pounds of feathers.

Action

Balancing a scale

In order to balance a scale with 24 on one side, how many 8’s do we need on the other? Record your Answer using a method of your choice.

Student Tips

Write your notes in a book!

Both sides must be equal for the scale to balance.

A balancing scale tipping down towards the right side. The number 24 is on this side. On the other side, there is a question mark.

Press ‘Answer’ to check your work.

8 + 8 + 8 = 24
We can also record that as 3 × 8 = 24

Task one

Complete the following fillable and printable document Balance Scales Equations. You can also complete this activity in your notebook or using the method of your choice.

Balance Scales Equations Press the ‘Activity’ button to access the Balance Scales Equations. Activity (Open PDF in a new window)

Understanding the relationship between addition and multiplication allows us to be more efficient. We can also solve equations when we know one symbol, but are trying to find the other. Let's examine the following question to understand how.

If a triangle is equal to 5, what is the value of a square? There is a scale with 2 triangles on the left side and 5 squares on the right side. The two sides are balanced. Followed by the balance scale is 2 fill-in-the-blank equations. Equation 1 is blank multiplied by blank equals blank multiplied by blank. Equation 2 is Square equals blank.

Press ‘Answer’ to check your work.

We have two triangles on the left side of the scale and 5 squares on the right side.
2 × 5 = 5 × 2
Square = 2

Task two

Reflect on the following questions and record your thoughts using a method of your choice.

If a triangle is equal to 8, what is the value of a square? There is a scale with 3 triangles on the left side and 6 squares on the right side. The two sides are balanced. Followed by the balance scale is 2 fill-in-the-blank equations. Equation 1 is three multiplied by eight equals six multiplied by blank. Equation 2 is square equals blank.

Press ‘Answer’ to check your work.

Square = 4

If a triangle is equal to 12, what is the value of a square? There is a scale with 4 triangles on the left side and 6 squares on the right side. The two sides are balanced. Followed by the balance scale is 2 fill-in-the-blank equations. Equation 1 is blank multiplied by blank equals blank multiplied by blank. Equation 2 is square equals blank.

Press ‘Answer’ to check your work.

Square = 8

Task three

Find the values using the clues provided. Record your ideas using a method of your choice.

Learner Facing

If both sides are equal to 45, what is the value of each symbol.There is a scale with 3 triangles on the left side and 5 squares on the right side. The two sides are balanced. Followed by the balance scale is 3 fill-in-the-blank equations. Equation 1 is blank multiplied by blank equals blank multiplied by blank. Equation 2 is square equals blank. Equation 3 is triangle equals blank.

Press ‘Answer’ to check your work.

Triangle = 15

Square = 9

If both sides are equal to 36, what is the value of each symbol. There is a scale with 2 squares on the left side and 3 triangles on the right side. The two sides are balanced. Followed by the balance scale is 3 fill-in-the-blank equations. Equation 1 is blank multiplied by blank equals blank multiplied by blank. Equation 2 is square equals blank. Equation 3 is triangle equals blank.

Press ‘Answer’ to check your work.

Triangle = 12

Square = 18

Consolidation

Values of objects

Use the numbers on the side and the bottom of the chart to figure out the value of each kind of fruit.

banana cherry banana 10
lemon lemon lemon 12
banana cherry cherry 14
8 16 12

Let’s examine the lemon - across the second row.

There are three lemons that add up to 12

Lemon + lemon + lemon = 12

12 ÷ 3 = 4

Since all the fruit in that row are the same, each lemon would have a value of 4.

If you then examine the first column there is a banana, a lemon, and a banana.

Banana + lemon + banana = 8

We know that the value of the lemon is 4 so we can put that value into our equation.

Banana + 4 + banana = 8, so:

8 − 4 = 4

If there are 2 bananas, then each banana would have a value of 2.

(2 + 2 = 4)

Let’s figure out if that is correct by putting those values into the equation:

Banana − lemon − banana = 8

2 + 4 + 2 = 8

Here is what we know so far:

Lemon = 4

Banana = 2

Now think about how you can find the value for the cherry using what is known and the information on the chart. Record your answers to the following questions in a method of your choice.

  • What strategies did you use to find the value for the cherry?
  • How do you know that your values for each kind of fruit are correct?

Complete the grids

Complete the following fillable and printable document Values of Objects Grid. You can also complete this activity in your notebook or using a method of your choice.

Values of Objects Grid Press the ‘Activity’ button to access the Values of Objects Grid. Activity (Open PDF in a new window)

Answer the following questions using a method of your choice.

  • What challenges did you encounter while completing this task?
  • What strategies did you use to persevere through the challenge?

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.