Minds On

Balance scales

Examine the following balance scales:

  • What do you notice about both sides of the scale?
  • What do the last two scales require?
  • Could you represent this in some other way?

Record your thoughts using a voice recorder, speech-to-text, or writing tool.

Action

Finding unknown values using balance strategy

The balance strategy can be used to find the value of a symbol.

Balance strategy

Applying the inverse operation to both sides of the equation removes a number. This makes it easier to solve and is called the balance strategy.

If it helps, you can write or imagine each side of the equation on each side of a balanced scale.

Let’s explore the following example:

Clue 1 → Δ + 40 = 60

Clue 2 → Δ × = 100

First, use the balance strategy to find the value of Δ.

In this case, you want to isolate Δ on the left side of the equation, so you need to eliminate (or get rid of) the 40 and make that a zero.

In order to eliminate the 40 from the left side of the equal sign, subtract 40 from 40 on the left side and subtract 40 from 60 on the right side to maintain balance on both sides of the equal sign.

Let’s expand on how we do it:

  • Δ + 40 = 60

The inverse of addition is subtraction. We need to subtract 40 from each side.

  • Δ + 40 - 40 = 60 - 40 Δ + 0 = 60 - 40 Δ = 20

Now that we know the value of Δ, we can move on to the second equation to find the value of . We substitute 20 whenever we see a Δ.

  • Δ × = 100

    20 × = 100

Using the balance strategy, we need to eliminate the 20 from the left side of the equation just like we did above to isolate the .

The inverse of multiplication is division:

  • 20 ÷ 20 × = 100 ÷ 20 = 100 ÷ 20 = 5

Your turn!

Find the value of symbols Δ and and any variables. Record your answers using a method of your choice.

a) Here is the first exercise. Follow each step to find out the value of the two symbols.

Clue 1 → Δ 15 = 35

Clue 2 → Δ × = 100

  • Δ 15 = 35

    Δ 15 + (Blank) = 35 + (Blank)

    Δ =(Blank)

    Δ × = 100

    (Blank) × = 100

    (Blank) ÷(Blank) × = 100 ÷ (Blank)

    = (Blank)

Press ‘Reveal’ to check your answer.

Δ = 50

= 2

b) Consider another example. Start with Clue 1 and try to find out the value of ☺. Then, continue the process to find the value of α in Clue 2.

Clue 1 → x 9 = 81

Clue 2 → α = 96

Press ‘Reveal’ to check your answer.

α = 105

= 9

c) Find the value of these two symbols.

Clue 1 → Δ × 8 = 64

Clue 2 → Δ = 75

Press ‘Reveal’ to check your answer.

= 83

Δ = 8

d) Here again, you have two symbols: α and Δ. Find their value.

Clue 1 → α × 7 = 49

Clue 2 → α + Δ = 100

Press ‘Reveal’ to check your answer.

α = 7

Δ = 93

e) This time you have 3 clues to work with.

Student Tips

Choose the first clue

Check the three clues and start with the clue where you can find the value of one symbol.

Clue 1 → 2 × = 3 × α

Clue 2 → 3 × α = 4 × Δ

Clue 3 → 6 × = 72

Press ‘Reveal’ to check your answer.

= 12

α = 8

Δ = 6

f) Consider the following set of 3 clues. Which clue should you start with? Find the value of each symbol.

Clue 1 → 5 × = 3 × α

Clue 2 → 4 × α = 60

Clue 3 → 45 ÷ = Δ ÷ 4

Press ‘Reveal’ to check your answer.

= 9

α = 15

Δ = 20

Consolidation

Finding unknown values

Three students brought in food for their school’s food drive.

A donation box with food cans.

Student A brought in 6 more items than Student B.

Student B brought in half as many as Student C.

Student C and Student A brought in a combined total of 15 items.

1.Create a set of equations for each of the statements using symbols or variables.

Press ‘Reveal’ to check your answer.

A = B + 6

B = ½ × C

C + A = 15

2. Altogether, the three students brought in a total of 18 items. How many items did each student bring for the school’s food drive?

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.