Solve discount GST and annual-interest problems

What you will learn

• Solve discount GST and annual-interest problems

Models used: number sentences, stories, tables.

Before you start

• Find a percentage of a quantity

Percent is a share of one hundred

This grid is one whole. It has 100 equal squares.

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   This grid is one whole. It has 100 equal squares.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   0/100 = 0 = 0%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Shade 25 squares. We have shaded one quarter of the whole.

   25 out of 100 = 25%

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

3. The full bar represents $80, which is 100%. The shaded share is 25%.

   Now the whole is $80. One quarter of $80 is $20.

   25% of $80 = $20

   Each section: 5% = $4

   0%100% = $80

   25% of $80 = $20

4. The complete bar is the whole. Each labelled section is one part of it.

   A 25% discount removes $20. The $60 left is the sale price.

   $80 − $20 = $60

   80

   20one quarter60three quarters

Worked example: A new example, together

An item costs $700 before a 25% discount. What is the sale price?

1. First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.

   Label every amount in the story before choosing which one the percentage acts on.

   The discount is a part removed from the original price.

   First find the percentage amount. Then decide whether the question needs that part or a final balance.

   Original amount ($)	Stated rate (%)
   700	25

2. First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.

   The percentage is calculated from $700.

   First find the percentage amount. Then decide whether the question needs that part or a final balance.

   Original amount ($)	Stated rate (%)
   700	25

   An item costs $700 before a 25% discount. What is the sale price?

   525 dollars

3. First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.

   25% × $700 = $175.

   First find the percentage amount. Then decide whether the question needs that part or a final balance.

   Original amount ($)	Stated rate (%)
   700	25

4. First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.

   Subtract the discount: $700 − $175 = $525.

   First find the percentage amount. Then decide whether the question needs that part or a final balance.

   Original amount ($)	Stated rate (%)
   700	25

5. First find the percentage amount. Then decide whether the question needs that part or a final balance. Read each value with the heading above its column.

   Check the result against the question we started with.

   The percentage amount is 25 parts out of every 100 of $700.

   We found 525 dollars. The discount is a part removed from the original price.

   First find the percentage amount. Then decide whether the question needs that part or a final balance.

   Original amount ($)	Stated rate (%)
   700	25

Common mistakes to discuss

• Using the wrong whole. Each percentage applies to a stated amount: a discount to the usual price, GST to the price before tax, interest to the amount at the start of the year.

Check your understanding

• Solve discount GST and annual-interest problems
• apply a percentage to the amount it refers to
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.