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Lesson 19 of 17

Year 7

Problem solving with integers and decimals

I can use my knowledge of calculating with integers and decimals to solve problems.

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Lesson 19 of 17

New

Year 7

Problem solving with integers and decimals

I can use my knowledge of calculating with integers and decimals to solve problems.

Download all

These resources were made for remote use during the pandemic, not classroom teaching.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

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Lesson details

Key learning points

Integers and decimals appear in many real-world contexts.
Calculating with money is an example of decimals.
Many measurements require decimal values for good accuracy.

Keywords

Integer - An integer is any positive or negative whole number or zero.
Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

Common misconception

Students are unsure where to start on problem solving questions.

Starting with one sentence at a time and isolating what the strategy is first before doing any calculation is important.

To help you plan your year 7 maths lesson on: Problem solving with integers and decimals, download all teaching resources for free and adapt to suit your pupils' needs...

Get students to be active in how they can use their problem solving skills to save money. In supermarkets, are multipacks the best deal? Ask students to give examples of where they have seen real life use of decimals.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Match each calculation to its correct answer. Use your knowledge of identifying a reasonable answer and do not work out the calculations.

Correct Answer:$$4.4\times7.4=$$,$$32.56$$

$$32.56$$

Correct Answer:$$2.9\times2.8=$$,$$8.12$$

$$8.12$$

Correct Answer:$$8.3\times3.1=$$,$$25.73$$

$$25.73$$

Correct Answer:$$5.7\times1.1=$$,$$6.27$$

$$6.27$$

Q2.
Without using a calculator, work out the answer to $$4\times8 + 6\times5 = $$

Correct Answer: 62

Q3.
Match each number with its additive inverse.

Correct Answer:81,(-81)

(-81)

Correct Answer:(-3),3

Correct Answer:18,(-18)

(-18)

Correct Answer:0.3,(-0.3)

(-0.3)

Correct Answer:0.81,(-0.81)

(-0.81)

Q4.
Starting with the calculation with the lowest answer, sort these calculations into order of size.

1 - $$11-4\times2 -1$$

2 - $$\frac{100+(-40)} {5-(-10)} +1$$

3 - $$18+(-6)\times2 +1$$

4 - $$(-12)\div(-3) + 2^2+1$$

Q5.
Work out the missing number: $$33 \times 0.6 + 33 \times$$ $$= 33$$

Correct Answer: 0.4, 4/10

Q6.
Work out the missing number: $$4.5 \times 0.23 + 4.5 \times$$ $$= 4.5$$

Correct Answer: 0.77, 77/100

Assessment exit quiz

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6 Questions

Q1.
Laura has £23.21. She spends £12.45 and then spends £9.29. She then finds £2.89. Without using a calculator, work out how much money she has left. £

Correct Answer: 4.36, £4.36, 436p, 436 p

Q2.
Lucas has a £20 note. He needs to buy 6 packets of donuts for a party. Each packet costs £3.12. Work out how much change Lucas will have left. £

Correct Answer: 1.28, £1.28, 128 p, 128p

Q3.
Some children each grow a tomato plant. Alex’s plant is 28.4 cm, Jacob’s plant is 35.8 cm, Sofia’s plant is 32.4 cm and Andeep’s plant is 24.4 cm. Work out the mean height of the plants. cm

Correct Answer: 30.25, 30 1/4, 121/4

Q4.
An isosceles triangle has one angle of $$43.6^\circ$$ and another angle of $$92.8^\circ$$. Three students work out the third angle. Who is correct?

Correct answer: Lucas: The last angle is $$43.6^\circ$$

Jacob: The last angle is $$92.6^\circ$$

Alex: The last angle is $$223.6^\circ$$

Q5.
The starting line is at 0. If you twist this combination clock anticlockwise 50, which number will the combination lock starting line be on?

Correct answer: 50

-50

-40

Q6.
A combination lock starts at 0. It is twisted 23 anticlockwise, then 78 clockwise, then 80 anticlockwise and then 13 clockwise. Which number is the combination lock now indicating?

Correct Answer: 12

Problem solving with integers and decimals

Problem solving with integers and decimals

These resources were made for remote use during the pandemic, not classroom teaching.

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Match each calculation to its correct answer. Use your knowledge of identifying a reasonable answer and do not work out the calculations.

Q2.Without using a calculator, work out the answer to $$4\times8 + 6\times5 = $$

Q3.Match each number with its additive inverse.

Q4.Starting with the calculation with the lowest answer, sort these calculations into order of size.

Q5.Work out the missing number: $$33 \times 0.6 + 33 \times$$ $$= 33$$

Q6.Work out the missing number: $$4.5 \times 0.23 + 4.5 \times$$ $$= 4.5$$

Assessment exit quiz

6 Questions

Q1.Laura has £23.21. She spends £12.45 and then spends £9.29. She then finds £2.89. Without using a calculator, work out how much money she has left. £

Q2.Lucas has a £20 note. He needs to buy 6 packets of donuts for a party. Each packet costs £3.12. Work out how much change Lucas will have left. £

Q3.Some children each grow a tomato plant. Alex’s plant is 28.4 cm, Jacob’s plant is 35.8 cm, Sofia’s plant is 32.4 cm and Andeep’s plant is 24.4 cm. Work out the mean height of the plants. cm

Q4.An isosceles triangle has one angle of $$43.6^\circ$$ and another angle of $$92.8^\circ$$. Three students work out the third angle. Who is correct?

Q5.The starting line is at 0. If you twist this combination clock anticlockwise 50, which number will the combination lock starting line be on?

Q6.A combination lock starts at 0. It is twisted 23 anticlockwise, then 78 clockwise, then 80 anticlockwise and then 13 clockwise. Which number is the combination lock now indicating?

Q1.
Match each calculation to its correct answer. Use your knowledge of identifying a reasonable answer and do not work out the calculations.

Q2.
Without using a calculator, work out the answer to $$4\times8 + 6\times5 = $$

Q3.
Match each number with its additive inverse.

Q4.
Starting with the calculation with the lowest answer, sort these calculations into order of size.

Q5.
Work out the missing number: $$33 \times 0.6 + 33 \times$$ $$= 33$$

Q6.
Work out the missing number: $$4.5 \times 0.23 + 4.5 \times$$ $$= 4.5$$

Q1.
Laura has £23.21. She spends £12.45 and then spends £9.29. She then finds £2.89. Without using a calculator, work out how much money she has left. £

Q2.
Lucas has a £20 note. He needs to buy 6 packets of donuts for a party. Each packet costs £3.12. Work out how much change Lucas will have left. £

Q3.
Some children each grow a tomato plant. Alex’s plant is 28.4 cm, Jacob’s plant is 35.8 cm, Sofia’s plant is 32.4 cm and Andeep’s plant is 24.4 cm. Work out the mean height of the plants. cm

Q4.
An isosceles triangle has one angle of $$43.6^\circ$$ and another angle of $$92.8^\circ$$. Three students work out the third angle. Who is correct?

Q5.
The starting line is at 0. If you twist this combination clock anticlockwise 50, which number will the combination lock starting line be on?

Q6.
A combination lock starts at 0. It is twisted 23 anticlockwise, then 78 clockwise, then 80 anticlockwise and then 13 clockwise. Which number is the combination lock now indicating?