Overestimating vs underestimating | Maths | Quizalize & Oak National Academy

Starter quiz

__________ are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first non-zero digit.
- Estimated numbers
- Important number
- Real numbers
- Significant figures ✓
Which of the following are good, quick estimate calculations for 577 ÷ 19.57?
- 580 ÷ 20 ✓
- 600 ÷ 20 ✓
- 580 ÷ 19.5
- 600 ÷ 19.5
Which of the following are a correct estimate for ${11.239\times3.12}\over{0.488}$ ?
- ${11\times3} \over {0.5}$ $= 16.5$
- ${10\times3} \over {0.5}$ $= 15$
- ${11\times3} \over {0.5}$ $= 66$ ✓
- ${10\times3} \over {0.5}$ $= 60$ ✓
Match each calculation to its approximate answer.
- $\frac{9.8}{0.120}$
  
  ⇔
  
  $100$ ✓
- $\frac{98}{0.111}$
  
  ⇔
  
  $1000$ ✓
- $\frac{9.8}{0.2003}$
  
  ⇔
  
  $50$ ✓
- $\frac{980}{0.199}$
  
  ⇔
  
  $5000$ ✓
- $\frac{980}{0.498}$
  
  ⇔
  
  $2000$ ✓
- $\frac{9}{0.51}$
  
  ⇔
  
  $18$ ✓
A square plot of grass has a length of 7.88 m (2 d.p). Select the correct estimate for the area of the square grass plot.
- 8 × 8 = 64 m² ✓
- 8 × 8 = 16 m²
- 8 + 8 + 8 + 8 = 32 m²
- 8 + 8 + 8 + 8 = 32 m
Izzy thinks of a number. Truncated to 1 s.f., it is 500. Rounded to the nearest 50, it is 600. It is multiple of 5 and a palindrome . All of its digits are prime numbers. Izzy's number is ______
- '575' ✓

Exit quiz

An __________ is an estimate for a calculation which is greater than the exact answer.
- average
- impossible number
- integer
- overestimate ✓
- underestimate
An __________ is an estimate for a calculation which is less than the exact answer.
- average
- impossible number
- integer
- overestimate
- underestimate ✓
Match each calculation with a calculation that gives its overestimate.
- 38.48 + 29.84
  
  ⇔
  
  $\approx$ 40 + 30 ✓
- 18.983 + 19.303
  
  ⇔
  
  $\approx$ 20 + 20 ✓
- 45.9348 + 39.84
  
  ⇔
  
  $\approx$ 50 + 40 ✓
- 8.548 + 2.84 + 19.203
  
  ⇔
  
  $\approx$ 9 + 3 + 20 ✓
- 38.48² + 29.84
  
  ⇔
  
  $\approx$ 40² + 30 ✓
Match the following calculations which give an overestimated area.
- $\approx \text{ }$ 8 × 8
  
  ⇔
  
  Area of a square with lengths 7.89 m ✓
- $\approx \text{ }$ 8 + 8 + 8 + 8
  
  ⇔
  
  Perimeter of a square with lengths 7.89 m ✓
- $\approx\text{ }$ 5 × 5
  
  ⇔
  
  Area of a square with lengths 4.67 m ✓
- $\approx \text{ }$ 5 + 5 + 5 + 5
  
  ⇔
  
  Perimeter of a square with lengths 4.67 m ✓
- $\approx\text{ }$ 0.5 × 0.5
  
  ⇔
  
  Area of a square with lengths 0.498 m ✓
- $\approx\text{ }$ 0.5 + 0.5 + 0.5 + 0.5
  
  ⇔
  
  Perimeter of a square with lengths 0.498 m ✓
Match which calculations are an overestimate, underestimate or hard to tell.
- Overestimate
  
  ⇔
  
  $\frac{899}{4.40+6.35}\approx\frac{900}{4+6}$ ✓
- Underestimate
  
  ⇔
  
  $\frac{712}{8.98+9.45}\approx\frac{700}{10+10}$ ✓
- Hard to tell
  
  ⇔
  
  $\frac{37.4}{4.49+6.41}\approx\frac{40}{5+6}$ ✓
Match which calculations are an overestimate, underestimate or hard to tell.
- Overestimate
  
  ⇔
  
  $\frac{59-42}{3.67+1.23}\approx\frac{60-40}{3+1}$ ✓
- Underestimate
  
  ⇔
  
  $\frac{59-42}{3.67+1.23}\approx\frac{55-45}{4+2}$ ✓
- Hard to tell
  
  ⇔
  
  $\frac{59-42}{3.67+1.23}\approx\frac{60-50}{4+2}$ ✓

Worksheet

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Lesson Details

Key learning points

When multiplying or adding, using a value which has been rounded up results in an overestimate.
When dividing or subtracting, using a value which has been rounded up results in an under or overestimate.
Calculations using rounding or truncating will give an over or underestimate.
By careful consideration of the calculation, it is possible to tell if an answer is an over or underestimate.

Common misconception

When subtracting or dividing, the largest value is found by subtracting or dividing the largest rounded number by the largest rounded divisor or additive inverse.

Drawing a number line to show the subtraction of the smallest number will help students see how to achieve an overestimate or underestimate. When using division, reiterating the division of number is the same as multiplying by its reciprocal.

Keywords

Overestimate - An overestimate is an estimate for a calculation which is greater than the exact answer.
Underestimate - An underestimate is an estimate for a calculation which is less than the exact answer.