1. Calculate upper and lower bounds.
Grade 7
Upper and Lower Bounds
Calculate upper and lower bounds.
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Calculate upper and lower bounds
Grade 7
Prior Knowledge
Rounding
Inequality signs
Duration
Suggested time to cover this objective is 50 minutes.
Resources
Print slides:
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
How to find upper and lower bounds given different degrees of accuracy.
Given students slide 17 printed. Show students slide 4 and discuss how to find upper and lower bounds when quantities have been rounded to various degrees of accuracy. Students to copy information into their table. 10
Find upper and lower bounds of single numbers
Show slide 5 with examples when numbers have been rounded to significant figures and then slide 6 decimal places. Students to then complete practice questions on slide 17. Use slide 8 to review answers. 15
Find upper and lower bounds of calculations
Give students slide 18 printed. Show slide 9 and discuss each different operation in particular division. Students to attempt the two questions on their slide 18. May need support with formulae.
Calculating upper and lower bounds in exam questions (from specimen papers)
Give students slide 19. This includes 5 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated.
Next Steps
Assessment
PLC/Reformed Specification/Target 7/Number/Upper and Lower Bounds

3. Key Vocabulary
Error Interval 1 Significant Figure Limits of Accuracy Upper Bound Lower Bound

4. Quantity given to the nearest...
Limits of Accuracy
Nothing that is measured can be 100% accurate. Whether you are using a ruler, a protractor, a thermometer or a set of kitchen scales, there will always be an error of ± half the unit of accuracy used.
Quantity given to the nearest...
Minimum value
Maximum Value
0.1 (to 1 decimal place)
Given value – 0.05
Given value
Whole Number
Given value – 0.5
Given value + 0.5
Ten
Given value – 5
Given value + 5
Hundred
Given value – 50
Given value + 50
Thousand
Given value – 500
Given value + 500

5. Upper & Lower Bounds
The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value.
(a) 23
(b) 0.56
(c) 830
(d) 200
Upper Bound = 23.5
Lower Bound = 22.5
Upper Bound =0.565
Lower Bound = 0.555
Upper Bound = 835
Lower Bound = 825
Upper Bound = 205
Lower Bound = 195

6. Upper & Lower Bounds
The following numbers have been rounded to two decimal places. Find the upper and lower bounds for each value.
(a) 6.17
(b) 0.40
Upper Bound = 6.175
Lower Bound = 6.165
Upper Bound =0.405
Lower Bound = 0.395

7. Now you try:
The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value.
(a) 78
(b) 0.91
(c) 0.011
(d) 6000
The following numbers have been rounded to two
decimal places. Find the upper and lower bounds for each
value.
(e) 23.55
(f) 0.82

8. Now you try:
The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value.
(a) 78
(b) 0.91
(c) 0.011
(d) 6000
The following numbers have been rounded to two
decimal places. Find the upper and lower bounds for each
value.
(e) 23.55
(f) 0.82
Upper Bound = 78.5
Lower Bound = 77.5
Upper Bound =0.915
Lower Bound = 0.905
Upper Bound =
Lower Bound =
Upper Bound = 6050
Lower Bound = 5950
Upper Bound =
Lower Bound =
Upper Bound = 0.825
Lower Bound = 0.815

9. Calculations Operation Minimum value Maximum Value Addition LB + LB
UB + UB
Subtraction
LB - UB
UB - LB
Multiplication
LB x LB
UB x UB
Division
LB/UB
UB/LB

10. Reason and Explain
The radius of a circle is 6.5cm to one decimal place.
(a) Calculate the minimum perimeter of the circle.
(b) Calculate the maximum area of the circle.
Upper Bound 6.55cm Lower Bound 6.45cm
(a) Minimum diameter = 2 x 6.45cm = 12.9cm
Circumference = π x 12.9 = 40.53cm
Minimum perimeter = 40.53cm
(b) Maximum radius = 6.55cm
Maximum Area = π x 6.55² = cm²

11. Reason and Explain
A car is driving a distance of 160 miles correct to the nearest 10 miles. The car is travelling for 4 hours correct to the nearest hour.
Calculate the maximum speed of the car.
Distance:
Upper Bound = 165 miles Lower Bound = 155 miles
Time:
Upper Bound = 4.5 hours Lower Bound = 3.5 hours
Speed = Distance ÷ Time
With division, we get the largest answer when we divide
the biggest number by the smallest number.
Maximum speed = 165 ÷ 3.5 = 47.1m.p.h

12. Exam Questions – Specimen Papers

13. Exam Questions – Specimen Papers

14. Exam Questions – Specimen Papers

15. Exam Questions – Specimen Papers
[5 marks]

16. Exam Questions – Specimen Papers
[4 marks]

17. Quantity given to the nearest...
Limits of Accuracy
Quantity given to the nearest...
Minimum value
Maximum Value
0.1 (to 1 decimal place)
Whole Number
Ten
Hundred
Thousand
The following numbers have been rounded to two significant figures.
Find the upper and lower bounds for each value. 23
0.56
830
200
PRACTICE
The following numbers have been rounded to two significant figures.
Find the upper and lower bounds for each value.
(a) 78
(b) 0.91
(c) 0.011
(d) 6000
The following numbers have been rounded to two decimal places.
(e) 23.55
(f) 0.82
EXAMPLES
The following numbers have been rounded to two decimal places.
Find the upper and lower bounds for each value.
6.17
0.40
Student Sheet 1

18. Using bounds in Calculations
Operation
Minimum value
Maximum Value
Addition
Subtraction
Multiplication
Division
The radius of a circle is 6.5cm to one decimal place.
(a) Calculate the minimum perimeter of the circle.
(b) Calculate the maximum area of the circle.
A car is driving a distance of 160 miles correct to the nearest 10 miles. The car is travelling for 4 hours correct to the nearest hour.
Calculate the maximum speed of the car.
Student Sheet 2

19. Exam Questions – Specimen Papers
Student Sheet 3