Calculate upper and lower bounds. Grade 7 Upper and Lower Bounds Calculate upper and lower bounds. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk
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: 17 - 19 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
Key Vocabulary Error Interval 1 Significant Figure Limits of Accuracy Upper Bound Lower Bound
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 + 0.05 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
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
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
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
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 = 0.0115 Lower Bound = 0.0105 Upper Bound = 6050 Lower Bound = 5950 Upper Bound = 23.555 Lower Bound = 23.545 Upper Bound = 0.825 Lower Bound = 0.815
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
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 = 134.78cm²
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
Exam Questions – Specimen Papers
Exam Questions – Specimen Papers
Exam Questions – Specimen Papers
Exam Questions – Specimen Papers [5 marks]
Exam Questions – Specimen Papers [4 marks]
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
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
Exam Questions – Specimen Papers Student Sheet 3