S3_General_Chapter3_TJ_Decimals_Numbers

S3_General_Chapter3_TJ_Decimals_Numbers - Decimal Numbers...

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Unformatted text preview: Decimal Numbers General Working with decimals Decimal Scales Rounding to 1 decimal place Addition and Subtraction Multiplying by a single digit Dividing by a single digit Multiplying by 10, 100, 1000 Dividing by 10, 100, 1000 Converting length Converting Volume Converting Weight 13 Feb 2012 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Starter Questions General www.mathsrevision.com 3 ? 1. Find t h e m is s ing va lue = 4 20 2 . C a lc ula t e 2 0 % o f 6 0 0 0 3 . W h a t is t h e ne x t t h r e e num b e r s in t h e s e q ue nc e 9 , 15 , 2 1, 2 7 , ...., ...., .... 4 . Ro und 7 2 t o t h e ne a r e s t 10 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals Learning Intention Success Criteria 1. Understand what a decimal number is. www.mathsrevision.com 1. To explain what a decimal number is. Write down the decimal number represented by a fraction diagram. 2. Write down the decimal number represented by a fraction diagram. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. means ten Decimal Numbers General Writing Decimals www.mathsrevision.com 0 .1 10 1.1 Imagine, 1 bar of chocolate as our UNIT of measure. 0 0.1 0.6 13 Feb 2012 When you take a single unit and divide it into 10 bits, what we then have are decimal fractions of a whole number 0.2 0.7 0.3 0.8 0.4 0.9 0.5 1.0 1 ( o f 1 b ar ) 10 or 0.1 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals Example : Write down the decimal number represented by the shaded area. 0 .3 3 " wh ic h m e ans 3 t e nt h s = " 10 www.mathsrevision.com (a) (b) 0 .5 " wh ic h m e ans 5 t e nt h s = 5 1 = " 10 2 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals Example : Write down the decimal number represented by the diagram. (b) www.mathsrevision.com (a) (c) (d) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals www.mathsrevision.com We can take one bit of the chocolate bar and split it into 10 1st Decimal place 0.1 0.01 2nd Decimal place 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals Example : Write down the decimal number represented by the diagram. (b) www.mathsrevision.com (a) (c) (d) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Writing Decimals www.mathsrevision.com Now try Exercise 1 Ch3 (page 27) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. Find t h e p e r im e t e r o f t h e s h a p e www.mathsrevision.com 3cm 2 . C a lc ula t e 3 0 % o f 9 0 0 3 . Find t h e a r e a o f t h e r e c t a ng le 6 c m in le ng t h b y 4 c m wid e . 4 . N a m e t h e s h a p e . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Reading Scales Learning Intention Success Criteria 1. Understand the steps to work out any decimal scale to 2 decimal places. 2. Solve problems by working out scales. www.mathsrevision.com 1. To explain the steps to read decimal scales. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General 0.1 0.2 0.3 0.4 0.5 Reading Scales 0.7 0.8 0.9 0.6 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 www.mathsrevision.com 0.0 1.0cm 2.0cm You must work out what number goes next to each mark on the scale. Step 1: Count the number of steps between numbers. In this case it takes 10 steps to get from 0.0 to 1.0cm. Step 2: Do the division by the step number " the difference between numbers" 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 1.0 10 = 0.1cm Decimal Numbers General Reading Scales Find the values of the arrows www.mathsrevision.com 8 9cm 10cm 8.3 Step 1: 8.8 9.5 9.8 Count the number of steps between numbers. In this case it takes 10 steps to get from 8 to 9cm. Step 2: 98=1 Do the division by the step number 10 " the difference between numbers" 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 1 10 = 0.1cm Decimal Numbers General Reading Harder Scales 3.02 3.04 3.06 3.08 3.01 3.03 3.05 3.07 3.09 3.12 3.14 3.16 3.18 3.11 3.13 3.15 3.17 3.19 www.mathsrevision.com 3.00cm 3.10cm 3.20cm You must work out what number goes next to each mark on the scale. Step 1: Count the number of steps between numbers. In this case it takes 10 steps to get from 3.00cm to 3.10cm. Step 2: Do the division " the difference between numbers" by the step number 0.1 10 = 0.01cm 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Reading Harder Scales www.mathsrevision.com 12.00cm 12.10cm 12.20cm 12.03 Step 1: 12.08 12.14 12.19 Count the number of steps between numbers. In this case it takes 10 steps to get from 12.00cm to 12.10cm. Step 2: Do the division by the step number " the difference between numbers" 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 0.1 10 = 0.01cm Decimal Numbers General Reading Scales www.mathsrevision.com Now try Exercise 2 Ch3 (page 29) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. N a m e t h e p a r t o f t h e c ir c le . www.mathsrevision.com 2 . C a lc ula t e 6 0 % o f 3 0 0 3 . I f I a m f a c ing N o r t h a nd t ur n 9 0 o c lo c k wis e , wh ic h d ir e c t io n a m I f a c ing 4 . Ho w m a ny line s o f s y m m e t r y h a s t h e s h a p e . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Rounding to 1 decimal place Learning Intention Success Criteria 1. To be able to round to 1 decimal place. www.mathsrevision.com 1. To show how to round to 1 decimal place by looking at the digit at the 2nd decimal place. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Rounding to 1 decimal place Find the values of the arrows. www.mathsrevision.com 8.2cm 8.24 8.28 Is 8.24 nearer to 8.2 or 8.3 ? Is 8.28 nearer to 8.2 or 8.3 ? Is 8.35 nearer to 8.2 or 8.3 ? 13 Feb 2012 8.3cm 8.4cm 8.35 8.2 8.3 Neither Created by Mr. Lafferty Maths Dept. Decimal Numbers General Rounding to 1 decimal place The rules for rounding to 1 decimal place are: www.mathsrevision.com If the 2nd decimal place is 0,1,2,3,4 leave 1st decimal place as it is If the 2nd decimal place is 5,6,7,8,9 add 1 to 1st decimal place Example : (a) 9.04 Round the numbers to 1 decimal place (b) (e) 18.08 102.09 (f) (c) 2636.55 24.25 (d) 12.73 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Rounding to 1 decimal place www.mathsrevision.com Now try Exercise 3 Ch3 (page 30) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. 13 x 7 www.mathsrevision.com 2 . C a lc ula t e 2 3 x 10 3 3 . o f 8 0 4 4 . Find t h e m is s ing num b e r 1, 1, 2 , 3 , 5 , 8 , ...., ...., .... Created by Mr. Lafferty Maths Dept. 13 Feb 2012 Decimal Numbers General Add and Subtract Decimals Learning Intention Success Criteria 1. Understand that you must keep the decimal point lined up when adding and subtracting decimal numbers. 2. Show all working. www.mathsrevision.com 1. To show how to add and subtract decimal numbers. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Add and Subtract Decimals www.mathsrevision.com When you add or subtract decimal numbers, it is important to lineup the decimal points. Example 1 : Calculate 7.8 + 0.92 7 .8 0 +0 .9 2 8 .7 2 1 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Add and Subtract Decimals www.mathsrevision.com When you add or subtract decimal numbers, it is important to lineup the decimal points. Example 1 : Calculate 4 0.84 4 . 0 0 0 . 8 4 3 1 6 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 3 9 1 1 Decimal Numbers General Add and Subtract Decimals Example 1 : Find the value x cm and y cm y cm 3.91cm 3.25cm y cm x cm 2.1cm 2.2cm www.mathsrevision.com x cm 2 . 10 3 . 2 5 + 3 .9 1 2 .2 0 6 .0 1 1. 0 5 1 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Add and Subtract Decimals www.mathsrevision.com Now try Exercise 4 Ch3 (page 32) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. 3 2 0 8 www.mathsrevision.com 2 . C a lc ula t e 2 0 % o f 3 6 0 3 . C a lc ula t e 7 2 5 8 4 . Ca lc ula t e t h e va lue o f t h e m is s ing a ng le . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 57o Decimal Numbers General Multiply a decimal by a single digit Learning Intention Success Criteria 1. Understand how to multiply and divide a decimal number by a single Digit. 2. Show appropriate working. www.mathsrevision.com 1. To explain how to multiply and divide a decimal number by a single Digit. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiply a decimal by a single digit www.mathsrevision.com When multiplying by a single digit the decimal point always stays in line. Example : Calculate 23.68 x 7 2 3 .6 8 x 7 16 5 .7 6 2 4 5 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiply a decimal by a single digit www.mathsrevision.com Example : Copy and complete. 3.5 x 6 18.43 x 4 76.97 x 6 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiply a decimal by a single digit www.mathsrevision.com Now try Ex 5 Ch3 (page 34) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. 4 0 0 8 0 www.mathsrevision.com 2 . C a lc ula t e 3 0 % o f 3 6 0 3 . C a lc ula t e 17 2 4 9 4 . Ca lc ula t e t h e va lue o f t h e m is s ing a ng le . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 45o Decimal Numbers General Division by a Single Digit Learning Intention Success Criteria 1. Understand how to divide a decimal number by a single Digit. www.mathsrevision.com 1. To explain how to divide a decimal number by a single Digit. 2. Show appropriate working. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Division by a Single Digit www.mathsrevision.com When dividing by a single digit the decimal point always stays in line. Example : Calculate 17.16 6 2 . 8 6 1 5 3 6 1 7 . 1 6 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Division by a Single Digit www.mathsrevision.com Example : Copy and complete. 6.52 2 95.05 5 204.84 6 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Division by a Single Digit www.mathsrevision.com Now try Ex 6 Ch3 (page 35) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. 4 6 x 3 www.mathsrevision.com 2 . Find t h e m is s ing va lue 35 ? = 5 0 10 1 3 . o f 4 9 0 7 4 . Ca lc ula t e t h e va lue o f t h e m is s ing a ng le . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 40 o Decimal Numbers General Multiplying & Dividing by 10, 100, 1000 Learning Intention Success Criteria 1. Understand the simple rules to multiply decimal numbers. 2. Be able do calculations. www.mathsrevision.com 1. To understand how to multiply decimal numbers by 10, 100, 1000. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiplying by 10, 100, 1000 www.mathsrevision.com To multiply a decimal number by 10, Simply move point 1 place to the right: e.g. 2.55 x 10 = 25.5 point is moved 1 place to right To multiply a decimal number by 100, Simply move point 2 places to the right: e.g. 13 Feb 2012 1.02 x 100 = 102.0 point is moved 2 places to right Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiplying by 10, 100, 1000 www.mathsrevision.com To multiply a decimal number by 1000, Simply move point 3 places to the right: e.g. 34.567 x 1000 = 34 567 point is moved 3 place to right 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiplying by 10, 100, 1000 Example : Multiply 1.8574 by 10, 100, 1000 www.mathsrevision.com 10 x 1.8574 = 100 x 1.8574 = 1000 x 1.8574 = 18.574 185.74 1857.4 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiplying & Dividing y 10, 100, 1000 www.mathsrevision.com Now try Ex 7 Ch3 (page 37) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General 1. 6 5 x 3 0 www.mathsrevision.com 2 . Find t h e m is s ing va lue 25 ? = 200 8 1 3 . o f 6 3 2 .1 7 4 . C a lc ula t e t h e va lue o f t h e m is s ing a ng le . 13 Feb 2012 Created by Mr. Lafferty Maths Dept. 118 o Decimal Numbers General Multiplying & Dividing by 10, 100, 1000 Learning Intention Success Criteria 1. Understand the simple rules to divide decimal numbers. 2. Be able do calculations. www.mathsrevision.com 1. To understand how to divide decimal numbers by 10, 100, 1000. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Dividing by 10, 100, 1000 www.mathsrevision.com To divide a decimal number by 10, Simply move point 1 place to the left: e.g. 89 10 = 8.9 point is moved 1 place to left To divide a decimal number by 100, Simply move point 2 places to the left: e.g. 13 Feb 2012 199 100 = 1.99 point is moved 2 places to left Created by Mr. Lafferty Maths Dept. Decimal Numbers General Dividing by 10, 100, 1000 www.mathsrevision.com To divide a decimal number by 1000, Simply move point 3 places to the left: e.g. 35 837 1000 = 35.837 point is moved 3 places to the left 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Dividing by 10, 100, 1000 Example : Divide 45 024 by 10, 100, 1000 www.mathsrevision.com 45 024 10 = 45 024 100 = 45 024 1000 = 4502.4 450.24 45.024 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Decimal Numbers General Multiplying & Dividing y 10, 100, 1000 www.mathsrevision.com Now try Ex 8 Ch3 (page 38) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General Q1. Solve the equation below Find two numbers that multiply to give 18 and subtract to give 3. Explain why the average of the numbers below is 7 2,8,8,10 www.mathsrevision.com Q2. 2 x + 16 = 2 8 Q3. Q4. 13 Feb 2012 True or false 6 0 % o f 2 4 0 = 14 4 Created by Mr. Lafferty Maths Dept. Units of Length General Learning Intention Success Criteria 1. To know the 4 units of length. 2. Be able to convert between them. www.mathsrevision.com 1. To explain the 4 metric units of length and how to convert between them. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Units of Length General The 4 units of length are : The metre : This is the standard unit of length and is approximately the distance from your nose th 100 to the end of your outstretched arm. The centimetre : The Millimetre : 1000 The Kilometre : 13 Feb 2012 www.mathsrevision.com 1 This is of a metre and is about 10 0 the width of your pinky nail. 1 This is of a centimetre and is 10 about the width of a sewing needle. 10 0 0 This is metres and is about the the length of 10 football pitches. Created by Mr. Lafferty Maths Dept. General Units of Length Converting Measurements 1000 Kilometres (km) metres (m) www.mathsrevision.com 100 1000 100 10 centimetres (cm) 10 13 Feb 2012 Created by Mr. Lafferty Maths Dept. millimetres (mm) General Units of Length Converting Measurements Examples www.mathsrevision.com Convert 2m to cm : Convert 4km to m : Convert 34cm to mm : Convert 50cm to m : 2 x 100 = 200 cm 4 x 1000 = 4000 m 34 x 10 = 340 mm 50 100 = 0.5 m 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Units of Length Converting Measurements General www.mathsrevision.com Extension Booklet Ex9E Now try Ch3 (page 8) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General Q1. Solve the equation below www.mathsrevision.com Q2. Find two numbers that multiply to give 14 and subtract to give 5. Explain why the average of the numbers below is 9 2,8,8,10,17 2 x + 5 = 11 Q3. Q4. 13 Feb 2012 True or false 4 0 % o f 3 2 0 = 12 8 Created by Mr. Lafferty Maths Dept. Units of Volume General Learning Intention Success Criteria 1. To know the 3 units of volume. 2. Be able to convert between them. www.mathsrevision.com 1. To explain the 3 metric units of volume and how to convert between them. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. General 1 litre = 1000ml Units of Volume Converting Measurements 100 1 litre = 1000cm3 www.mathsrevision.com Litres (l) Centilitres (cl) 10 100 10 13 Feb 2012 Millilitres (ml) Created by Mr. Lafferty Maths Dept. 1 ml = 1cm3 General Units of Volume Converting Measurements Examples www.mathsrevision.com Convert 4 l to cl : Convert 500 cl to l : Convert 3 cl to ml : Convert 2 l to ml : 4 x 100 = 400 cl 500 100 = 0.5 l 3 x 10 = 30 ml 2 x 1000 = 2000 ml 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Units of Volume Converting Measurements General www.mathsrevision.com Extension Booklet Ex10E Now try Ch3 (page 10) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Starter Questions General Q1. Solve the equation below www.mathsrevision.com 4 x - 7 = 17 Q2. Find two numbers that multiply to give 2 and subtract to give 1. True or false Q3. 2 0 % o f 4 0 = 2 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Units of Weight General Learning Intention Success Criteria 1. To know the 4 units of weight. 2. Be able to convert between them. www.mathsrevision.com 1. To explain the 4 metric units of weight and how to convert between them. 13 Feb 2012 Created by Mr. Lafferty Maths Dept. General Units of Weight Converting Measurements 1000 Tonnes (t) Kilogram (kg) www.mathsrevision.com 1000 1000 1000 1000 Gram (g) 1000 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Milligrams (mg) General Units of Weight Converting Measurements Examples www.mathsrevision.com Convert 4 t to kg : Convert 500 mg to g : Convert 3 kg to g : Convert 2000000 g to t : 4 x 1000 = 4000 kg 500 1000 = 0.5 g 3 x 1000 = 3000 g 2000000 1000 1000 = 2 t 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Units of Weight Converting Measurements General www.mathsrevision.com Extension Booklet Ex11E Now try Ch3 (page 12) 13 Feb 2012 Created by Mr. Lafferty Maths Dept. ...
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