Mighty Maths. More Accomplishments. MathematicsKim. With. Master Mathematician BOOK 2. for 8-10 year olds

Transcription

1 Mighty Maths for 8- year olds Master Mathematician BOOK 2 More Accomplishments With MathematicsKim Freeman

2 Mighty Maths for8-year olds Master Mathematician BOOK 2 More Accomplishments With MathematicsKim Freeman

3 Mighty Maths for Mighty Maths for 8- year olds - Master Mathematician Book 2 More Accomplishments with Mathematics Author, K. Freeman ebook published in New Zealand in 2011 by: Mahobe Resources (NZ) Ltd P.O. Box Newmarket, Auckland New Zealand. Mahobe Resources (NZ) Ltd. ISBN Print Production by Imago Print Productions (F.E.) Pte. Ltd., Singapore. Visit our website: 2

4 HOW CAN YOU HELP YOUR CHILD IN MATHEMATICS? As you progress through the school years, mathematics becomes slightly more complex but even more fascinating. There are many new concepts to learn, however being able to master the basics is still the key to developing confidence and being able to progress further. This orange Mighty Maths series, Master Mathematician, introduces a number of new concepts such as adding and subtracting larger numbers, arithmetic order of operation and integers. Other topics such as number, decimals and fractions are expanded upon. The work is progressively more challenging and new concepts are introduced in each book at various points. To help reinforce mathematical skills as well as to maintain motivation, the same type of question is asked in different ways and contexts. Don t worry if your child cannot understand one of the concepts. Quite often that same concept will be introduced in a different way later on in the book. If your child becomes comfortable with a particular way of solving a problem then let them carry on using this method. A common question that is asked of mathematics teachers is whether a child should use a calculator at this stage of their learning. It is important that they learn and understand each basic concept and the underlying principles. Once that is achieved then there is a case for using the calculator so that they can further explore ways of solving the same problem and therefore increasing their understanding a lot quicker. This specific book covers number place value and relationships, fractions and decimals, graphs and handling data, perimeter and area, money calculations, angles, multiplication strategies, division and averages. For best results: Go over the pages that your child will work on and familiarise yourself with the exercises. Make sure your children understand the different concepts. Try and explain what is happening on each of the pages. Encourage your children to write neatly. Many errors in solving mathematics problems can be traced back to sloppy number writing. Provide help immediately when needed. Mathematics is a subject in which everything builds upon what has been previously learned. For example, a failure to understand fractions and decimals will lead to problems later with percentages. We hope that you and your children have fun with Mighty Maths. At Mahobe, we certainly had fun putting it all together and trialling it with 8- year olds. 3

5 What is found in this book? In this book you look at: NUMBER RELATIONSHIPS =2ø00+4ø0+1ø+5ø1 FRACTIONS AND DECIMALS MEASUREMENT =4 +0= Kg DATA AND GRAPHS ANGLES MULTIPLICATION = 2 books Week Master Mathematician 4 Mahobe Resources (NZ) Ltd

6 PLACE VALUE Write each as digits in the place-value table. a. b. a. TH H T U c. d. e. Five thousand, nine hundred and twenty seven. 9x00+3x0+2x1 27 hundreds + 7 tens + 3 units b. c. d. e. Write these numbers as digits and list them in decreasing order: one thousand two hundred and eighteen, four hundred and six, eighty nine, five hundred and thirty, two thousand four hundred and forty four. Write these as numbers Mahobe Resources (NZ) Ltd 5 Master Mathematician

7 PLACE VALUE Write each as digits in the place-value table. a. b. c. a. b. c. TH H T U Write these numbers with words. Write these as expanded numbers. =2ø00+4ø0+1ø+5ø1 Master Mathematician 6 Mahobe Resources (NZ) Ltd

8 NUMBERs Write the number that is represented at the arrow point. Round the numbers. Rounded to the nearest: ten hundred thousand Number Complete the number pyramid. The sum of any two numbers is the number directly above. Mahobe Resources (NZ) Ltd 7 Master Mathematician

9 NUMBER RELATIONSHIPS Do the additions and subtractions. Look for the relationships. Calculate the products. Look for the relationships. Calculate the products. Look for the relationships. Study the pattern. What would the shape be on the 0th card? Master Mathematician 8 Mahobe Resources (NZ) Ltd

10 UNIT CUBES How many unit cubes make up each shape? Draw how this solid would appear from three different views. Top View Top View Side View Front View Side View Front View Mahobe Resources (NZ) Ltd 9 Master Mathematician

11 ADDING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator Master Mathematician Mahobe Resources (NZ) Ltd

12 SUBTRACTING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator Mahobe Resources (NZ) Ltd 11 Master Mathematician

13 VALUE RELATIONS = = = = Find the value of each. Master Mathematician 12 Mahobe Resources (NZ) Ltd

14 FRACTIONS AND DECIMALS Some important fractions and decimals are below. Rewrite these fractions and mixed numbers as decimals Kg Mahobe Resources (NZ) Ltd 13 Master Mathematician

15 FRACTIONS & DECIMALS Write the decimal equivalents of these fractions. 02 I said get a tenth of the sugar, not a tent full of sugar! Master Mathematician 14 Mahobe Resources (NZ) Ltd

16 FRACTIONS & DECIMALS Draw a line between the decimals and the correct place on the ruler. Show where these numbers go on the number line: 7.6, 2.5, 3.7, 4.2, 1.1, 5.4, 8.3 Mahobe Resources (NZ) Ltd 15 Master Mathematician

17 Which is bigger? Master Mathematician 16 Mahobe Resources (NZ) Ltd

18 Brad has an orchard which has 80 fruit trees. Two eighths of the trees are apple trees, one quarter of them are nectarine trees, four sixteenths of them are pear trees and the rest are plum trees. How many of each tree does Brad have? Apple:... Nectarine:... Pear Trees:... Plum Trees:... Tom and Kate collect apples from Brad s orchard. On the way home Tom eats one third of the apples. If Tom ate 4 apples, how many were picked? Tom and Kate picked... apples David and Victoria purchase an aquarium for their new home. One sixth of the fish in the aquarium are Black Tails. Two sixths of the fish in the aquarium are Blue Fins. The rest of the fish are Goldfish. David counts 3 black tails. Therefore there are: Maddox took 5 oranges and cut them into quarters. How many quarters are there?... Blue Fins... Goldfish... quarters Suri s fruit punch contains one and three quarter litres of apple juice, two eights of a litre of lime juice and four and a quarter litres of orange juice. In one particularly hot day, Suri drinks 3 litres of the fruit punch. She then adds four and a quarter litres of mango juice. How many litres of fruit punch does she now have? Total =... Litres Mahobe Resources (NZ) Ltd 17 Master Mathematician

19 DECIMALS A decimal number contains a decimal point. The whole part, four. The fractional part, six tenths. This is read as four point six. Four whole parts. Write the numbers that each diagram represents Master Mathematician 18 Mahobe Resources (NZ) Ltd

20 DECIMALS & MIXED NUMBERS A decimal number can also be written as a mixed number (a number with a fraction) or expressed in words. Decimal Number Mixed Number Description Three and two tenths Seven and five tenths Six and eight tenths Eight and nine tenths Mahobe Resources (NZ) Ltd 19 Master Mathematician

21 DECIMALS Give the number that is represented by each of the diagrams. Master Mathematician 20 Mahobe Resources (NZ) Ltd

22 Hundreds Tens Ones Tenths DECIMALS Write the numbers into the place value chart. three and seven tenths eighteen and two tenths twenty four and one tenths fifty six and three tenths forty seven and nine tenths one hundred and twelve and four tenths eight hundred and sixty five and eight tenths three hundred and six tenths seven hundred and ninety and seven tenths Write these numbers in decimal form. 47 Mahobe Resources (NZ) Ltd 21 Master Mathematician

23 DECIMAL & EXPANDED FORM Write each number in expanded form Rewrite these into decimal form. Master Mathematician 22 Mahobe Resources (NZ) Ltd

24 DECIMALS Draw a line to show where each number is on the number line. Below are some pairs of numbers. Circle the larger number in each pair. Mahobe Resources (NZ) Ltd 23 Master Mathematician

25 ADDING TENTHS Master Mathematician 24 Mahobe Resources (NZ) Ltd

26 HUNDRETHS When a tenth is divided times each block represents a hundreth. Shade the diagrams to represent the given number. Mahobe Resources (NZ) Ltd 25 Master Mathematician

27 HUNDREDTHS The first two fractions (below) are equal. They do not equal the last. Write each of these as: 1. Decimal numbers. 2. Expanded form. 3. Mixed numbers. Decimal Expanded form Mixed number Decimal: Expanded form: Mixed number: Master Mathematician 26 Mahobe Resources (NZ) Ltd

28 Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: Mahobe Resources (NZ) Ltd 27 Master Mathematician

29 DECIMALS Decimals come between whole numbers. three hundredths seven tenths Each digit to the right becomes ten times smaller. This also means that each digit to the left becomes ten times bigger. hundredths tenths units (ones) tens hundreds The in is: six tenths The in is: The in is: The in is: The in is: The in is: The in is: Master Mathematician 28 Mahobe Resources (NZ) Ltd

30 Complete these sums. Complete the sums. Complete the table. Fraction Decimal Mahobe Resources (NZ) Ltd 29 Master Mathematician

31 DECIMALS Write these numbers onto the place value chart. Five and twenty three hundredths Twenty four and sixteen hundredths Thirty six and twelve hundredths Eighteen and fifty one hundredths Ninety nine and ten hundredths Eighty two and four hundredths Tens Units Tenths Hundredths Locate each of the numbers on the number line. All the numbers above should be located on the number line. Use less than (<) or greater then (>) to make these statements true. Master Mathematician 30 Mahobe Resources (NZ) Ltd

32 ADDING DECIMALS =4 +0= Now add these. Write the numbers underneath each other so that the decimal points line up. Mahobe Resources (NZ) Ltd 31 Master Mathematician

33 DECIMAL ADDITION Rewrite these numbers in columns with the decimal points in line. Then complete the additions. Master Mathematician 32 Mahobe Resources (NZ) Ltd

34 DECIMAL SUBTRACTION Rewrite these numbers in columns with the decimal points in line. Then complete the subtraction. Mahobe Resources (NZ) Ltd 33 Master Mathematician

35 DECIMAL TEST Write the number that is represented by the shading. Complete the table. Decimal Number Mixed Number Description Three and six tenths One hundred and twenty eight hundreths Master Mathematician 34 Mahobe Resources (NZ) Ltd

36 Write the value of the 5 in each of these numbers. Locate each number on the number line. Use a greater than (>), equals (=), or less than (<), to make each a true statement. Add Mahobe Resources (NZ) Ltd 35 Master Mathematician

37 Add Rewrite these mixed numbers as decimal numbers. Rewrite these decimal numbers as mixed numbers. Subtract Hair stylist Terrence charges $ for a style, colour and haircut. Josette pays with two $0 notes. How much change should she get? Add up all the correct answers from the last 3 pages. Put your score in the box. 45 and above: A+ student 40 and above: A student Always strive to be an A+ student. Find out where you went wrong. If needed rub out your answers and try the test again another day. Master Mathematician 36 Mahobe Resources (NZ) Ltd

38 GRAPHS The graph shows the number of books that Katie read last week. The symbol represents 1 book. Mo Tu We Th Fr Sa Su Katie read the least number of books on... Katie read the most books on... Katie read a total of 11 books on... &... Katie read... more book on Saturday than on Friday. Katie did a survey on children s favourite colours. Below are her survey results. Write underneath how many chose each colour. = 3 children Blue Purple Yellow Black White Green Red Mahobe Resources (NZ) Ltd 37 Master Mathematician

39 Complete the graph by drawing a to represent 2 apples. 6 apples apples 5 apples 21 apples If an apple costs $0.50 then six apples cost $ If an apple costs $0.50 then 21 apples cost $ Give the total cost of apples in the graph. $ $ $ $ $ 6 apples apples 5 apples 21 apples Number of Stickers Collected Class Sticker Collection Mrs Robert s class. Mr Daniel s class. Ms Lee s class. Mr Scott s class. Which class has collected the most stickers? Which teacher does not give out many stickers? Mr Daniel s class has Altogether there were more stickers than Mrs Roberts class. stickers collected. Master Mathematician 38 Mahobe Resources (NZ) Ltd

40 On the graph below draw columns to represent the mass of each student. Kevin 42kg Leo 46kg Daniel 55kg Brad 48kg Damon 35kg Kevin Leo Daniel Brad Damon The heaviest student is: The lightest student is: Brad is kg heaver than Leo. If all 5 boys were put on the scales then their total mass would be: A supermarket has made a pictogram of how many pies they sell in the first five months of the year. Each picture pie means 0 real pies. Fill in the missing numbers and pies. Jan Feb Mar Apr May Mahobe Resources (NZ) Ltd 39 Master Mathematician

41 HANDLING DATA When counting items use a tally chart with 1 dash recording each item. The frequency column adds up all the tally marks. Complete the frequency column then complete the graph. Favourite Soup Tally Frequency Tomato Chicken Ham and Bacon Creamed Corn Favourite Soup What was the most favoured soup? How many of the people surveyed chose Ham and Bacon? How many were surveyed? Complete the frequency column then complete the graph below. Favourite Pancake Toppings Tally Frequency Maple Syrup Honey Jelly and Whipped Cream Lemon and Sugar Favourite Pancake Topping Master Mathematician 40 Mahobe Resources (NZ) Ltd

42 We asked some students their favourite sport. The results are below. Complete the frequency column then complete the graph. Sport Athletics Football Tally Frequency Rugby Swimming Netball Cycling Kayaking How many students were surveyed? The most popular sport was How many students said netball as their favourite? Favourite Sports Mahobe Resources (NZ) Ltd 41 Master Mathematician

43 REPRESENTING DATA Each morning Amanda and Wayne take a note of the number of cars parked in a public car park. Write the number of cars parked each day. = 20 cars Mon Tue We Thu Fri Sat Sun Here are the number of books taken out of the library by Brad. Complete all the charts. Week 1 Week 2 Week 3 Week 4 Week 5 Tally Frequency Which chart do you prefer?... Why?... 5 = 2 books Week Week Master Mathematician 42 Mahobe Resources (NZ) Ltd

44 TIME 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours How many seconds in: 1 minute 15 minutes 20 minutes How many minutes in: 1 hour 1.5 hours 8 hours How many hours in: 1 day 3 days 7 days How many years in 36 months? How many months in 5 years? How many months in 52 weeks? 1 year = days or 366 days in a year. 1 year = weeks. 1 year = months. 1 month = (approximately) weeks. 1 week = days. 1 century = years. 1 millennium = years. Mahobe Resources (NZ) Ltd 43 Master Mathematician

45 UNITS OF MEASURE Join up the measures to the matching units. Day Minute Metre Centimetre Time Volume Mass Length Millilitre Kilogram Gram Litre Complete the missing numbers and units. = = = litres = = December = weeks days Today s date...(day)/...(month)/...(year) My height...(cm) =... (m)...(cm) My weight... My age... (years)... (months) I go to bed at... I get up at... I sleep for... hours... minutes Master Mathematician 44 Mahobe Resources (NZ) Ltd

46 17mm 1 7cm Mark on the ruler the following measurements. What is 1 kg in grams? Change 3 litres into ml. ml Write the real distances indicated on each map scale. Mahobe Resources (NZ) Ltd 45 Master Mathematician

47 UNITS OF MEASURE Circle all the units that measure length. kg, mm, l, g, ml, cm, m, km Kg Circle all the units that measure mass. km, m, cm, ml, g, l, mm, kg. Circle all the units that measure volume. 3 ml, g, m, mile, cm, l. What units of measure would you use to measure: The height of a tree. The amount of juice in a glass. Your mass. The distance from home to your school. The mass of an apple. The amount of water in a swimming pool. The length of a pen. A chicken s mass. Master Mathematician 46 Mahobe Resources (NZ) Ltd

48 Fill in the missing quantities. The graph below shows the variation in temperature over one day. The temperature was measured each hour starting at 1am. Temperature ( C) What was the temperature at am? When was it the hottest? 15 During which time was the temperature rising? Time (hours) There was a rainstorm during the day. When do you think that happened? Mahobe Resources (NZ) Ltd 47 Master Mathematician

49 PERIMETERS The perimeter of a shape is the total distance around the shape. To calculate the perimeter add up all the side lengths. Write down the lengths of all the sides. Perimeter = mm Perimeter = mm Fill in the missing measurements. Calculate the perimeter. Perimeter = cm Master Mathematician 48 Mahobe Resources (NZ) Ltd

50 Fill in the missing measurements. Calculate the perimeters. Means that these sides all have the same length. Perimeter = cm Perimeter = cm Mahobe Resources (NZ) Ltd 49 Master Mathematician

51 AREA How many square centimetres make up each shape? Count the squares and give the area of each shape. A B C D E F G Area D = Area A = Area E = Area B = Area F = Area C = Area G = Master Mathematician 50 Mahobe Resources (NZ) Ltd

52 The area of a rectangle is obtained by multiplying the length by the width. Make sure both are measured with the same units. Area = L W Find the areas. or = Area = L W Area = L W Area = L W Area = L W Area = L W Note: The figures on this page are not drawn to scale. Mahobe Resources (NZ) Ltd 51 Master Mathematician

53 AREA Some figures are made up of different shapes. To find the shaded area calculate the area of each separate shape, then add (or subtract) to find the total area. Area = Area 1 + Area 2 =L W + L W 6ø5 3ø2 36 cm 2 Area = L W + L W Area = Area = Master Mathematician 52 Mahobe Resources (NZ) Ltd

54 MONEY CALCULATIONS Mahobe Resources (NZ) Ltd 53 Master Mathematician

55 MONEY CALCULATIONS Subtract the following. Count and write each amount in numerals and in words. Master Mathematician 54 Mahobe Resources (NZ) Ltd

56 ANGLES This is a right angle. This is a straight angle. Quarter turn 90 Half turn 180 Three quarter turn 270 Full turn 360 Which of these angles is bigger than 90? Which of these angles is bigger than 180? Measure these angles. Mahobe Resources (NZ) Ltd 55 Master Mathematician

57 ANGLES Write the value then draw each angle. Half a right angle. One and a half right angles. Three right angles. Three and a half right angles. Write down the time and angles formed on each clock. Time Angle Master Mathematician 56 Mahobe Resources (NZ) Ltd

58 Measure the angles of the triangle then add them up. Draw each angle in the triangle. B A B C A C Measure or calculate the angles between these compass directions. N NW NE South and West W SW S SE E North and North East East and West North and South East. Measure the angles of the quadrilateral then add them up. W Z X Y Mahobe Resources (NZ) Ltd 57 Master Mathematician

59 GRID POSITIONS Master Mathematician 58 Mahobe Resources (NZ) Ltd

60 READING SCALES G J George Jennifer Mahobe Resources (NZ) Ltd 59 Master Mathematician

61 ROUNDING Master Mathematician 60 Mahobe Resources (NZ) Ltd

62 Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Actual answer = Mahobe Resources (NZ) Ltd 61 Master Mathematician

63 UnderstandIng Complete each of the following: and Master Mathematician 62 Mahobe Resources (NZ) Ltd

64 MULTIPLICATION STRATEGIES To make multiplication easier, split the numbers into units, tens and hundreds, multiply each part then add the products. Mahobe Resources (NZ) Ltd 63 Master Mathematician

65 PEASANT MULTIPLICATION STEP 1 Column 1 Column 2 STEP 1 STEP 2 STEP 2 THE ANSWER Use the Russian Peasant Method of Multiplication to multiply: Master Mathematician 64 Mahobe Resources (NZ) Ltd

66 Use the Russian Peasant Method of Multiplication to multiply: Mahobe Resources (NZ) Ltd 65 Master Mathematician

67 MULTIPLICATION When multiplying by a single digit number: 1. Multiply the number by each digit of the larger number. 2. Each time you get an answer of or more carry the left hand digits to the next column (similar to addition) x 8= 56 7x 20 = =190 Multiply these without using a calculator. Master Mathematician 66 Mahobe Resources (NZ) Ltd

68 8 08 3x 6 =18 3x30 = = 0 Multiply these without using a calculator x 0 = = 400 When multiplying by a two digit number start the second line with a zero (because you are multiplying by s). 4 2x 7= x 90= = x 7 = x 90 = = 2900 Mahobe Resources (NZ) Ltd 67 Master Mathematician

69 MORE MULTIPLICATION Multiply these without using a calculator. Master Mathematician 68 Mahobe Resources (NZ) Ltd

70 1 DIVISION x4= = x7= = 1 remainder 42 1 Use the method above to do these division sums. Mahobe Resources (NZ) Ltd 69 Master Mathematician

71 AVERAGES An average helps to summarise data. One type of average is the mean. The example below shows how to find the mean of a set of numbers: 1. Find the total Divide the total by the number of values. Find the mean of each set of numbers: Mean = Master Mathematician 70 Mahobe Resources (NZ) Ltd

72 THAT S DIABOLICAL Cells that form a row. Mahobe Resources (NZ) Ltd 71 Master Mathematician

73 Master Mathematician 72 Mahobe Resources (NZ) Ltd

74 Kg PLACE VALUE Write each as digits in the place-value table. a. PLACE VALUE Write each as digits in the place-value table. a. b. NUMBERs Write the number that is represented at the arrow point b. c. d. e. Five thousand, nine hundred and twenty seven. 9x00+3x0+2x1 27 hundreds + 7 tens + 3 units a. b. c. d. e. TH H T U Write these numbers as digits and list them in decreasing order: one thousand two hundred and eighteen, four hundred and six, eighty nine, five hundred and thirty, two thousand four hundred and forty four Write these as numbers c. Write these numbers with words. Write these as expanded numbers. TH a. b. c. H T U Four thousand and twenty seven Six thousand one hundred and three One thousand and nine Eight thousand five hundred and thirty one =2ø00+4ø0+1ø+5ø1 3ø00 + 2ø0 + 8ø + 4ø1 5ø00 + 5ø0 9ø0 + 6ø + 2ø1 1ø00 + 7ø0 + 2ø + 1ø1 4ø00 + 5ø + 9ø Round the numbers Rounded to the nearest: ten hundred thousand Number Complete the number pyramid. The sum of any two numbers is the number directly above NUMBER RELATIONSHIPS Do the additions and subtractions. Look for the relationships Calculate the products. Look for the relationships Calculate the products. Look for the relationships Study the pattern. What would the shape be on the 0th card? UNIT CUBES How many unit cubes make up each shape? ADDING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator = Draw how this solid would appear from three different views. = 13 Top View Top View Side View = Front View = 13 Side View Front View = = SUBTRACTING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator. VALUE RELATIONS FRACTIONS AND DECIMALS Some important fractions and decimals are below = 1 12 = = = = Find the value of each. = 1 12 Rewrite these fractions and mixed numbers as decimals = x = = = Mahobe Resources (NZ) Ltd 73 Master Mathematician

75 Hundreds Tens Ones Tenths FRACTIONS & DECIMALS FRACTIONS & DECIMALS Draw a line between the decimals and the correct place on the ruler Show where these numbers go on the number line: 7.6, 2.5, 3.7, 4.2, 1.1, 5.4, Which is bigger? < 32 I said get a tenth of the sugar, 01 not a tent full of sugar! < Write the decimal equivalents of these fractions Brad has an orchard which has 80 fruit trees. Two eighths of the trees are apple trees, one quarter of them are nectarine trees, four sixteenths of them are pear trees and the rest are plum trees. How many of each tree does Brad have? Apple: Nectarine: Pear Trees: Plum Trees: Tom and Kate collect apples from Brad s orchard. On the way home Tom eats one third of the apples. If Tom ate 4 apples, how many were picked? Tom and Kate picked... apples David and Victoria purchase an aquarium for there new home. One sixth of the fish in the aquarium are Black Tails. Two sixths of the fish in the aquarium are Blue Fins. The rest of the fish are Goldfish. David counts 3 black tails. Therefore there are: 6 1 = 3 black tails This means a total of 18 fish. Maddox took 5 oranges and cut them into quarters. How many quarters are there? ø 4 quarters = Blue Fins... Goldfish... quarters Suri s fruit punch contains one and three quarter litres of apple juice, two eights of a litre of lime juice and four and a quarter litres of orange juice. In one particularly hot day, Suri drinks 3 litres of the fruit punch. She then adds four and a quarter litres of mango juice. How many litres of fruit punch does she now have? Remember 2 8 = 1 4 DECIMALS 12 DECIMALS A decimal number contains a decimal point. The whole part, four. This is read as four point six. The fractional part, six tenths. Four whole parts. 6 Write the numbers that each diagram represents DECIMALS & MIXED NUMBERS A decimal number can also be written as a mixed number (a number with a fraction) or expressed in words. Decimal Number Mixed Number Description Three and two tenths Four and six tenths Five and one tenth Seven and five tenths Nine Six and eight tenths Two and four tenths Eight and nine tenths One and three tenths = Total =... Litres = Ten and seven tenths Give the number that is represented by each of the diagrams DECIMALS Write the numbers into the place value chart. three and seven tenths eighteen and two tenths twenty four and one tenths fifty six and three tenths forty seven and nine tenths one hundred and twelve and four tenths eight hundred and sixty five and eight tenths three hundred and six tenths seven hundred and ninety and seven tenths Write these numbers in decimal form DECIMAL & EXPANDED FORM Write each number in expanded form Rewrite these into decimal form Master Mathematician 74 Mahobe Resources (NZ) Ltd

76 DECIMALS Draw a line to show where each number is on the number line. ADDING TENTHS HUNDRETHS When a tenth is divided times each block represents a hundreth. Shade the diagrams to represent the given number Below are some pairs of numbers. Circle the larger number in each pair HUNDREDTHS The first two fractions (below) are equal. They do not equal the last. Write each of these as: 1. Decimal numbers. 2. Expanded form. 3. Mixed numbers. Decimal Expanded form Mixed number Decimal: Expanded form: Mixed number: Complete these sums. Complete the sums Decimal: Expanded form: Mixed number: 071 Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: DECIMALS Decimals come between whole numbers. Each digit to the right becomes ten times smaller. This also means that each digit to the left becomes ten times bigger. The in is: The in is: The in is: The in is: The in is: The in is: The in is: hundredths tenths units (ones) tens hundreds Complete the table. Fraction Decimal DECIMALS Write these numbers onto the place value chart. Five and twenty three hundredths Twenty four and sixteen hundredths Thirty six and twelve hundredths Eighteen and fifty one hundredths Ninety nine and ten hundredths Eighty two and four hundredths Locate each of the numbers on the number line. Tens Units Tenths Hundredths All the numbers above should be located on the number line. Use less than (<) or greater than (>) to make these statements true. < < > > > < < >. three hundredths seven tenths six tenths Eight units (ones) Five hundreths One hundred Nine hundreths Zero (no) tenths Two units (ones) ADDING DECIMALS Write the numbers underneath each other so that the decimal points line up =4 +0= Now add these Mahobe Resources (NZ) Ltd 75 Master Mathematician

77 DECIMAL ADDITION Rewrite these numbers in columns with the decimal points in line. Then complete the additions DECIMAL SUBTRACTION Rewrite these numbers in columns with the decimal points in line. Then complete the subtraction DECIMAL TEST Write the number that is represented by the shading Complete the table. Decimal Number Mixed Number Description Write the value of the 5 in each of these numbers. Locate each number on the number line. Use a greater than (>), equals (=) or less then (<) to make each a true statement. Add < > Five tenths Five hundreths Complete the graph by drawing a < = Fifty Five (ones) > > Add Rewrite these mixed numbers as decimal numbers. Rewrite these decimal numbers as mixed numbers. 8 Subtract Hair Doctor Terrence charges $ for a style, colour and haircut. Josette pays with two $0 notes. How much change should she get? $200 - $ = $45 05 Add up all the correct answers from the last 3 pages. Put your score in the box. 0 GRAPHS The graph shows the number of books that Katie read last week. The symbol represents 1 book. Mo Tu We Th Fr Sa Su 25 Katie read the least number of books on... Katie read the most books on... Sunday Katie read a total of 11 books on... Saturday &... Sunday 1 Katie did a survey on children s favourite colours. Below are her survey results. Write underneath how many chose each colour. = 3 children Mr Scott Mar Ms Lee Apr more stickers than Mrs Roberts class. May stickers collected Five and four tenths Three and six tenths One hundred and twenty eight hundreths Thirty five and sixteen hundreths and above: A+ student and above: A student Always strive to be an A+ student. Find out where you went wrong. If needed rub Blue Purple Yellow Black White Green Red out your answers and try the test again another day to represent 2 apples. 6 apples apples 5 apples 21 apples If an apple costs $0.50 then six apples cost $ If an apple costs $0.50 then 21 apples cost $ Give the total cost of apples in the graph. $ 3 $ 5 $ $ 50 $ 6 apples apples 5 apples 21 apples Class Sticker Collection Number of Stickers Collected Mrs Roberts class. Mr Daniels class. Ms Lee s class. Mr Scott s class. Which class has collected the most stickers? Which teacher does not give out many stickers? Mr Daniel s class has Altogether there were On the graph below draw columns to represent the mass of each student. 60 Kevin 42kg 50 Leo 46kg 40 Daniel 55kg 30 Brad 48kg Damon 35kg 20 Kevin Leo Daniel Brad Damon The heaviest student is: The lightest student is: Brad is 2 kg heaver than Leo. If all 5 boys were put on the scales then their total mass would be: A supermarket has made a pictogram of how many pies they sell in the first five months of the year. Each picture pie means 0 real pies. Fill in the missing numbers and pies. Jan Feb Daniel Damon = HANDLING DATA Tuesday When counting items use a tally chart with 1 dash recording each item. The frequency column adds up all the tally marks. Complete the frequency column then complete the graph. Frequency Favourite Soup 5 Favourite Soup Tally Tomato Chicken Ham and Bacon Creamed Corn Ham and Bacon 12 What was the most favoured soup? How many of the people surveyed chose Ham and Bacon? How many were surveyed? 25 people Favourite Pancake Toppings Tally Frequency Maple Syrup Complete the frequency 11 Honey column then complete 4 Jelly and Whipped Cream the graph below. 128 Lemon and Sugar Favourite Pancake Topping Maple Syrup Honey Jelly& Cream Lemon& Sugar Master Mathematician 76 Mahobe Resources (NZ) Ltd

78 Kg We asked some students their favourite sport. The results are below. Complete the frequency column then complete the graph. Sport Athletics Football Rugby Swimming Netball Cycling Kayaking Tally How many students were surveyed? The most popular sport was How many students said netball as their favourite? Favourite Sports 5 Frequency REPRESENTING DATA Each morning Amanda and Wayne take a note of the number of cars parked in a public car park. Write the number of cars parked each day. = 20 cars Mon Tue We Thu Fri Sat Sun Here are the number of books taken out of the library by Brad. TIME How many seconds in: 1 minute 15 minutes 20 minutes How many hours in: 1 day 24 3 days 72 7 days minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours Complete all the charts. 40 = 2 books Tally Frequency Football Week Week Week 3 1 year = 52 weeks. Week 4 11 Week year = 12 months. Week Picture graphs look 4 15 nicer however they 1 week = 7 days. can sometimes be 5 1 century = 0 years. harder to read. Week millennium = 00 years How many minutes in: 1 hour hours 90 8 hours year = days or 366 days in a year. 1 month = (approximately) weeks. How many years in 36 months? 3 How many months in 5 years? 60 How many months in 52 weeks? 12 UNITS OF MEASURE Join up the measures to the matching units. Day Minute Metre Centimetre Time Volume Mass Length Complete the missing numbers and units. = = = = December = litres 134 = weeks days Millilitre Kilogram Gram Litre Remember mm = 1cm 0cm = 1m 00mm = 1m 00ml = 1 litre 00g =1kg 17mm 29mm 46mm 85mm 0 7cm 1 7cm 3 2cm 7 1cm Mark on the ruler the following measurements. What is 1 kg in grams? Change 3 litres into ml grams 3000 Write the real distances indicated on each map scale. 1 6km 5km7km ml 05 0 UNITS OF MEASURE Circle all the units that measure length. kg, mm, l, g, ml, cm, m, km. Circle all the units that measure mass. km, m, cm, ml, g, l, mm, kg. Circle all the units that measure volume. 3 ml, g, m, mile, cm, l. What units of measure would you use to measure: The height of a tree. The amount of juice in a glass. Your mass. The distance from home to your school. The amount of water in a swimming pool. Today s date...(day)/...(month)/...(year) My height...(cm) =... (m)...(cm) My weight... My age... (years)... (months) I go to bed at... I get up at... I sleep for... hours... minutes 44 80m 540m The mass of an apple. The length of a pen. 900m A chicken s mass. Fill in the missing quantities PERIMETERS The perimeter of a shape is the total distance around the shape. To calculate the perimeter add up all the side lengths. Fill in the missing measurements. Calculate the perimeters Perimeter = Write down the lengths of all the sides. mm Perimeter = mm Perimeter = Means that these sides all have the same length. 5cm 28 cm The graph below shows the variation in temperature over one day. The temperature was measured each hour starting at 1am. Temperature ( C) What was the temperature at am? C 18 When was it the hottest? 2pm 4 Fill in the missing measurements. Calculate the perimeter. During which time was the temperature rising? Between 1am - 2pm Time (hours) There was a rainstorm during the day. When do you think that happened? 6 Perimeter = 24 cm 3pm Perimeter = 36 cm Mahobe Resources (NZ) Ltd 77 Master Mathematician

79 AREA A B C The area of a rectangle is obtained by multiplying the length by the width. Make sure both are measured with the same units. or = AREA Some figures are made up of different shapes. To find the area calculate the area of each separate shape, then add (or subtract) the areas. D E F Area = L W 2cm cm Area = L W 20cm 2 3cm 3cm 9cm 2 Area = L W + L W 36cm Area = L 8 W L W 48cm 4 2 G Area = L W 6cm 6cm 36cm 2 Area = = 22cm 2 Area A = Area B = Area C = 8 4 Area D = Area E = Area F = Area G = Area = L W 8cm 5cm 40cm 2 Area = L W 12cm 3cm 36cm 2 Note: The figures on this page are not drawn to scale = 56cm Area = MONEY CALCULATIONS MONEY CALCULATIONS Subtract the following. $3 75 $ 22 0 $1 45 $2 55 $0 85 $5 45 $6 25 $7 05 $8 85 $2 65 ANGLES Quart Half Three Full Count and write each amount in numerals and in words c 65c 50c 45c 70c 25c 40c 85c 20c 95c $15 80 Fifteen dollars and eighty cents $46 20 Forty six dollars and twenty cents $ One hundred and twenty two dollars and seventy cents ANGLES Write the value then draw each angle. Half a right angle. 45 One and a half right angles. 135 Measure the angles of the triangle then add them up. Draw each angle in the triangle. B A B 0 C A Measure or calculate the angles between these compass directions. C GRID POSITIONS Three right angles. 270 Three and a half right angles. 315 Coffee mug ( 5, 1 ) Fruit Bowl 2 2 W = 360 Chicken meal ( 9, 5 ) Battery ( 11, 3 ) 80 Tick box ( 2, 5 ) Fish ( 9, 2 ) Z 55 Ace of clubs ( 4, 4 ) 3 o clock 1 o clock 7 o clock X Y Write down the time and angles formed on each clock. Time Angle W NW SW N S NE South and West E North and North East SE East and West North and South East Measure the angles of the quadrilateral then add them up. When giving the position of an object give the horizontal position then the vertical position. Give the position of the: Fire extinguisher (, ) (, ) On the grid above draw a square at (1, 6), a circle at (3, 3), a triangle at (7, 2), a rectangle at (11, 5) and a pentagon at (9, 4). Master Mathematician 78 Mahobe Resources (NZ) Ltd

80 STEP 1 READING SCALES Mat (each division = ) 1250 (each division = 30) 1375 (each division = 15) (each division = 7 5) ROUNDING Actual answer = 70 Actual answer = 0 Actual answer = 60 Actual answer = 120 Actual answer = 430 Actual answer = 670 Actual answer = 630 Actual answer = 8 Actual answer = 800 Actual answer = 400 Actual answer = UnderstandIng Complete each of the following: and MULTIPLICATION STRATEGIES To make multiplication easier, split the numbers into units, tens and hundreds, multiply each part then add the products PEASANT MULTIPLICATION STEP 1 Column 1 Column 2 STEP 2 STEP 2 THE ANSWER Use the Russian Peasant Method of Multiplication to multiply: MULTIPLICATION When multiplying by a single digit number: 1. Multiply the number by each digit of the larger number. 2. Each time you get an answer of or more carry the left hand digits to the next column (similar to addition) x 8= 56 7x 20 = =190 Multiply these without using a calculator x 6 =18 3x30 = = 0 Multiply these without using a calculator x 0 = = When multiplying by a two digit number start the second line with a zero (because you are multiplying by s). 2x 7= x 90= = x 7 = x 90 = = 2900 Mahobe Resources (NZ) Ltd 79 Master Mathematician

81 1 MORE MULTIPLICATION Multiply these without using a calculator DIVISION x4= = x7= = 1 remainder Use the method above to do these division sums. ( ) 3 = ( ) 6 = ( ) 4 = ( ) 5 = ( ) 4 = ( ) 8 = ( ) 6 = ( ) 4 = ( ) 3 = ( ) 7 = AVERAGES An average helps to summarise data. One type of average is the mean. The example below shows how to find the mean of a set of numbers: 1. Find the total Divide the total by the number of values. Find the mean of each set of numbers: Mean = All the sums are the same. They equal Master Mathematician 80 Mahobe Resources (NZ) Ltd

82 Are you looking to give your child a powerful head start at school? Introduce your child to mathematics with Mighty Maths This is a structured, easy-to-follow series of fun activities designed to stimulate and challenge the master mathematician. This book covers: place value and number relationships adding and subtracting fractions decimals and decimal arithmetic graphs and handing data units of measure, perimeter, area and angles multiplication strategies, division and averages By the end of this book, children will have gained confidence when approaching mathematics at school especially with number relationships, fractions, decimals and measurement. Mighty Maths Choose and observe a marked improvement in your child s mathematical ability. Success and confidence in mathematics will lead to an increase in motivation and an enjoyment of learning. Mighty Maths reinforces the mathematics that children are studying at school. Study habits begin at home, complement school work and have an enormous impact on future academic achievement. Mighty Maths Master Mathematician for 8- year olds BOOK 2 ISBN MAHOBE