Mighty Maths for 8- year olds Master Mathematician BOOK 2 More Accomplishments With MathematicsKim Freeman
Mighty Maths for8-year olds Master Mathematician BOOK 2 More Accomplishments With MathematicsKim Freeman
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 9-760 Newmarket, Auckland New Zealand. Mahobe Resources (NZ) Ltd. ISBN 9781877489211 Print Production by Imago Print Productions (F.E.) Pte. Ltd., Singapore. Visit our website: www.mahobe.co.nz 2
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
What is found in this book? In this book you look at: NUMBER RELATIONSHIPS =2ø00+4ø0+1ø+5ø1 FRACTIONS AND DECIMALS MEASUREMENT 1 1 4. 1 31 2 0 0 0 1 0 13 3 5 7 1 1 0+3+1=4 +0= 11 0 1 2 9 3 8 Kg 4 7 6 5 DATA AND GRAPHS ANGLES MULTIPLICATION = 2 books Week 1 2 3 4 5 Master Mathematician 4 Mahobe Resources (NZ) Ltd
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. 3860 Mahobe Resources (NZ) Ltd 5 Master Mathematician
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
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
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
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
ADDING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator. 8 + 5 20 20 Master Mathematician Mahobe Resources (NZ) Ltd
SUBTRACTING FRACTIONS Add the fractions on this page. Before adding make sure each fraction has the same denominator. 5 4 12 12 Mahobe Resources (NZ) Ltd 11 Master Mathematician
VALUE RELATIONS = = = = Find the value of each. Master Mathematician 12 Mahobe Resources (NZ) Ltd
FRACTIONS AND DECIMALS Some important fractions and decimals are below. Rewrite these fractions and mixed numbers as decimals. 11 9 8 7 0 1 2 3 Kg 4 6 5 Mahobe Resources (NZ) Ltd 13 Master Mathematician
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
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
Which is bigger? Master Mathematician 16 Mahobe Resources (NZ) Ltd
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
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. 6 2. 3 Master Mathematician 18 Mahobe Resources (NZ) Ltd
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
DECIMALS Give the number that is represented by each of the diagrams. Master Mathematician 20 Mahobe Resources (NZ) Ltd
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
DECIMAL & EXPANDED FORM Write each number in expanded form. 400 + 30+ 2+ 2 Rewrite these into decimal form. Master Mathematician 22 Mahobe Resources (NZ) Ltd
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
ADDING TENTHS Master Mathematician 24 Mahobe Resources (NZ) Ltd
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
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
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
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
Complete these sums. Complete the sums. Complete the table. Fraction Decimal Mahobe Resources (NZ) Ltd 29 Master Mathematician
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. 5 2 3 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
ADDING DECIMALS 1 1 4. 1 31 2 0 0 0 1 0 13 3 5 7 1 1 0+3+1=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
DECIMAL ADDITION Rewrite these numbers in columns with the decimal points in line. Then complete the additions. Master Mathematician 32 Mahobe Resources (NZ) Ltd
DECIMAL SUBTRACTION Rewrite these numbers in columns with the decimal points in line. Then complete the subtraction. Mahobe Resources (NZ) Ltd 33 Master Mathematician
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
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
Add Rewrite these mixed numbers as decimal numbers. Rewrite these decimal numbers as mixed numbers. Subtract Hair stylist Terrence charges $154.95 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
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
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 150 125 0 75 50 25 0 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
On the graph below draw columns to represent the mass of each student. Kevin 42kg Leo 46kg Daniel 55kg Brad 48kg Damon 35kg 60 50 40 30 20 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
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
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
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 1 2 3 4 5 15... Week 1 2 3 4 5 Master Mathematician 42 Mahobe Resources (NZ) Ltd
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
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
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
UNITS OF MEASURE Circle all the units that measure length. kg, mm, l, g, ml, cm, m, km. 11 0 1 2 9 3 8 Kg 4 7 6 5 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
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) 25 20 What was the temperature at am? When was it the hottest? 15 During which time was the temperature rising? 5 0 5 15 20 Time (hours) There was a rainstorm during the day. When do you think that happened? Mahobe Resources (NZ) Ltd 47 Master Mathematician
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
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
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
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
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
MONEY CALCULATIONS Mahobe Resources (NZ) Ltd 53 Master Mathematician
MONEY CALCULATIONS Subtract the following. Count and write each amount in numerals and in words. Master Mathematician 54 Mahobe Resources (NZ) Ltd
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
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
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
GRID POSITIONS 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 11 12 Master Mathematician 58 Mahobe Resources (NZ) Ltd
READING SCALES G J George Jennifer Mahobe Resources (NZ) Ltd 59 Master Mathematician
ROUNDING Master Mathematician 60 Mahobe Resources (NZ) Ltd
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
UnderstandIng Complete each of the following: and Master Mathematician 62 Mahobe Resources (NZ) Ltd
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
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
Use the Russian Peasant Method of Multiplication to multiply: Mahobe Resources (NZ) Ltd 65 Master Mathematician
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). 5 6 196 7x 8= 56 7x 20 = 140 140 +50=190 Multiply these without using a calculator. Master Mathematician 66 Mahobe Resources (NZ) Ltd
8 08 3x 6 =18 3x30 =90 90 + = 0 Multiply these without using a calculator. 408 3 x 0 = 300 300 + 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=14 194 19 4 19 0 29 1 4 0 2x 90=180 180+=190 2 1 30 x 7 = 2 19 4 291 0 3 1 04 30 x 90 = 2700 2700 + 200 = 2900 Mahobe Resources (NZ) Ltd 67 Master Mathematician
MORE MULTIPLICATION Multiply these without using a calculator. Master Mathematician 68 Mahobe Resources (NZ) Ltd
1 DIVISION 4 4 7 24 24 4 4 3 4 7 24 4 3 1 6 6x4=24 28-24 = 4 42 1 6x7=42 43-42 = 1 remainder 42 1 Use the method above to do these division sums. Mahobe Resources (NZ) Ltd 69 Master Mathematician
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. 60 2. Divide the total by the number of values. Find the mean of each set of numbers: Mean = Master Mathematician 70 Mahobe Resources (NZ) Ltd
THAT S DIABOLICAL Cells that form a row. Mahobe Resources (NZ) Ltd 71 Master Mathematician
Master Mathematician 72 Mahobe Resources (NZ) Ltd
11 9 3 8 Kg 4 7 6 5 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. 1300 1700 20 2500 2900 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. 2444 Write these as numbers. 4 3 9 2 4 3 6 5 9 2 7 9 3 0 2 2 7 7 3 1218 530 406 89 4050 3860 903 570 1304 40 6040 2009 3601 9200 2071 c. Write these numbers with words. Write these as expanded numbers. TH a. b. c. H T U 5 7 5 6 2 1 3 0 9 4 0 1 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 + 9ø1 70 7500 7900 8300 8700 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. 450 550 0 150 300 5 6 7 NUMBER RELATIONSHIPS Do the additions and subtractions. Look for the relationships. 60 160 560 860 Calculate the products. Look for the relationships. 30 21 64 36 300 2 640 360 Calculate the products. Look for the relationships. 500 200 700 48 39 84 480 390 840 480 390 840 Study the pattern. What would the shape be on the 0th card? UNIT CUBES How many unit cubes make up each shape? 0 0 0 30 0 0 600 600 00 570 600 00 9850 9900 000 90 10 00 20 2000 2000 ADDING FRACTIONS 620 300 80 230 70 Add the fractions on this page. Before adding make sure each fraction has the same denominator. 36 8 5 136 20 + 20 436 = 13 936 20 5 7 4 8 3 18 + 18 Draw how this solid would appear from three different views. = 13 Top View 300 3000 18 Top View 2 20 640 6400 4 5 + 360 3600 Side View = 9 800 1200 Front View 240 480 4 9 18 + 18 40 1680 = 13 Side View Front View 18 4 15 20 + 20 = 19 20 6 5 15 + 15 = 11 15 8 9 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. 0 5 4 12 12 = 1 12 = = = = 8 12 7 12 Find the value of each. = 1 12 Rewrite these fractions and mixed numbers as decimals. 5 6 2 6 05 025 075 = 3 6 15+30 24+30 12+30+30 15x6 15 225 575 7 8 4 8 45 54 72 90 95 18 25 775 = 3 8 5 20 25 37 75 8 3 = 5 12+30 30+15 6+30 18+15 8 9 6 9 42 45 36 33 075 25 1 2 = 2 9 11 12 13 Mahobe Resources (NZ) Ltd 73 Master Mathematician
Hundreds Tens Ones Tenths FRACTIONS & DECIMALS FRACTIONS & DECIMALS Draw a line between the decimals and the correct place on the ruler. 36 12 18 9 12 36 12 48 Show where these numbers go on the number line: 7.6, 2.5, 3.7, 4.2, 1.1, 5.4, 8.3 37 54 83 6 3 27 4 24 30 4 20 12 24 Which is bigger? 05 025 075 120 240 02 04 06 08 60 13 30 < 32 I said get a tenth of the sugar, 01 not a tent full of sugar! 600 130 03 13 36 07 09 130 360 24 < 27 14 15 16 Write the decimal equivalents of these fractions. 11 25 42 76 20 21 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:... 20 Nectarine:... 20 Pear Trees:... 20 Plum Trees:... 20 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? 6 9 5 ø 4 quarters = 20... 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. 20 21 22....... 2 3 1 9 55 68 32 47 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 3 4 + 1 81 13 One and three tenths 1 4 + 4 1 4 = 6 1 4 1 7 Total =... Litres 6 1-3+ 4 1 4 4 = 7 1 7 2 74. Ten and seven tenths 2 17 18 19 Give the number that is represented by each of the diagrams.. 0 1 1. 7 0. 5 4. 8 3. 2 5. 3 1. 4 2. 6 3. 0 4. 9 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 3 7 1 8 2 2 4 1 5 6 3 4 7 9 1 1 2 4 8 6 5 8 3 0 0 6 7 9 0 7 Write these numbers in decimal form. 47 82 51 16 8 37 1 46 7 59 6 20 3 46 75 90 68 89 6 5 7 8 2 8 1 5 4 9 DECIMAL & EXPANDED FORM Write each number in expanded form. 400 + 30+ 2+ 2 50+2+ 8 5 60+4+ 70+1+ 9 80 + 5 + 2 300 + + 3 + 900 + 20 + 3 200 + 7 + 4 500 + 30 + 6 + Rewrite these into decimal form. 85 1 6 597 2 640 7 8 5 7 Master Mathematician 74 Mahobe Resources (NZ) Ltd
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. 35 49 Below are some pairs of numbers. Circle the larger number in each pair. 47 28 HUNDREDTHS 38 23 24 25 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: 348 4 3 + + 3 48 0 Complete these sums. Complete the sums. 1 2 2 3 1 1 4 1 1 5 0 1 3 8 0 236 Decimal: Expanded form: Mixed number: 071 Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: Decimal: Expanded form: Mixed number: + + 2 3 20 36 9 1 + 7 + 1 0 71 0 1 9 0 3 63 0 9 0 363 6 3 + + 6 0 3 0 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 26 27 28 Complete the table. Fraction 19 0 8 2 3 0 0 Decimal 023 007 31 1 3 4 2 2 5 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 5 2 3 2 4 1 6 3 6 1 2 1 8. 5 1 9 9.. 1 0 8 2 0 4 All the numbers above should be located on the number line. Use less than (<) or greater than (>) to make these statements true. < < > > 29 30 31 > < < >. 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. 1 1 4. 1 31 2 0 0 9 0 11 1 0 1 5 7 1 13 1 3 0+3+1=4 +0= Now add these. 3 7 4 5 5 1 77 33 83 55 1 5 37 27 5 824 4 23 1 0 9 22 73 53 Mahobe Resources (NZ) Ltd 75 Master Mathematician
DECIMAL ADDITION Rewrite these numbers in columns with the decimal points in line. Then complete the additions. 005 009 014 0 27 4 00 4 27 DECIMAL SUBTRACTION Rewrite these numbers in columns with the decimal points in line. Then complete the subtraction. 5 43 0 0 0-2 - 20 0 03 0 23 DECIMAL TEST Write the number that is represented by the shading. 3 9 4 3 1 80 725 346 1 8 5 5 2 6 9 1 0 1 2 135-08 - 065 0 4 0 70 2 14 1 66 0 5 4 1 6 5 2 5 3 0 0 8 3 0 7 1 7 3 0 70-0 4 5 0 25 1 70-0 95 0 75 0 4 0 8 0 55 0 78 Complete the table. Decimal Number Mixed Number Description 068 1 1 6 3 1 0 00 6 42 0 9 0 9 8 2-14 - 5 0 1 1 5 8 2 1 4 5 9 86 1 4 1 5 4 36 3 6 276 5 99 68 8 00 1 3 7 1 0 9 889 5 1 3 0 28 0 0 28 1 79 2 87 4 1 3 7 0 8 32 33 34 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 9 40 24 63 25 22 325 18 5 35 75 24 20 36 0 0 15 25 20 75 Hair Doctor Terrence charges $154.95 for a style, colour and haircut. Josette pays with two $0 notes. How much change should she get? $200 - $154 95 = $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 5 425 25 more stickers than Mrs Roberts class. May 350 275 stickers collected. 38 39 40 3 25 0 15 4 1 Five and four tenths Three and six tenths One hundred and twenty eight hundreths 35 16 Thirty five and sixteen hundreths 98 18 6 45 and above: A+ student 13 7 11 0 40 and above: A student 12 5 12 0 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. 15 6 9 2 7 11 4 35 36 37 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 150 125 0 75 50 25 0 Number of Stickers Collected 3 50 2 50 21 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 854 555 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 42+46+55+48+35 = 226 300 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 3 9121 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
11 9 8 Kg 4 7 6 5 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 5 12 6 3 8 4 2 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 0 60 70 120 30 5 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 168 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours Complete all the charts. 40 = 2 books Tally Frequency Football Week 1 12 365 Week 2 14 8 Week 3 1 year = 52 weeks. Week 4 11 Week 5 13 1 year = 12 months. Week 1 2 3 4 5 Picture graphs look 4 15 nicer however they 1 week = 7 days. can sometimes be 5 1 century = 0 years. harder to read. Week 1 2 3 4 5 1 millennium = 00 years. 41 42 43 60 900 1200 How many minutes in: 1 hour 60 1.5 hours 90 8 hours 480 1 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 = 5 32 2 16 8 1 319 2 litres 134 = 225 720 4 3 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. 2 8000 00grams 3000 Write the real distances indicated on each map scale. 1 6km 5km7km ml 05 0 UNITS OF MEASURE 0 1 2 3 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 45 46 A chicken s mass. Fill in the missing quantities. 60 15 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. 30 225 135 1 90 1200 72 40 40 50 130 Perimeter = Write down the lengths of all the sides. mm 35 35 35 35 140 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 47 48 49 Perimeter = 36 cm Mahobe Resources (NZ) Ltd 77 Master Mathematician
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 6 5+2 3 2 Area = L 8 W 3+6 + L W 48cm 4 2 G Area = L W 6cm 6cm 36cm 2 Area = 5 5-3 1 = 22cm 2 Area A = Area B = Area C = 8 4 Area D = Area E = Area F = Area G = 4 15 12 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. 9 9-5 5 = 56cm 2 50 51 52 Area = MONEY CALCULATIONS 37 90 27 90 37 75 33 80 27 80 39 00 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. 39 90 50 80 56 30 90c 65c 50c 45c 70c 25c 40c 85c 20c 95c $15 80 Fifteen dollars and eighty cents $46 20 Forty six dollars and twenty cents $122 70 One hundred and twenty two dollars and seventy cents 30 90 45 150 53 54 55 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 30 50 30 0 50 180 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 80 + 90 + 135 + 55 = 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 90 135 X Y 90 30 2 56 57 58 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. 90 45 180 135 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
STEP 1 READING SCALES Mat 250 1250 1375 62 5 250 (each division = ) 1250 (each division = 30) 1375 (each division = 15) 262 5 (each division = 7 5) 600 385 900 342.5 16 145 ROUNDING 50 70 80 45 57 68 71 84 96 200 500 800 59 60 61 60 70 0 219 381 468 650 822 954 400 700 00 20+50 70+30 20+40 50+70 4+20 630+40 570+60 5 + 300 500 + 300 300 + 0 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 = 70 97 62 121 433 669 626 807 780 390 UnderstandIng Complete each of the following: 22+22+22 and 6 90 88 8 144 5 60 MULTIPLICATION STRATEGIES To make multiplication easier, split the numbers into units, tens and hundreds, multiply each part then add the products. 7 490 497 35 300 335 16 180 196 18 120 138 28 80 8 PEASANT MULTIPLICATION STEP 1 Column 1 Column 2 STEP 2 STEP 2 THE ANSWER 11-11-11-11 36-36 11 36 27 4 45 360 1800 2205 48 240 3000 3288 56 630 20 2786 56 45 12 320 200 360 6400 00 3200 6776 1245 3572 62 63 64 33 66 132 264 528 66 528 594 18 9 4 2 1 25 20 12 40 6 80 3 160 1 80 160 250 20 41 40 20 80 52 160 320 640 1 20 160 640 820 Use the Russian Peasant Method of Multiplication to multiply: 13 19 26 9 52 4 4 2 208 1 13 26 208 247 20 25 40 12 80 6 160 3 320 1 20 160 320 500 30 20 15 40 7 80 3 160 1 20 40 80 160 300 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). 5 6 196 7x 8= 56 7x 20 = 140 140 +50=190 Multiply these without using a calculator. 8 08 3x 6 =18 3x30 =90 90 + = 0 Multiply these without using a calculator. 408 3 x 0 = 300 300 + 0 = 400 2060 1645 468 700 1950 895 1692 1512 25 6 50 3 0 1 0 50 150 12 15 24 7 48 3 96 1 24 12 48 96 180 30 50 60 25 120 12 240 6 480 3 960 1 60 480 960 1500 252 141 150 165 416 448 774 156 273 222 294 425 232 768 112 216 3144 3624 2925 3325 2538 1144 1170 1701 When multiplying by a two digit number start the second line with a zero (because you are multiplying by s). 2x 7=14 65 66 67 4 194 19 4 19 0 29 1 4 0 2x 90=180 180+=190 2 1 30 x 7 = 2 19 4 291 0 3 1 04 30 x 90 = 2700 2700 + 200 = 2900 Mahobe Resources (NZ) Ltd 79 Master Mathematician
1 MORE MULTIPLICATION Multiply these without using a calculator. 141 940 8 1 378 1260 1638 1701 4860 6561 2421 5380 780 1 142 2130 2272 324 540 864 58 1160 1218 DIVISION 4 4 7 24 24 4 4 3 6x4=24 28-24 = 4 42 1 6x7=42 43-42 = 1 remainder Use the method above to do these division sums. (3 + + 5) 3 = 6 3 1 2 322 160 192 71 5 248 52 9 1380 640 240 (15+7+9+5+3+15) 6 = 9 1702 800 432 35 16 45 85 33 20 (3+7+5+13) 4 = 7 32 18 3 1 2 (20+7+9+12+7) 5 = 11 1 6 89 6 48 75 7 1506 556 724 ( + 17 + 13 + 8) 4 = 12 25 8340 7240 48 12 49 4016 8896 7964 55 24 41 54 24 35 (1+1+1+3+8+8+4+6) 8 = 4 1 0 6 1 3 (16 + 32 + 45 + 27 + + 50) 6 = 30 1824 263 49 5 (22 + 25 + 30 + 23) 4 = 25 3256 675 1 532 4 4 20 4070 2700 1 1 490 32 12 48 7326 3375 13022 32 (86 + 83 + 92) 3 = 87 12 45 0 98 0 66 3 (12 + 16 + 15 + 14 + + 11 + 6) 7 = 12 1 0 68 69 70 4 7 24 4 3 42 1 1 6 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. 60 2. Divide the total by the number of values. Find the mean of each set of numbers: Mean = 34 34 34 34 34 All the sums are the same. They equal 34. 42 14 72 Master Mathematician 80 Mahobe Resources (NZ) Ltd
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 978-877489-21-1 9 781877 489211. MAHOBE