Section A Number Facts

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1 Grade Play! Mathematics Answer Book Section A Number Facts Concept -digit Numbers. Study: In 0 there are 0 units (ones). In there are units (ones). 0 + The value of the. The value of the. ten + units or 0 units + units units. Write down the total number of units in: units units units. Write down the value of each underlined digit Study: 0 consists of tens or 0 units. Therefore: tens + units or 0 units + units or units In the value of the: is 0. is.. Write down the number of tens in: 90 9T 0 T 0 T d) 0 T. Write down the total number of units in each number. units 0 0 units units 0 0 units units. Underline the units digit in each number.. Underline the tens digit in each number. d) 9 d). Write down the value of each underlined digit: Complete each number sentence: tens + units tens + units Concept -digit Numbers: Part. Study: hundred consists of 0 tens or 00 units. 0 units + units 0 units + units units units. 00 hundreds or 0 tens or 00 units. 00 hundreds or 0 tens or 00 units. 00 hundreds or 0 tens or 00 units. d) 00 hundreds or 0 tens or 00 units.. Study: One hundred and thirty consists of tens or 0 units The value of the. The value of the. 0 H + T or 0 0 T + T or 0 0 U T. Complete: 0 tens or 0 units. 0 tens or 0 units. 0 tens or 0 units. d) 0 tens or 0 units.

2 Grade Play! Mathematics Answer Book Concept -digit Numbers: Part. Study: hundreds + tens + units Remember hundreds 0 tens or tens + units or units. Underline the tens digit in each number.. Underline the (total) number of tens in: d) 09 d) 9. Underline the units digit in each number.. Underline the (total) number of units in: d) 0 d). Complete each number sentence: H + T + U T + U U H + T + U T + U U. Fill in the missing numbers to make correct statements. 0 tens T + U Fifteen tens 0 d) 0 tens + units 0 e) Fifty-four tens 0 f) T + U. Write down the value of each underlined digit d) Complete: In there are hundreds, or tens or units. In there are hundreds, or tens or units. Concept -digit Numbers. Study: One thousand consists of: 0 hundreds or 00 tens or 000 units Complete: 000 thousands or 0 hundreds or 00 tens or 000 units. 000 thousands or 0 hundreds or 00 tens or 000 units.. One thousand four hundred is made up of: hundreds or 0 tens or 00 units Complete: 00 hundreds or 0 tens or 00 units. 00 hundreds or 0 tens or 00 units. Underline the hundreds digit in each number.. Underline the (total) number of hundreds in: d) d). Underline the tens digit in each number.. Underline the (total) number of tens in: d) 0 d) 9 9. Write down the value of each underlined digit Complete: In there are thousands, or hundreds, or tens or units. In there are thousands, or hundreds, or tens or units.

3 Grade Play! Mathematics Answer Book 9 Concept -digit and -digit numbers. Study: In there are thousands, or hundreds, or tens or units. HTh TTh Th H T U TTh Th H T U In 9 there are thousands, or hundreds, or 9 tens or 9 units.. The above must not be confused with the following: In the value of the: is 0 000, is 000, is 00, is 0 and is. In 9 the value of the: is , is 0 000, is 000, is 00, 9 is 90 and is.. Underline the (total) number of tens in: 9 9 d). Underline the (total) number of hundreds in: 90 d) 09. Complete: In there are thousands, hundreds, tens or units. In there are thousands, hundreds, tens or units. Concept Rounding Off Section B Rounding Off. To round a number off to the nearest 0, we use the units digit to decide whether to round down to the previous ten or to round up to the next ten. Examples: rounded off to the nearest ten is 0. Use the (the units digit) to decide. rounded off to the nearest ten is 0. Use the (the units digit) to decide.. Round off each -digit number to the nearest d) 0 e) 0. Round off each -digit number to the nearest d) 0 *e) To round a number off to the nearest 00, we use the tens digit to decide whether to round down to the previous hundred or to round up to the next hundred. Examples: 9 rounded off to the nearest hundred is 00. Use the (the tens digit) to decide. 9 rounded off to the nearest hundred is 00. Use the (the tens digit) to decide.. Round off each -digit number to the nearest d) 9 00 *e) Round off each -digit number to the nearest to the nearest 0. 0 to the nearest to the nearest to the nearest *d)

4 Grade Play! Mathematics Answer Book 0 Section C Number Sentences Concept Subtracting Three Numbers (without grouping). Study: ( ) is not equal to ( ). This means that how we group the numbers together affects the answer. But, if we simply subtract two numbers, one after the other, the order in which the numbers are subtracted does not affect the answer. From the example we see that whether we subtract and then, or and then, we get the same answer. In both cases, the overall effect is the same as subtracting from.. Complete each pair of number sentences, working from left to right. Show your steps *. Why is is not correct. Find each answer, using the easiest order. Show your steps d) 0 e) f) 00. Bonga has R. She spends R on Monday and R on Tuesday. How much money does she have left R R R R0 R R Concept Dividing Three Numbers (without grouping). Study: ( ) is not equal to ( ). This means that how we group the numbers together affects the answer. But, if we simply divide by two numbers, one after the other, the order in which the numbers are written does not affect the answer. For example: From the example we see that whether we divide by and then, or by and then, we get the same answer. In both cases, the overall effect is the same as dividing by.. Complete each pair of number sentences, working from left to right. Show your steps.. Find each answer, using the easiest order. Show your steps. and Correct answers: 0 or: may not be subtracted from separately as it changes the overall meaning of the number sentence. 0 or in step: 0 For example: and Correct answers: *. Why is 0 not correct or: divided by may not be done separately as it changes the overall meaning of the number sentence. or in step: 9 d) 9 e) 9 f)

5 Grade Play! Mathematics Answer Book Section D Time Concept Number of days from vs Number of days between. Let s determine the number of days from one date until another date. Examples: There are days from April until 0 April. Notice: 0 April April April April 9 April 0 April There are days from September until October. NB: September 0 days Sept Sept 9 Sept 0 Sept Oct Oct Oct Oct Oct. If the date is 0 May, there are: days until May. days until May. * days until June. *d) + 9 days until June.. Hanna has her birthday on June. If today is the 9 th of June, how many days must she wait until her birthday 9 d. School closes on September. If today is the th of September, how many days are there until school closes d NB: Sept to (and including) 0 Sept days. *. Vasi s party is on October. The date is September. How many days are there until her party + d. What is the date weeks before Christmas Day December days December. Let s determine the number of days between two dates. Examples: There are days between 0 May and May. Notice: 0 and We do not count the first day (0 May) or the last day ( May). We We do not count the first day ( May) or the last day ( June). We count the first day ( April) but not the last day (0 April). We count the first day ( Sept) but not the last day ( Oct). Count days from 0 May to (and including) May. 0 May May May May May May May May days There are days between May and June. NB: May has days. May 9 May 0 May May June June June June June June 9 days. There are: days between June and 9 June. days between April and 0 April. days between July and July. d) days between August and 9 August. *9. There are: days between January and February. days (left) in Jan + days in Feb days days between 0 June and July. 0 days (left) in June + days in July days 0. School closes on March and opens again on March. How long, in weeks, is the school holiday days weeks ( and ) First calculate the number of days between March and March. 0 9 days. School closes on June and opens again on 9 July. day days The school holiday days. days days days (left) in June + days in July days

6 Grade Play! Mathematics Answer Book Concept Capacity and Volume Section E Capacity and Volume. Study the difference between capacity and volume: Capacity is the maximum amount of liquid a container can hold. In other words, 0 m of liquid will fill the jug. This jug can not hold more than 0ml. Volume refers to the amount of space that a liquid occupies within a container. The jug is not full. The volume of liquid inside the jug is less than its capacity. Volume is also the amount of space that a solid object, occupies. The volume of this cube is cm.. True or False 00 m of water can be poured into a -litre jug. True. Study the jug below. A -litre bottle can contain of Coke. False The volume of liquid inside a container can never be greater than the capacity of the container. True The capacity of the jug is litre. The volume of liquid in the jug is ½ litre / 00 ml. The volume of liquid needed to fill the jug is ½ litre / 00 ml.. Study the -litre jug below. Each interval on the jug is 00 m. (000m 00m ) 000m The volume of liquid in the jug is 00ml. The volume of liquid needed to fill the jug is 00ml. 000m 00 m 00m. Study the -litre bottle of milk below.. Study the bottle of milk below. 000ml 00ml How much milk is needed to fill the bottle 000m 00 m 00m 00m Each interval 000 ml 0 00 ml 0ml How much milk is needed to fill the bottle 000m 0m 0m ¾ Each interval 000 ml 0 ml

7 Grade Play! Mathematics Answer Book Section F Common Fractions Concept Equivalent Fractions ( and ). To write equivalent fractions, multiply the top and the bottom by the same number. The inverse of this is to divide the top and the bottom by the same number: Examples: 9 9 because quarters is equal to 9 twelfths. 9 twelfths is equal to quarters... Complete:. Complete: We have divided by 0. Write equivalent fractions. Fill in what the bottom and the top are divided by in each. d) 0 e) 0 f) *. Complete to write equivalent fractions, working backwards, from right to left. Fill in what the bottom and the top are multiplied or divided by in each. 0 d) e) 9 f) 9 *. Complete to write equivalent fractions. 0 d) 9 e) f) 0 Concept Comparing Fractions. Fill in >, < or between each pair of fractions. We want to compare quarters and quarters. < quarters < quarters We want to compare sixths and sixths. > sixths > sixths We want to compare twelfths and twelfths. < 9 twelfths < 9 twelfths d) < e) > f) 0 > 0 g) > h) i) 9 > 9 j) < k) < 0 l) m) 0 < 0 n) 9 > 9 o) > 9

8 Grade Play! Mathematics Answer Book Concept Simplest Form. Complete: d) quarters half eighths half sixths third eighths quarter e) f) g) h) sixths half eighths quarters twelfths third twelfths thirds. A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. Consider writing the following fractions in the simplest form: Option : Divide by the biggest number fits exactly into and. Let s picture it: Option : Keep dividing by a small number that fits into the top and the bottom exactly. Repeat until you can t go any further. Check your work. Option : Divide by the biggest number fits exactly into and. sixths is a simpler form, but it is not in the simplest form. twelfths half Let s picture it: Option : Keep dividing by a small number that fits into the top and the bottom exactly. Repeat until you can t go any further. Check your work. twelfths thirds. Write each fraction in the simplest form. Show your steps, if necessary. 9 d) 0 e) f) g) h) i) *j) 0 This is the same as dividing by.. Write each improper fraction in the simplest form. Show your steps, if necessary. 9 Concept Writing one quantity as a fraction of another quantity sixths is a simpler form, but it is not in the simplest form.. When writing one quantity as a fraction of another quantity, there are no units in the final answer. Always write the answer in the simplest form. What fraction is: m of m m m R R of R0 R0. What fraction is: km of km km kg of 0 kg kg 0s of 0s 0 s km 0 kg 0 s d) g of g g e) of l f) 0mm of 0mm 0mm g l 0mm *. What fraction is: m of m m of l R9 of R R9 m l R d) h of 0 h h e) 0 kg of kg 0 kg f) R0 of R0 R0 0 h kg R0 d) 9 e)

9 Grade Play! Mathematics Answer Book Concept Problem Solving. Complete: If I shade of squares, I have shaded of the squares. If Amy eats of apples, Amy has eaten of the apples. If I spend R of my R, I have spent or of the money. d) If Jake runs km of a km race, Jake has run or of the race.. If four pizzas are shared among four people: each person gets pizza out of the pizzas. each person gets of the pizzas.. If four pizzas are shared between people: each person gets pizzas out of the pizzas. each person gets or of the pizzas.. Six cakes are shared between people. Each person gets cakes out of the cakes. Each person gets or of the cakes.. Six cakes are shared among people. Each person gets cake out of the cakes. Each person gets of the cakes.. Six cakes are shared among people. Each person gets cakes out of the cakes. Each person gets or Sharing between, think halves. of the cakes. Sharing among, think quarters. Sharing between, think halves. Sharing among, think sixths. Sharing among, think thirds. Concept Division and Common Fractions: Part. Study: divided by is : divided by is third: whole divided into equal parts. A whole number has an invisible denominator of. It is not usually written. Think: + +. Complete: Answer in fraction form, where necessary.. Complete: Complete: There are thirds in whole. There are sixths in whole. whole halves d) whole quarters eighths.. One pizza is shared between friends.. One pizza is shared amongst friends. Each friend gets of the pizza. Each friend gets of the pizza.. One melon is shared between Zoe, Jen and Amy. Zoe gets of the melon, Jen gets of the melon and Amy gets of the melon.

10 Grade Play! Mathematics Answer Book *Concept Division and Common Fractions: Part. Study: If is divided by the answer, in fraction form, is thirds. Conversely, divided into equal parts is halves. This is an improper fraction. See concept below.. Complete: Answer in fraction form d). Study: Let s divide by : Let s divide by : In fraction form, the answer is quarters, or half in simplest form. In fraction form, the answer is eighths, or quarters in simplest form.. Complete: Answer in simplest fraction form.. Share pizzas equally amongst children. pizzas + or or d) Answer: Each child gets: quarters of a pizza, or half of a pizza. f) Take note: The pizzas are shared amongst, therefore it is also correct to say that each child gets of the pizzas.. Share pizzas equally amongst children. Each child gets or of a pizza. s. Share apples equally between girls. Each girls gets or of an apple. ( apples ). Six boys must share two juices, equally. Each boys gets or of a juice. ( juices ) Concept Division and Common Fractions: Part. Study: We know that.. Write each fraction as a whole number. This can be written in fraction form: d). Study: If one number doesn t divide into another an exact number of times, we get a remainder. Examples: r r because ( ) + because ( ) + or or fits into once remainder third. fits into 9 twice remainder thirds.. Complete: Answer in improper fraction and mixed number form. d) 9 e) 9 9 f) 0 0 g) h) 9

11 Grade Play! Mathematics Answer Book Concept 9 Real-life problems with remainders that can be shared: Part. Share apples between friends, Sally and Sam. Using fractions: apples apple rem apple The remaining apple must also be shared. Answer: Sally and Sam get apples each. Take note: The apples are shared between friends, therefore it is also correct to say that each friend gets of the apples.. Share apples equally between two girls.. Share chocolates equally amongst boys. Each girl gets apples. Each boy gets chocolates.. Three boys share oranges equally. *. 0 kg of sugar is shared equally between bags. Each boy gets oranges. Each bag contains 0 kg of sugar. *Concept 0 Real-life problems with remainders that can be shared: Part. Three cakes are shared equally between Joe and James. Joe gets one half of the cakes and James gets the other half of the cakes. Out of the cakes, each boy gets one and a half (½) cakes.. Four cakes are shared equally between Zoe, Jen and Amy. Zoe gets of the cakes, Jen gets of the cakes and Amy gets Out of the cakes, each girl gets cakes. of the cakes.. Four boys share 9 lemons equally. Each boy gets of the lemons. Out of the 9 lemons, each boy gets lemons. 9 Concept Problem solving with remainders that cannot be shared. Study: Sally has puppies. She must share them equally between two friends. puppies puppies r puppy Friend Friend A puppy cannot be halved! Therefore, each friend gets puppies and puppy remains. r. Share pens equally between learners.. Share monkeys equally among zoos. Each learner gets pens. pens remain. Each zoo gets monkeys. monkey remains. r. Fifteen kids must divided into teams of equal. chairs must be equally arranged in rows. size. Each teams has kids. kid remains. Each row has chairs. chair remains. r r. This must not be confused with problems with remainders that mean extra is needed. e.g. Four girls can be seated at one table. How many tables are needed to seat girls tables are needed. r tables will be full and girls will be seated at the rd table.

12 Grade Play! Mathematics Answer Book Concept Subtraction of Mixed Numbers using Inverse Operations. Complete: How much must be added to to get Shade your answer. + How much must be added to to get Shade your answer. + d) How much must be added to to get Shade your answer. +. Complete by inspection. In other words, without doing a calculation. How much must be added to to get Shade your answer. + Think: + d). Complete: How much must be added to to get How much must be added to Shade your answer. + Shade your answer.. Complete by inspection. + to get + Think: d). Complete: How much must be added to Shade your answer. + *. Complete by inspection. to get How much must be added to Shade your answer. + to get + Think: d) Concept Subtraction of Mixed Numbers using Improper Fractions. Calculate by changing both mixed numbers into improper fractions.. Complete. Use improper fractions. Show your steps. d) 9

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