Problem-Solving Strategies & Skills – Number & Algebra: Year 4

1

Number and algebra Thousands

Hundreds

Tens

Ones

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What is the sum of the three numbers represented by the place value chart?

R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra Thousands

Hundreds

Tens

Ones

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31

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15

7

3.

72 ©R I .

C.Publ i cat i o ns •f orr evi ew pur posesonl y• 60

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What number is one hundred ‘tens’ and ninety-four ‘ones’ less than the total of the numbers represented in the place value chart?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Sally is making a necklace in a repeating pattern with three red beads, three blue beads and three yellow beads.

© R. I .

C.Publ i cat i ons If she continues•the pattern f or r evi ewuntil pur posesonl y• there are 81 beads in total, how many of each coloured bead does Sally need?

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Number and algebra

Sally is making a necklace in a repeating pattern with one red bead, two blue beads and three yellow beads.

© R. I .

C.Publ i cat i ons If the pattern continues until •f orr ev i ew pur posesonl y• there are 72 beads in total, how many blue beads does Sally need?

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Number and algebra

Jack is three times as old as his brother Sam and half as old as his sister Mikayla. Their mum, Claire, © R. I .

C .Publ i cat i ons now 45, gave birth to Mikayla when •f orr evi ew pur posesonl y• she was 27.

How old is each of Claire’s children?

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Number and algebra

Jack is three times as old as his brother Sam and half as old as his sister Mikayla. Their mum, Claire, now 45, gave birth to Mikayla © R. I .

C.Publ i cat i ons when she was 27.

•f orr evi ew pur posesonl y•

By how many times is Claire older than each child?

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Number and algebra A box of chocolates contains 32 individual chocolates. The recommended serving size is one-eighth of a box.

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If Barry eats one serve of •f orr evi ew pur posesonl y• chocolate each day, how many individual chocolates will he eat in one non-leap year?

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Extension

Number and algebra A box of chocolates contains 32 individual chocolates. The recommended serving size is one-eighth of a box.

Barry shares three equally © boxes R. I .

C. Publ i cat i ons among himself and his •f o rr e vi ethree w pur posesonl y• friends.

What fraction of a whole box will they each get? Write the fraction in its simplest form.

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Number and algebra

Four children swam in a 50-m freestyle relay. The finish times of each swimmer were: 62.35 seconds, 57.09 seconds, 60.34 seconds and 59.18 seconds.

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C.Publ i cat i ons How many seconds did• itf take orr evi ew pur posesonl y• to swim the whole relay?

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Number and algebra

Four children swam in a 50-m freestyle relay. The finish times of each swimmer were: 62.35 seconds, 57.09 seconds, 60.34 seconds and 59.18 seconds. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

What is the difference between the fastest and slowest times?

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Number and algebra

6

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What is the second largest four-digit number that can be made using each digit only once?

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Extension

Number and algebra

6

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C.Publ i cat i ons •f orr evi ew pur posesonl y• Write the three smallest five-digit numbers that can be made using each digit only once.

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Number and algebra

A factory does a stocktake of its current stock. It has 1634 small boxes, 6749 medium boxes and 15 287 large boxes of goods. They must leave a minimum of 250 small ©R .

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C.Publ i cat i ons boxes, 750 medium boxes and 1000 •f o r etimes. vi ew pur posesonl y• large boxes in the factory atr all What is the maximum amount of stock they can sell altogether?

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Number and algebra

A factory does a stocktake of its current stock. It has 1634 small boxes, 6749 medium boxes and 15 287 large boxes of goods.

The following day they received an © R. I .

C.Publ i cat i ons additional 525 of each box and sold •f orr evi ew pur posesonl y• 94 small boxes, 162 medium boxes and 2973 large boxes.

What are the new stock levels of each sized box?

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Number and algebra For dinner, five friends ordered a pizza which was cut into eight pieces.

The five plates show how much pizza was eaten.

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What is the total fraction of pizza eaten and how much was left over?

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Number and algebra

Five friends ordered three pizzas for dinner. Each pizza was cut into eight pieces. Each person ate 28 of a pizza.

What is the total fraction oft pizza ©R .

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Write the answer as a mixed •f orr ewas vi ew pu r pos eson l y• fraction in its simplest form.

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Number and algebra The sum of three hundred and sixty-four and ninety-seven is one more than the difference between one thousand, two hundred and eighteen and aPubl © R. I .

C. i cat i ons mystery number. •f orr evi ew pur posesonl y• What is the mystery number?

Write it in numerals.

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Extension

Number and algebra

The total of 1628, 4267 and 2080 is equal to 10 915 minus 2106 minus a mystery number.

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C.Publ i cat i ons •f orr evi ew pur posesonl y• What is the mystery number?

Write it in words.

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Number and algebra In Miss Murray’s class, there are 10 females including the teacher and 15 males. She wants the children to sit evenly in groups.

© R. I .

C.Publ i cat i ons

How many groups will she need •f orr evi ew pur posesonl y• if she wants the largest sized groups possible and how many children will be in each group?

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Number and algebra

There is an odd number of children in Miss Nolan’s class and she wants them to sit in groups. Miss Nolan realises the children can only sit ©R .

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C .Publ i cat i ons equally in groups of three or five.

•f orr evi ew pur posesonl y•

If class sizes cannot be bigger than 32 children, how many are in the class?

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Number and algebra

Albert is making a pattern with matchsticks.

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How many small triangles (including face-up and face-down triangles) will make a large triangle that is 10 small triangles in height?

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Number and algebra Albert is making a pattern with matchsticks.

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

How many matches will he need to make a large triangle that is 10 small triangles in height?

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Number and algebra George’s birthday party was on 17 May from 2 p.m. to 4 p.m. During the party, George spent 13 of the time playing indoor games with friends, 18 of the time opening gifts and 14 of the time eating. He spent the R. I .

C.Publ i cat i ons remaining time playing©outside.

•f orr evi ew pur posesonl y•

How many minutes in total did George spend opening gifts and playing inside?

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Extension

Number and algebra George’s birthday party was on 17 May from 2 p.m. to 4 p.m. During the party, George spent 13 of the time playing indoor games with friends, 18 of the time opening gifts and 14 of the time eating. He spent the R. I .

C.Publ i cat i ons remaining time playing©outside.

•f orr evi ew pur posesonl y•

For how many minutes did George play outside?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A B C GI D 4 2 + AHC F A B E © R. I .

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FrposeG H •f orr evi ew pu sonl y• 9

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D 6

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J

If the letters A–J represent a number from 0–9 inclusive, what number does J represent?

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Number and algebra A B C FDAEE 7 3 4 — CJJA I .

C.Publ i cat i ons G F B D© R.

FrposeG H •f orr evi ew pu sonl y•

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What numbers are represented by the letters F, G and J? R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The lady at the airport terminal weighed each item of luggage before it could be loaded onto the plane. Item A weighed 24.68 kg, item B weighed 26.27 kg, item C weighed 23.97 kg and item D weighed ©must R. I .

Cbe .Publ i cat i ons 26.99 kg. The heaviest items loaded first, continuing• to the smallest f o rr e vi ew pur posesonl y• items last.

Write the weights of each luggage item in descending order.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The lady at the airport terminal weighed each item of luggage before it could be loaded onto the plane. Item A weighed 16.06 kg, item B weighed 16.4 kg, item C weighed 16.97 kg and item D weighed ©must R. I .

C. Publ i cat i ons 16.90 kg. The heaviest items be •to f or r esmallest vi ew pur posesonl y• loaded first, continuing the items last.

Write the weights of each luggage item in ascending order.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Matthew and Sam love writing silly stories. Matthew writes 9 words per line and Sam writes 12 words per line. The boys alternate writing a line each before swapping.

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How many words will they have •f orr evi ew pur posesonl y• written in total at the end of their 16-line story?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra Matthew and Sam love writing silly stories. Matthew writes 9 words per line and Sam writes 12 words per line. The boys alternate writing a line each before swapping. © R. I .

C.Publ i cat i ons

•f or r evi ew pur posesonl y• If the boys wrote a story that was 3906 words long, how many lines did they each write?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The delivery man has to deliver parcels to five people on Russell Street. George lives at number 4492, Evan lives at number 4317, Sarah lives at number 4371, Marie lives at number 4409 Peter lives ©and R. I .

C .Pu bl i cat i ons at number 4420.

•f orr evi ew pur posesonl y• Write the house numbers in descending order.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

The delivery man has to deliver parcels to five people on Russell Street. George lives at number 4492, Sarah lives at number 4371, Peter lives at number 4420, Evan lives at number 4317 and Marie©lives R. I .

C.Publ i cat i ons at number 4409.

•f orr evi ew pur posesonl y• If the delivery man has just left 4309 Russell Street, write the names of the people in the order they will receive their deliveries.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A

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Find the value of A, B and C as fractions in their simplest forms.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A 2

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Find the value of A, B and C as mixed fractions in their simplest forms.

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Number and algebra

Four boys—Billy, Ben, Bradley and Brayden—are competing in a high jump competition. Billy jumped 1.04 m, Ben jumped 0.8 m, Bradley jumped 0.69 m and Brayden jumped 1.4 m. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

Write the boys’ names and the heights of each jump in ascending order.

R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

Four boys—Billy, Ben, Bradley and Brayden—are competing in a high jump competition. On day one, Billy jumped 1.04 m, Ben jumped 0.8 m, Bradley jumped 0.69 m and I .

C.Publ i cat i ons Brayden jumped 1.4 m. © R.

•f orr evi ew pur posesonl y•

What is the difference between the highest jump and the lowest jump?

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Number and algebra

Three girls are skip counting from 0–100. Jamie is skip counting in threes, Lucy is skip counting in sevens and Michele is skip counting in nines.

© R. I .

C.Publ i cat i ons Which number will they• all f osay? rr evi ew pur posesonl y•

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Three girls are skip counting from 0–100. Jamie is skip counting in fours, Lucy is skip counting in sixes and Michele is skip counting in eights.

© R. I .

C.Publ i cat i ons •f or r evi ew pur posesonl y• Which numbers will they all say?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

A farmer has 45 cows, 16 chickens and 30 sheep on his farm. The farmer collects 20 L of milk from each cow and six eggs from each chicken per week. The farmer receives nothing © R. I .

C.Publ i cat i ons from his sheep.

•f orr evi ew pur posesonl y•

How much produce will the farmer collect in total from the cows and the chickens each fortnight?

R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

A farmer has 45 cows, 16 chickens and 30 sheep on his farm. The farmer collects 20 L of milk from each cow and six eggs from each chicken per week. The farmer packs a dozen eggs into cartons and fills 150© L storage R. I .

C.Publ i cat i ons containers with milk.•f orr evi ew pur posesonl y• How many cartons and how many storage containers is he able to fill each week?

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Number and algebra

While playing ‘Guess the number’, the teacher gave the following clues: – It is made using the digits 2, 3, 4, 6 and 8 © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y• – It is an odd number

– It is between 86 200 and 86 400 What is the mystery number?

R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

While playing ‘Guess the numbers’, the teacher gave the following clues: – They are made using the digits 2, 3, 4, 6 and 8 © R. I .

C.Publ i cat i ons

•f o rr e vi ew pur posesonl y• – They are between 86 200 and 86 400 Which numbers are the mystery numbers?

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

Johnny is making tropical juice for his friends. He needs 12 a cup of pineapple juice, 18 of a cup of mango juice, 58 of a cup of orange © R. I .

C.Publ i cat i ons juice and 14 of a cup of apple juice.

•f orr evi ew pur posesonl y•

If one cup equals 250 mL, how many millilitres of tropical juice will Johnny make?

R.I.C. Publications® Prim-Ed Publishing

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Extension

Number and algebra

Johnny is making tropical juice for his friends. He needs 12 a cup of pineapple juice, 18 of a cup of mango juice, 58 of a cup of orange juice and © R. I .

C.Publ i cat i ons 1 of a cup of apple juice.

4

•f orr evi ew pur posesonl y•

If Johnny doubles the recipe, how many cups or fractions of cups will he need of each ingredient? Simplify all the fractions.

R.I.C. Publications® Prim-Ed Publishing

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Number and algebra

B

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C.Publ i cat i ons •f orr evi ew pur posesonl y•

Count in tenths on the number line to find the value of A, B and C as decimals.

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Extension

Number and algebra

A teacher used a ruler to draw a one-metre line on the board.

She marked 100 intervals of one-centimetre widths along the line. She then drew a second line measuring from 0 to the 6th© mark R. I .

C.Publ i cat i ons on the original line.

•f orr evi ew pur posesonl y• What is the length of the second line, written as a fraction and a decimal of one metre? Simplify the answer.

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Number and algebra

Jake had been collecting big sticks to make a hut. He collected 15 sticks each day; however, each night Jake noticed his dog had taken some of the sticks. On the first night, Jake’s dog took two sticks. On the .

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Cthird .Publ i cat i ons second night, he took three.© OnRthe f o rr evi ew pur posesonl y• night, he took four; and• so on.

Before Jake embarks on his eighth trip, how many sticks will he have?

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Number and algebra

Jake had been collecting big sticks to make a hut. He collected 15 sticks each day; however, each night Jake noticed his dog had taken some of the sticks. On the first night, Jake’s dog took two sticks. On the second night, he took three.

On © R. I .

Cthe .Publ i cat i ons third night, he took four;•and so on. f orr evi ew pur posesonl y• If Jake’s dog continues to take the sticks, on which morning will Jake have no sticks left at all?

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Number and algebra

The shaded area shows how many parts of a whole are selected.

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C.Publ i cat i ons •f orr evi ew pur posesonl y•

Add the two shaded areas shown. Write the answer as a fraction and as a decimal.

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Number and algebra

The shaded area shows how many parts of a whole are selected.

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

Subtract the two shaded areas shown. Write the answer as a fraction and as a decimal.

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Number and algebra

Sally is making cookies for her class party. She arranges them in columns and rows, with three cookies along the short edge and four cookies along the long edge of each tray.

© R. I .

C.Publ i cat i ons

If there are 30 children in the class •f orr evi ew pur posesonl y• and each child receives one cookie, how many trays of cookies will Sally need to put in the oven?

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Number and algebra

Sally is making cookies for her class party.

She arranges them in columns and rows, with three cookies along the short edge and four cookies along the long edge of each tray.

© R. I .

C.Publ i cat i ons If Sally makes six trays • off cookies, o rr evi ew pur posesonl y• how many whole cookies will each of the thirty children receive and how many leftover cookies will there be?

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Number and algebra

Jasmine loves to visit the beach. She always spends 24 of the visit building sandcastles and digging in the sand, 1 of the visit swimming in the sea, 8 2 of the visit collecting shells © R. I .

C.Publ i cat i ons 8 1 and 16 of the time eating.

The •f o rr evi ew pur posesonl y• remaining time is spent doing other things.

What does Jasmine spend most of her time doing when at the beach?

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Number and algebra

Jasmine loves to visit the beach. She always spends 24 of the visit building sandcastles and digging in the sand, 2 of the visit swimming in the sea, 8 1 of the visit collecting shells © R. I .

C.Publ i cat i ons 8 1 and 16 of the time eating.

The •f o rr evi ew pur posesonl y• remaining time is spent doing other things.

Order the fractions from smallest to largest.

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Number and algebra

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

What is the value of the pentagon?

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Number and algebra

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

What is the value of the pentagon?

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Number and algebra Craig is paving his patio with bricks. The diagram he is following uses large and small square bricks and rectangular bricks. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

How many large square bricks and how many small square bricks will Craig need to cover an area of 16 m2?

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Extension

Number and algebra Craig is paving his patio with bricks. The diagram he is following uses large and small square bricks and rectangular bricks. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

How many rectangular bricks will Craig need to cover an area measuring 12 m by 5 m?

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Number and algebra

For a roast dinner, Sonia bought 8 large potatoes weighing a total of 1.2 kg, 4 medium onions weighing a total of 0.44 kg, half of a © R. I .

C.Publ i cat i ons pumpkin weighing 1.06 kg •f o evi ew pur posesonl y• and 6 carrots weighing arr total of 0.31 kg.

What is the total weight of her purchase?

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Extension

Number and algebra

For a roast dinner, Sonia bought 8 large potatoes weighing a total of 1.2 kg, 4 medium onions weighing a total of 0.44 kg, half of a pumpkin weighing 1.06 kg and 6 carrots weighing a total of 0.31 kg. She also bought meat to roast weighing 2.7 kg.

What is the weight © R. I .

C.Publ i cat i ons difference, in kilograms, •f orr evi ew pur posesonl y• between the meat and the vegetables?

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Number and algebra – Answers Card 1 Extension

59 283 58 189

Card 6 Extension

9641 13 469, 13 496, 13 649

Card 12 Extension

55 minutes 35 minutes

Card 2

27 of each coloured bead 24 blue beads

Card 7 Extension

21 670 2065 small boxes, 7112 medium boxes, 12 839 large boxes

Card 13 Extension

5 F = 1, G = 8, J = 6

Card 14

26.99 kg, 26.27 kg, 24.68 kg, 23.97 kg 16.06 kg, 16.4 kg, 16.90 kg, 16.97 kg

Extension Card 3

Extension

Card 4 Extension Card 5 Extension

Mikayla is 18 years old, Jack is 9 years old and Sam is 3 years old 1 2 2

times older than Mikayla, 5 times older than Jack and 15 times older than Sam 1460 individual chocolates 3 4

of a box

238.96 seconds 5.26 seconds

7 8

Card 8

eaten, 1 4

1 8

left over 3 4

Extension

left

Extension

1 eaten, 1 over

Extension

Eight hundred and thirty-four

Card 16

Card 10

Extension

Extension

2 groups of 12 children 15 children

Card 17

A=

Card 11 Extension

100 small triangles 165 matchsticks

Extension

A = 2 8 , B = 2 16 ,

C=28

© R. I .

C.Pub l i c t i o n s 168 Card 15 a words Extension 186 lines each 758rr Card 9 •f o evi ew pur posesonl y •

,B= 1

Card 19 Extension

63 24, 48, 72, 96

Card 20

1800 L of milk, 192 eggs 8 cartons, 6 storage containers

Extension

4492, 4420, 4409, 4371, 4317 Evan, Sarah, Marie, Peter, George 1 8

Extension

Bradley 0.69 m, Ben 0.8 m, Billy 1.04 m, Brayden 1.4 m 0.71 m

Card 18

1 4

,C= 9

Card 21 Extension

86 243 86 234, 86 243, 86 324, 86 342

1 2

7

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Number and algebra – Answers Card 22 Extension

375 mL 1 cup pineapple juice, 1 cup mango juice, 4 1

1 4 orange juice,

Card 23 Extension

1 2

cup apple juice

A = 1.7, B = 3.3, C = 4.9 6 100

m (or

3 50

m),

0.06 m

Card 24 Extension

70 sticks The morning of the 28th day

Card 25 Extension Card 26 Extension

63 100 3 100

Card 27

Building sandcastles and digging in the sand

Extension

1 16

Card 28 Extension

8 12

Card 29

Extension

4 large square bricks and 16 small square bricks 60 rectangular bricks

Extension

0.31 kg

1 8

,

,

2 8

,

2 4

© R. I .

C.Publ i cat i ons o rkgr evi ew pur posesonl y• Card 30 •f 3.01

, 0.63 , 0.03

3 trays 2 each, 12 leftover cookies R.I.C. Publications® Prim-Ed Publishing

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