Problem-Solving Strategies & Skills – Number & Algebra: Year 3

1

Number and algebra

Alex is selling cupcakes at the local market. He baked 212. By mid-morning he had sold 23 and by lunchtime the © R. I .

C.Publ i cat i ons total sold was 112!

•f orr evi ew pur posesonl y•

How many cupcakes does he have left to sell?

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

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Extension

Number and algebra

Alex is selling cupcakes at the local market.

He baked 350. By mid-morning he had sold 89 and by lunchtime the total sold was 249!

At the end of the day he had 2. cupcakes ©only R. I .

C Publ i cat i ons remaining.

•f orr evi ew pur posesonl y• How many cupcakes did he sell after lunch?

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

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Number and algebra

Cassie has a large collection of marbles.

She has three tens, two hundreds and nine ones more than Rosie,© who has four R. I .

C.P ubl i cat i ons hundred and two.

•f orr evi ew pur posesonl y• How many marbles does Cassie have?

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Extension

Number and algebra

Cassie’s ant farm is growing bigger every day.

She started with four hundred and two ants, but now she has six ones, three thousands © R. I .

C.Publ i cat i ons and two tens more.

•f orr evi ew pur posesonl y•

How many ants are there now?

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Number and algebra

Monique is a very odd manager.

She sets her business meetings on very specific days throughout the year.

The first meeting was on the day of the year, ©6th R. I .

C.P ub l i ca t i ons and next on the 13th day, followed by the •f orr evi ew pur posesonl y• 27th day of the year, and the 55th day.

How many more meetings will she have this year, and on what number days?

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

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Extension

Number and algebra

Monique is a very odd manager.

She has scheduled meetings on 20 February, 15 April and 11 June.

© R. I .

C.Publ i cat i ons How many more meetings will she have for •f or r ev i ew pur posesonl y• the rest of the year and when will they occur?

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

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4

Number and algebra

Leigh is helping her father carry freshly picked nuts off the farm. Each step she takes causes her to lose some of the 360 nuts from her overflowing basket.

She manages to make it back to the car in 18 steps with 324 nuts left in her basket. © R. I .

C.Publ i cat i ons

•f orr evi ew pur posesonl y•

How many nuts did she drop at each step if she dropped an equal amount each time?

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Extension

Number and algebra

Leigh is helping her father carry freshly picked nuts off the farm. Each step she takes causes her to lose some of the 587 nuts from her overflowing basket. She manages to make itat © R. I .

C .P ubl i c i ons back to the car with 479•nuts left in her basket. f orr evi ew pur posesonl y• How many steps did she take back to the car if she drops four nuts at each step?

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

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5

Number and algebra

Isabella cut her birthday cake into six slices.

If three people have one slice and one R. I .

C.P l i cat i ons person has two slices, what©fraction ofub the orr evi ew pur posesonl y• whole cake is left over?•f

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Extension

Number and algebra

Isabella has two birthday cakes of different flavours. She cuts each cake into 21 slices. © R. I .

C.Publ i cat i ons 5

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If everyone ate 7 of each cake, how many slices are left altogether?

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6

Number and algebra

Each day, Lola goes to the local shop and asks for a certain number of lollipops. On Monday she buys 5, on Tuesday she buys 16, on Wednesday she buys 27 I .

C.Publ i cat i ons and on Friday she buys 49. © R.

•f orr evi ew pur posesonl y•

How many did she buy on Thursday?

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Extension

Number and algebra

Each day, Lola goes to the local shop and asks for a certain number of lollipops. On Day 1 she buys one lollipop, on the next two days she buys two lollipops each day, and on the next three days she buys three © R. I .

C.Publ i cat i ons lollipops each day.

•f orr evi ew pur posesonl y•

On what day will Lola first buy 6 lollipops?

How many lollipops will Lola have in total after she first buys 6 lollipops?

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Number and algebra

The pet store has 46 new puppies, but they only have five beds for them to sleep on.

What is the most puppies they can fit equally on each bed, and how many puppies won’t have a bed?

© R. I .

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

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Extension

Number and algebra

The pet store has 47 new birds.

They need to be placed into four separate cages.

Three of the cages can hold the same number of ©three R. I .

C. Publ i cat i ons birds, and one cage can hold more birds orr evi ew pur posesonl y• than the other cages. •f How many birds can fit in each cage?

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Number and algebra

The manager of a grocery store counts his profits every day. On Monday, he made three hundreds, two ones and six tens. On Tuesday, he made four tens, eight ones, two ©On R. I .

C.Publ i cat i ons hundreds and one thousand.

Wednesday, •f orr evi ewand pur posesonl y• he made nine ones, two thousands nine tens.

What was the highest amount of money he made?

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Extension

Number and algebra

The manager of a grocery store counts his profits every day. On Thursday, he made six thousands, five tens and eight hundreds. On Friday, he made two tens of thousands, six hundreds, one ten and two thousands. On © Rtwo .

I .

C. Pub l i cat i ons Saturday, he made seven tens, tens of •f or r ev i ewones. pur posesonl y• thousands, two thousands and nine What was the difference between the highest and lowest amounts he made?

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Number and algebra HAPPY

A local lemonade stand is selling cups of lemonade in different sizes. Max buys half 1 a cup, Betty buys 5 of a cup and Danny © R. I .

C.Publ i cat i ons buys an eighth of a cup.

STAND

•f orr evi ew pur posesonl y•

Who has the most lemonade?

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Extension

Number and algebra

HAPPY

A local lemonade stand is selling cups of lemonade in different sizes.

2 Max buys 8 of a cup, Betty buys one ©aRsixth .

I .

C.P i cat i ons quarter of a cup, Danny buys ofub al 4 •f rr evi ew pur posesonl y• aocup. cup and Missy has 16 of

STAND

Who has the least lemonade?

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Number and algebra

Zorax lives on a planet that is 123 light years away from Earth. Zimba lives on a planet that is 49 light years further away from Earth than Zorax’s planet.

Klaxo lives on a planet that is 21 light years closer to Earth than Zorax’s planet.

Who lives the furthest from Earth, and by how many more light years © R. I .

C.Publ i cat i ons than the next planet?

•f orr evi ew pur posesonl y•

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Extension

Number and algebra

Zorax lives on a planet that is 312 light years away from Earth. Zimba lives on a planet that is 113 light years from Earth. Klaxo lives on a planet that is 134 light years further away from Earth than Zimba’s planet. Rix lives on a planet that is 25 light years further away from Earth than Klaxo’s planet.

© R. I .

C.Publ i cat i ons

Who lives the furthest from •f orEarth, r evi ew pur posesonl y• and by how many more light years than the third furthest?

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

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11

Number and algebra

The local dance school received a donation of 355 pairs of ballet shoes.

If there are 54 children enrolled in the © R. I .

C .Publ i cat i ons school, and each child can one ofos •f ohave rr evi ew pair pur p esonl y• shoes each year, how many full years will the donation last?

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Extension

Number and algebra

The local dance school received a donation of 355 pairs of ballet shoes. Each child needs 2 pairs of shoes, and the number of children enrolled in the school is.

85 aPyear. ©R I .

C. ubl i cat i ons

•f orr ev i ewand pur posesonl y• How many years will the shoes last, how many shoes would be left over?

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

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Number and algebra

What is the sum of every odd number between 10 and 20, plus the©sum of. every R. I .

C Publ i cat i ons even number between • 59f and 69? o rr e vi ew pur posesonl y•

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Extension

Number and algebra

What is the sum of every odd number between 60 and 70, plus the sum of every even number ©R .

I .

C. Pu bl i ca t i ons between 129 and 139, less the sum of every odd •f orr evi ew pur posesonl y• number between 20 and 30?

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Number and algebra

Fiona ordered one mushroom pizza for her and her friends to enjoy. Drake ate two slices, Jen ate three slices and Fiona had four slices. © R. I .

C.Publ i cat i ons 1

•f orr evi ew pur posesonl y•

If there is 4 of the pizza left, how many slices were there to begin with?

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Extension

Number and algebra

Fiona ordered one mushroom pizza, one cheese pizza and one chicken pizza. She 1 1 ate 8 of the mushroom pizza, 2 of the 1 cheese pizza and 4 of the chicken © R. I .

Cpizza. .Publ i cat i ons

•f orr evi ew pur posesonl y•

What is the total amount of pizza left over?

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

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Number and algebra

Harry loves reading books. He often finishes 5 books in a week! He started reading a new book. By Day 1 he had read 10 pages.

By the end of the second day he had read 6 more pages. At the end of Day 3 he read © R. I .

C.Publ i cat i ons 36 pages in total, and by the fourth day he orr evi ew pur posesonl y• read another 17 pages.•f If Harry wants to read 70 pages by the end of the week, how many pages does he have left to read?

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

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Extension

Number and algebra

Harry loves reading books. He often finishes 5 books in a week! He started reading a new book. By Day 1 he had read 12 pages. By the end of the second day he had read 11 more pages. At the end of Day 3 he read 39 pages in total, and by © R16 .

I .

C .Publ i cat i ons the fourth day he read another pages.

•f orr evi ew pur posesonl y•

If the book is 195 pages long, and he reads 20 pages a day from Day 5 onwards, how long will it take Harry to finish the book?

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

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Number and algebra

Kesha is expecting 35 friends at her birthday party.

She needs to set up tables for the event but isn’t sure how many tables she needs or how many people to place at each table.

How can Kesha arrange her© tables R. I .

Cso .Pthat ubl i cat i ons there is an equal number ofr people •f o r evi ewatpeach ur posesonl y• table?

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Extension

Number and algebra

Kesha is expecting 36 friends at her birthday party.

She wants to set up tables for the event so that there are four people at each table. She also wants to decorate each table with balloons and vases of flowers. She has 27 flowers © R. I .

C.Publ i cat i ons available in total, and 45 balloons.

•f orr evi ew pur posesonl y•

How many flowers will be in each vase, and how many balloons will be at each table?

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Number and algebra

Milton baked muffins for his school fete. He made two batches with a baking tray that holds three rows of five muffins, and two batches with a baking tray that four © Rholds .

I .

C.P ubl i cat i ons rows of three muffins. •f orr evi ew pur posesonl y• How many muffins did Milton make in total?

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Extension

Number and algebra

Milton baked biscuits for his school fete.

He used a baking tray which holds four rows of three biscuits to make three chocolate-chip batches and four shortbread He had ©batches.

R. I .

C.Pu bl i cat i ons some chocolate-chip mixture left, which he used •f orr evi ew pur posesonl y• to make a further two rows of biscuits.

How many biscuits are there altogether?

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Number and algebra

JoJo’s fruit shop is selling baskets of fruit. 15 baskets of fruit are sold, 3 so he managed to sell 5 .

© R. I .

C.Publ i cat i ons f o rr ev i ew pur posesonl y• How many baskets did • he have to begin with?

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Extension

Number and algebra

JoJo’s fruit shop is selling baskets of fruit. Each basket contains 10 pieces of fruit. He manages to sell 18 baskets of fruit, but he still ©R .

I .

C.Publ i cat i ons 3 has 5 left.

•f orr evi ew pur posesonl y• How many baskets did he have to begin with?

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Number and algebra

Bongo the clown likes to have a certain number of balloons in different colours. He always has 43 blue balloons. He wants 15 less red balloons than blue balloons, and R. I .

C.Publ i cat i ons 28 less green balloons than© blue f or r evi ew pur posesonl y• balloons. He also wants•19 more orange balloons than blue balloons.

How many balloons does he have in total?

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Extension

Number and algebra

Bongo the clown likes to have a certain number of balloons in different colours.

He always has 68 blue balloons. He wants 46 less red balloons than blue balloons, and 33 more green balloons than blue © R. I .

C.Publ i cat i ons balloons. He also wants 19 more orange •f orr evi ew pur posesonl y• balloons than red balloons.

What is the difference between the number of orange balloons and green balloons?

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Number and algebra

There are six houses on Lizzy’s side of the street. Each house has four windows and each window has four © R. I .

C.Publ i cat i ons panes of glass.

•f orr evi ew pur posesonl y•

How many panes are there in total?

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Extension

Number and algebra

On Lizzy’s street there are 12 houses altogether. Each house has three trees planted in front of it, and each tree has five large R. I .

C.Publ i cat i ons branches. On each branch, © two •f orr evi ew pur posesonl y• birds sit and chirp all morning.

How many chirping birds in total are in the trees?

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Number and algebra

Jamie is trying to find his favourite radio station.

The frequency of his favourite radio station is three decimal 88 FM 87 © R .

I .

C .

P u b l i c a t i o n s spaces after the radio station •f orr evi ew pur posesonl y• shown.

89

90

What is the radio frequency Jamie is trying to find, written as a decimal?

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Extension

Number and algebra

Jamie is trying to find his favourite radio station. The frequency is greater than 95.1 but less than 96.2. The numerals in the frequency add © R. I .

C.Pub i ca i ons 95 FMl 94t up to 20.

•f orr evi ew pur posesonl y•

96

97

What frequency is Jamie’s favourite radio station?

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Number and algebra

A mouse is scampering up a slippery drainpipe. Each day the mouse climbs 6 metres. At night when the rain starts falling the poor mouse slips© down R. I .

C.Publ i cat i ons 1 metre.

•f orr evi ew pur posesonl y• How high has the mouse climbed after nine days?

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Extension

Number and algebra

A spider is using its silk threads to pull itself up a slippery drainpipe. On the first day the spider climbed 5 metres, and each day it climbs 1 metre higher than the day before. At night the spider rests and drops down © R. I .

C.Publ i cat i ons 2 metres.

•f orr evi ew pur posesonl y• How many days will it take the spider to reach the top of the drainpipe, which is 33 m high?

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Number and algebra

Farmer Joe looks after many animals. He has 14 cows, 12 horses and 23 ducks.

© R. I .

C.Publ i cat i ons

If Farmer Joe counted 148 legs in total, •f orr evi ew pur posesonl y• how many legs did he miss?

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Extension

Number and algebra

Farmer Joe looks after many animals.

He has 87 ducks and 15 pigs. He also has 48 chickens and horses combined. There © R. I .

C ubl i cat i ons are three times as many chickens as.P there are horses.

•f orr evi ew pur posesonl y• How many animal feet in total are on his farm?

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Number and algebra

Farmer Tess has three henhouses for her different hens. A red hen sits in one, a black hen in the other and a white hen in the last house. Each day the black hen lays five eggs, R. I .

C.P ubl i cat i ons the red hen lays seven eggs© and the white •f orr evi ew pur posesonl y• hen lays four eggs.

How many days will it take for Farmer Tess to collect a total of 80 eggs?

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

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Extension

Number and algebra

Farmer Tess has three henhouses for her different hens. A red hen sits in one, a black hen in the other and a white hen in the last house.

Each day the black hen lays six eggs, the red hen lays five eggs and the white hen lays seven eggs. Each afternoon a sly fox sneaks into the ©R .

I .

C.Pu bl i c at i ons henhouses and takes one ofrthe red •f o r evi ewhen’s pur peggs osesonl y• and two of the black hen’s eggs.

Farmer Tess needs at least 253 eggs to sell at the local market. How many days will it take?

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

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Number and algebra

Over the weekend, Grandma baked twenty-four cookies for her friends and family. She gave one-sixth of the cookies to her granddaughter Maisy. Half of the remaining cookies went to her old friend Tilly, who gave half to her husband. Tilly then gave one-fifth of her cookies to her daughter.

© R. I .

C.Publ i cat i ons How many cookies did • Tilly’s f orr evi ew pur posesonl y• daughter receive?

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Extension

Number and algebra

Over the weekend, Grandma baked twenty-four cookies for her friends and family. She gave one-sixth of the cookies to her grandson Xavier.

Two-quarters of the remaining cookies went to her old friend Tilly, who gave half to her husband. Tilly then gave one-fifth of her cookies to her daughter, and then a quarter of the rest to her son.

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• How many cookies does Grandma have left over?

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

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Number and algebra

Jack’s age is two tens and three ones. Jenny’s age is one ten and five ones. Jemima’s age is two © R. I .

C.Publ i cat i ons tens and two ones.

•f orr evi ew pur posesonl y•

Who is the oldest, and by how many years?

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Extension

Number and algebra

Jack’s age is nine tens and one one. Jenny’s age is one hundred and two ones.

Jemima’s age is eight tens © R. I .

C.Publ i cat i ons and nine ones.

•f orr evi ew pur posesonl y• Who is the youngest, and by how many years?

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Number and algebra

R. I .

CA .P ubl i cat i ons A metal pipe is cut into ten © pieces. construction worker uses three pieces.

•f orr evi ew pur posesonl y• What fraction of the pipe is left over? Write your answer as a decimal number.

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

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Extension

Number and algebra

R. I .

CA .P ubl i causes t i ons A metal pipe is cut into ten © pieces. builder four pieces and a •f orr evi ew pur posesonl y• plumber takes two pieces.

What fraction of the pipe is left over? Write your answer as a decimal number.

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

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27

Number and algebra

Izzy and his two friends decided to explore the hiking trails around their neighbourhood.

2 On the first day they hiked 3 of the trail 3 and on the second day they hiked 5 of the I .

C.Publ i cat i ons 4© R. trail. On Day 3 they hiked 7 of the trail and •f orr evi ew pur posesonl y• 5 continued to hike 9 of the trail on the fourth day.

If they follow the trend, how much of the trail will they hike on Day 10?

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

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Extension

Number and algebra

Izzy and his two friends decided to explore the hiking trails around their neighbourhood. On the first day they hiked 1 2 of the trail and on the second day they © R. I .

C.Publ i cat i ons 1 hiked 4 of the trail. On Day 4 they trekked •f orr evi ew pur posesonl y• 1 of the trail.

16 If they follow the trend, how much of the trail will they hike on Day 7?

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Number and algebra

Ethan loves to eat chocolate. He buys one box of milk chocolates and one box of white chocolates. The box of milk chocolates contains ten rows of 4 pieces, and the box of white chocolates contains 9 rows of 3 pieces.

© R. I .

C.Publ i cat i ons He eats two rows from• each box, and his friends f orr evi e w pgives ur pos es onl y• four rows of the milk chocolate and six rows of the white chocolate.

How many pieces of chocolate are left altogether?

WH

COLITE ATE

CHO

KLATE L I M CO

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Extension

Number and algebra

Ethan loves to eat chocolate. He buys one box of milk chocolates and one box of white chocolates.

The box of milk chocolates contains ten rows of 4 pieces, and the box of white I .

C.Publ i cat i ons chocolates contains 9 rows © of R 3. pieces.

•f orr evi ew pur posesonl y•

He wants to eat the same number of pieces of both white and milk chocolate. What are the combinations of rows of each he should eat?

WH

COLITE ATE

CHO

KLATE L I M CO

CHO

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

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29

Number and algebra

Jon has taken a ticket in line at the bank. His number is M659. Another customer has M076, and two others have M490 and M507.

© R. I .

C.Publ i cat i ons If the tickets were given•out f orin r evi ew pur posesonl y• ascending order, who will be called up first and what place in the queue is Jon?

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

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Extension

Number and algebra

Jon has taken a ticket in line at the bank.

His number is K1031. Another customer has K9099, and two others have K8987 R. I .

Cout .Pu bl i cat i ons and K2006. The tickets were©given in •f orr evi ew pur posesonl y• descending order.

What ticket will be called second, and where is Jon placed in the queue?

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

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30

Number and algebra

A bricklayer is laying bricks in the shape of a pyramid.

His first pyramid has two steps and looks like this:

© R. I .

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

How many bricks will he require to build a pyramid with five steps?

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

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Extension

Number and algebra

A bricklayer is laying brick steps for various houses.

His first set of steps looks like this:

© R. I .

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

How many bricks will he require in total for seven steps?

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

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Number and algebra – Answers Card 1 Extension

100 99

Card 8 Extension

2099 15 760

Card 2 Extension

641 3428

Card 9 Extension

Max Danny

Card 3 Extension

2, on day 111 and 223 3 more on 8 August, 6 October, 5 December

Card 10

Card 4 Extension

2 27

Zimba, by 49 light years Zorax by 40 light years

Card 5 Extension

1 6

12 slices

Card 6 Extension

38 Day 16. Total of 61 lollipops

Card 7

9, 1 puppy won’t have a bed 11 and 14

Extension

Extension

Extension

7 tables of five, or 5 tables of seven 3 flowers, 5 balloons

Card 16 Extension

54 90

Card 17 Extension

25 baskets 45 baskets

Card 18 Extension

148 balloons 60 balloons

Card 15

© R. I .

C.Publ i cat i ons Card 19 96 panes •f orr evi ew pu r poses onl y• Extension 360 birds

Card 11 Extension

6 years 2 years, 15 pairs left over

Card 12 Extension

395 870

Card 13 Extension

12 slices 1 17 8 or 2 8

Card 14 Extension

17 pages 11 days

Card 20 Extension

89.2 95.6

Card 21 Extension

45 metres 6 days

Card 22 Extension

2 legs 354 feet

Card 23 Extension

5 days 17 days

Card 24 Extension

1 cookie 10 cookies

Card 25 Extension

Jack, by one year Jemima, by two years

Card 26 Extension

0.7 0.4

Card 27 Extension

11 21 1 128

Card 28 Extension

19 3 rows of milk chocolate and 4 rows of white chocolate, or 6 rows of milk chocolate and 8 rows of white chocolate R.I.C. Publications® Prim-Ed Publishing

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Number and algebra – Answers Card 29 Extension Card 30 Extension

M076, Jon is 4th (last) K8987, Jon is 4th (last) 25 bricks 28 bricks

© R. I .

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

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