Quick Practice - Solving Problems

Learning objectives

Year 1: Pupils should be taught to:• Solve one-step problems that involve addition and subtraction using concrete objects, pictorial representations and missing number problems such as 7 = ? - 9.• Solve one-step problems involving multiplication and division by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Year 2: Pupils should be taught to:• Solve problems involving multiplication and division using materials, arrays, repeated addition and mental methods and multiplication and division facts including problems in context.• Solve problems in a practical context involving addition and subtraction of money of the same unit, giving change.

Year 3: Pupils should be taught to:• Solve problems including missing number problems using number facts and place value. More complex addition and subtraction.• Solve one-step and two-step questions (How many more? How many fewer?) using information from scaled bar charts, pictograms and tables.

Year 4: Pupils should be taught to:• Solve number and practical problems with increasingly large positive numbers.• Solve simple measure and money problems involving fractions and decimals to two decimal places.

Year 5 Pupils should be taught to:• Solve problems involving addition, subtraction, multiplication and division and a combination of these including understanding the meaning of the equals sign• Solve problems converting between units of time.

Year 6 Pupils should be taught to:• Solve problems involving addition, subtraction, multiplication and division.• Solve problems involving calculating and converting units of measure using decimal numbers up to three decimal places, where appropriate.

Each of these symbols equal a different number.

Use the table above to complete the sums.

Activity 1- Year 1

+

-

+ +

+

4. +

+

+

= 1

5.

7.

+ +

+ -6.

=

=

=

=

2.

+ ++ =1.

=

+3.

+

=

= 2 = 4 = 5

Activity 2a - Year 1

This array of balloons shows: four rows of balloons three columns of balloons.

This array can be written as a number sentence: 4 (rows) x 3 (columns) =12 balloons

Draw arrays of balloons to show the number sentences. Find the answer for each sentence.

Which array has the most balloons? ....................................

Which has the least?....................................

Number sentence = 5 x 2 Number sentence = 1 x 4

Number sentence = 3 x 5 Number sentence = 4 x 4

Answer =

Answer =

Answer =

Answer =

Activity 2b - Year 1

1. Roll two dice. 2. Multiply one of the numbers by 5 and multiply the other number by 2. 3. Add your answers together. Try to make the highest total each time.

Record your sums and answers in the table below.I threw ... I multiplied... Highest answer:

Example 2 and 4 2 x 2 and 4 x 5.

2 x 2 =44 x 5 =20

4 + 20 = 24

1.

2.

3.

4.

Activity 1a - Year 2

Link the pairs of numbers that can be multiplied together to make 24. The first one has been done for you. Which number is left?

Which number is left?

6 2 24

1 4 8

3 16 12

Answer as many of these questions as you can in 1 minute. Use a stopwatch to time yourself.

Set 1:

2 x 10 = 3 x 3 = 5 x 3 =

8 x 3 = 4 x 10 = 2 x 7 =

3 x 9 = 5 x 0 = 6 x 4 =

Set 2:

7 x 6 = 9 x 6 = 7 x 7 =

8 x 7 = 9 x 8 = 9 x 9 =

8 x 6 = 5 x 9 = 4 x 12 =

Ready... Set...Go!

00:00

Activity 1b - Year 2

Complete the cross-number puzzle. Show your working in the box at the bottom of the page.

1 2 3

4

5 6

7 8

9 10

Across:

1. 34 x 4 4. 51 x 8 5. 17 x 5 7. 61 x 4 9. 4 x 7 10. 17 x 4

Down:

1. 56 x 3 2. 8 x 8 3. 12 x4 6. 66 x 8 8. 23 x2

! Show your working here:

Wake up:

Activity 2a - Year 2

Make these money amounts using the fewest number of coins:

To make 27p I will use:

To make 49p I will use:

To make 61p I will use:

To make 84p I will use:

Wake up:

Activity 2b - Year 2

Solve these money problems. You will need to carry out at least two steps to get the answer. Show your workings in the box at the bottom of this page.

1. Sanjay has a 50p coin, a 20p coin and a 5p coin. How much more money does he need to buy a notebook costing 85p? Answer: .....................................

2. If you spent 24p on sweets and 35p on a comic, how much change would you have from £1? Answer: .....................................................

3. Mary has two 50p coins and a 10p coin. Ann has four 20p coins and a 5p

coin. How much more money does Mary have? Answer: ...................................

4. Ahmed empties his moneybox. He has five 10p coins, three 5p coins and two 2p coins. He loses one of each kind of these coins. How much does he have left? Answer: .....................................................

! Show your working here:

Activity 2

Activity 1a - Year 3

!

!

!

Answer: ...................................

Answer: ...................................

Answer: ...................................

Farmer Bell and Farmer Price own farms next to each other. Help them to solve these problems.

Calculate the answers in the boxes below. Show all your workings and how you have checked your answers.

1. Farmer Bell has 75 cows and Farmer Price has 139 cows. How many cows do they have altogether?

2. Farmer Price planted 365 potatoes in Daisy Field and 128 fewer in Clover Field. So how many potatoes did he plant in Clover Field?

3. Farmer Bell did have 147 sheep but he sold 55 at market. How many sheep does he have now?

Activity 2

Activity 1b- Year 3

Here are some more problems that Farmer Bell and Farmer Price need to solve. Can you help them?

Calculate the answers in the boxes below. Show all your workings and how you have checked your answers..

4. Farmer Price had 202 hens. At market he sold 43 and bought 36 new ones. How many hens does he have now?

5. Farmer Bell keeps 127 pigs in one field, 35 in another and 154 in another. What is the total number of pigs he keeps?

6. Farmer Price and Farmer Bell decide to put their apple harvests together. Farmer Bell picks 252 apples and Farmer Bell picks 169 apples. If 85 apples turn out to be rotten, how many good apples do they have to sell between them?

!

Answer: ...................................

!

Answer: ...................................

!

Answer: ...................................

Activity 2- Year 3Here is the attendance record for a children’s day nursery. The lighter coloured columns are for morning attendance and the darker coloured columns are for afternoon attendance.

24 2421

32

26

2123

25

30

19

0

5

10

15

20

25

30

35

Monday Tuesday Wednesday Thursday Friday

Num

ber o

f chi

ldre

n

Days of the week

Attendance record for a children’s day nursery

Attendance am Attendance pm

1. How many children attend on Wednesday morning? ........................................................

2. How many children attend on Thursday afternoon? .........................................................

3. Which morning is busiest? .......................................................................................................

4. Which afternoon is quietest? ..................................................................................................

5. Which day is busiest overall? ...................................................................................................

6. What is the difference in attendance on Monday and Friday mornings?.......................

7. How many children attend in total during the week? ........................................................

8. Can you explain the low attendance on Friday afternoon? ..............................................

9. What is the advantage of using a dual bar graph like this? ..............................................

Activity 1- Year 4

1. Round these numbers to the nearest thousand. Write the rounded number next to the original number

Colour in the rectangles with numbers that round to 3000. How many boxes have you coloured in? ...................

2. Complete the table below by rounding each price to the nearest whole pound. Then use the code in the box below to spell a popular shopping place.

2871 3004 34992399 3567 25603723 2905 25042487 3602 31232602 3333 3450

Price £4.80 £7.29 95p 35p £3.99 £2.38 £5.55 £4.30 £2.61 49p £7.56

Rounded Price

Letter

£0 £1 £2 £3 £4 £5 £6 £7 £8

E P M K R S A U T

3. Round each of these prices to the nearest 10p.

£2.57 rounds to £ ............

£2.22 rounds to £ ............

£2.65 rounds to £ ............

£2.49 rounds to £ ............

£2.83 rounds to £ ............

£2.34 rounds to £ ............

£2.12 rounds to £ ............

£2.96 rounds to £ ............

£2.09 rounds to £ ............

Code box:

Activity 2 - Year 4

Look at Tom's shopping bill and answer the questions below. Show your workings in the box at the bottom of the page.

Greens' Grocery Shop

Thank you for shopping at Greens

Free range eggs x 6 £1.32Carrots 250g £0.45Potatoes 5kg £3.50Oranges x 12 £1.98Yoghurt x 4 £0.88Kiwi fruits x 5 £1.20Apples 500g £0.75Grapes 100g £0.65Coffee 100g £1.95Tea bags (200) £1.99Milk 2 litres £1.60Beef joint 1.5kg £7.50

How much did Tom spend on fruit? ...........................................

How much is one egg? ..................................................................

What is the price of one kilogram of carrots? .........................

How much per kilogram are potatoes?......................................

How much does one yoghurt cost? ............................................

How much is one kiwi fruit? .........................................................

How much are grapes per kilogram? .........................................

How much is the total bill? ..........................................................

How much change would Tom have from £25? .....................

Give the change in the least number of coins ........................

! Show your working here:

Activity 2

Activity 1 - Year 5

Find the missing numbers in these equations. Write the answers in the boxes.

1. 3 + ? = 15

2. 14 - ? = 9

3. ? ÷ 2 = 6

4. 7 + ? = 13

Find the missing numbers shown by a letter in these equations.

Solve these equations. Remember the brackets should be done first.

1. (6 + 2) x 5 = h

2. (10 – 7) x 2 = w

3. 6 + (5 x 3) = r

5. ? x 4 = 32

6. 15 ÷ ? = 3

7. 9 x 2 = 14 + ?

8. ? - 5 = 16 ÷ 8

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

? = ........

4. 22 = 17 + m

5. 3s = 24

6. 2n + 3 = 11

4. 4 x (6 – 3) = y

5. (15 + 3) ÷ 6 = v

6. j = 2 x (28 ÷ 4)

1. 12 + z = 23

2. t – 15 = 9

3. 30 ÷ p = 10

Activity 2 - Year 5

Penny travels by train with Oldtown’s rugby team. They play in all the local towns.

Railway timetable

Oldtown 0700 0810 1015 1140 1330

Warmley 0720 0830 1035 1200 1350

Kingswood 0730 1045 1400

Grafton 0745 0850 1100 1220

Broadoak 0800 1115

Weston 0815 0915 1130 1245 1430

1. How long does it take the team to get from Oldtown to Weston if they take the 0700 train?

2. Which is the fastest train from Oldtown to Weston?

3. How long does it take to travel from Oldtown to Kingswood?

4. How many trains do not stop at Broadoak?

5. Which is the latest train arrving at Grafton before 1230?

6. Which trains stop at every station?

7. Trains also travel from Weston to Oldtown. The trains leave Weston at 0700, 0810, 1015, 1140 and 1330. They travel at the same speed and stop at the same stations. On a separate piece of paper, can you make a new timetable for the trains from Weston to Oldtown?

Activity 1 - Year 6

DessertsPavlova £5.20Cheesecake £4.75Ice cream £3.95

StartersGarlic mushrooms £4.95 Soup of the day £3.75 Pate £4.75

Main coursesFish and Chips £15.45Crab salad £14.25Spaghetti £13.99

Answer the following questions. Think about what operations you need to use. Show your workings on a seperate piece of paper.

1. Twelve friends go out for a meal. They hire five-seater taxis to take them to the restaurant. How many taxis will they need?

2. Kate orders soup, fish and chips and ice cream. How much does her meal cost?

3. What is the difference in price between the spaghetti and the crab salad?

4. What is the cost of four cheesecakes?

5. Work out the cost of a meal of garlic mushrooms, crab salad and pavlova.

6. How much would nine fish and chips cost?

7. How much more than the ice cream does the pavlova cost?

8. At the end of the meal, coffees are an extra £2.30 each. If all but three of the friends have coffee, how much do the group pay for the coffees?

9. The total bill comes to £270. If everyone shares the cost equally, how much does each person pay?

10. If the restaurant decided to make a service charge of 10% for parties over ten people, how much extra would the bill cost?

Activity 2 - Year 6

1. Convert these measurements so that they are in millimetres. Then put them in order of size from the shortest to the longest.

4.5cm = ...................... mm 3cm and 4mm = ...................... mm

7.9cm = ...................... mm

36cm and 8mm = ...................... mm

3.2cm = ...................... mm

kilograms grams2750

0.056320

0.008

millilitres litres680

3.1249

0.065

2. Write in the correct metric unit for each statement.

A giraffe is about 4.95 …………............. tall.

A fingernail is about 12 ……………........... wide.

Basketball nets are 300 …………….high

The distance from London to Leeds is about 195 ………….............

3. Fill in the empty spaces in these tables.