Why children do not perform as well as they could in maths tests

Not performing the correct calculation. For example, adding when subtraction is what needed. Carefully read the question! This is a massive problem. Please take extra care with questions that involve two steps. For example: 4 + 12 - 3. The answer is not 15. It involved both addition and subtraction.

Not lining up numbers correctly when using a column method.

To make sure you line up numbers correctly, write: o above the ones column; t above the tens column; h above the hundreds column; th above the thousands column, 100th; above the hundred thousands column; m above the millions column.

If the numbers have a different number of digits, write a 0 in place of where a digit would be so that the numbers end up having the same number of digits. 

Example:

4568 - 358 becomes 4568 - 0358.

Not checking effectively

Making simple mistakes (e.g. adding, subtracting, multiplying or dividing) and coming up with the incorrect answer. Check every question has been answered. Put a tick by each page number when you have finished answering the paper.

A very effective checking system is to cover up each answer. Answer the question again without looking at what you wrote before. 

Not estimating

Estimate every answer before answering the question. Rounding is a key part of estimation. Compare your answer with the estimate to make sure your answer seems reasonable.

Working too Slowly

If you know your times tables and the inverse for each of them e.g. 3 x 8 = 24 and 24 divided by 3 = 8, then you can answer much of the test paper very easily. If you have time, you might use repeated addition to work out the answer. For example, 4 x 6 is the same as: 

1) 4

2) 4 + 4 = 8

3) 8 + 4 = 12

4) 12 +4 = 16

5) 16 + 4 = 20

6) 20 + 4 = 24.

See Times Tables for help with learning these.

Not knowing what squared means. Squared is represented by a 2 in a small font that is written above the line. 

5² 

Not knowing what cubed means. Cubed is represented by a 3 in small font that is written above the line.

4³ means 4 x 4 x 4.

When a question asks you to multiply by 0, not giving the answer: 0. Anything multiplied by zero gives the answer: zero.

Not writing the answer in the box provided.

Not knowing the difference between 'factor' and 'multiple'

A factor cannot be greater than the number you start with. e.g. A factor of 6 cannot be larger than 6. A multiple on the other hand, cannot be smaller than the number you start with e.g. the factors of 10 are all 10 greater.

Types of Maths Questions

In my experience, it is the Reasoning paper that children find most difficult. Below are some examples of reasoning questions that children in Year 5 or 6 might encounter: Step-by-step answers are below the questions section:

David is 1.5m tall.

Eva is 24 cm shorter than David.

Frank is 17 cm taller than Eva.

How tall is Frank?

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James buys four pears for £2.72.

James sells three pears for £1.30 each.

How much profit does James make?

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A train travels at 40 mph. It travels for 45 minutes. How far does the train travel?

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Alex's book is 230 pages long. He has read 60% of it. How many pages has he read? 

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Sunil throws a tennis ball 17.4m. Nina throws a tennis ball 16cm further. How far did Nina throw the tennis ball?

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The school librarian wants to buy shelves for books. A bookshelf holds 16 books. The librarian has 215 books. How many shelves will she need to buy to hold all the books?

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At Alpha Sports a Super Score tennis cricket bat costs £55.00

At Beta Sports, a Super Score cricket bat costs £102 but they have a sale at which everything is 40% off. 

At which shop is the cricket bat the cheapest? 

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Emily owns a bag of marbles. All the marbles are either red, green or blue. The colours have the ratio 5 red : 3 green: 1 blue.

Emily has a total of 72 marbles.

How many of Emily's marbles are green?

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Zara is thinking of a number.

The number is < 40 >90.

The two digits that form it total 9.

The number is a square number.

What number is Zara thinking of?

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What are the common factors of 36 and 20?

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Put the following numbers in order from largest to smallest:

4.5, -6.8, 4.05, - 6.09, 5.45, 

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In the Shah family there are 3 adults and Prisha and Saanvi, both aged 10, Umar, age 8, Asher aged 6 and Ranbeer aged 3. They all want to go to the zoo.

Adult tickets are £16.75 each.

Tickets for children (aged 0-16) are £9.50 each.

A family ticket (for 2 adults and 2 people aged 0-16) costs £42.00

What is the cheapest way for the family to go to the zoo? What change would they get from £100?

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How many minutes is 2/3 of 2 hours?

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What fraction of 3 hours is 35 minutes?

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Explain the difference between regular and irregular shapes

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What is the value of 'a' if 4a + 2 = 14?

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Ranbeer bought 3 cakes and bottles of water for £2.05.

Alfie bought 2 cakes and 2 bottles of water for £1.70.

What is the total cost of 1 bottle of water and 1 cake?

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The temperature in Toronto was -4 degrees Celsius. It fell by 3 degrees. What did the temperature become?

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What are the next three numbers in the sequence?

13, 10, 7, 4, ___, ___, ___

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Complete the gaps in the sequence?

4, ___, 16, 32, ____, 128, 256, ____

Tickets to go bowling are £4.80 each. £1728 worth of tickets are sold. How many tickets were purchased?

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Here are the ingredients for chocolate ice-cream

Cream 400 ml

milk 500 ml

egg yolks 4

chocolate 120g

sugar 100g

Stefan only has 300 ml of cream. How can he still make ice-cream?

STEP-BY-STEP ANSWER

Step 1: Think of this as a fraction. 300 (ml of cream)/400 (ml of cream). 

Step 2: Simplify 300/400 to 3/4 by dividing both the numerator and the denominator by 100.

Step 3: Divide the 120 (g of chocolate) by 4, which gives: 30.

Step 4: Multiply the answer to Step 3 (30) by the numerator from 3/4. This produces 90.

Step 5: The Remember the units (g) so the final answer is 90g.

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QUESTION TOPICS COMING SOON

Formulae

Symmetry

Translation

How many degrees has X shape been rotated?

Algebra

Proportion

Calendars

Pictographs

Other topics:

How to find the area of a rectlinear (composite) shape

Carroll Diagrams

Venn Diagrams

Algebra

Interpret tally charts

4-quadrant coordinates

How much less did X pay than Y.

Number patterns

Speed/distance time

Describe the journey (based on a graph)

What is the missing angle?

Volume of a cube

Put the following fractions into order of size (smallest to largest): 4/5, 7/10 and 2/3

Match the following decimals, percentages and fractions.

Tip: It is extremely worthwhile learning the equivalent fractions, decimals and percentages for some of the more common fractions e.g. 1/2 = 0.5 or 50%, 1/4 = 0.25 or 25%, 1/5 = 0.2 or 20%.

Nets

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David is 1.5m tall.

Eva is 24 cm shorter than David.

Frank is 17 cm taller than Eva.

How tall is Frank?

STEP-BY-STEP ANSWER

Step 1: Convert 1.5m into cm (150 cm)

Step 2: Subtract 17 from 150.

Step 3: Add 17 to the answer to Step 2.

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James buys four pears for £2.72.

James sells three pears for £1.30 each.

How much profit does James make?

STEP-BY-STEP ANSWER

Step 1: Convert the pounds into pence. (272 and 130)

Step 2: Multiply the 130 by 3 (390)

Step 3: Subtract  272 from 390. The answer is 118p.

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A train travels at 40 mph. It travels for 3/4 of an hour. How far does the train travel?

STEP-BY-STEP ANSWER

Step 1: Convert an hour into minutes (60)

Step 2: Find 3/4 of 40 by dividing 40 by the denominator (4). 

Step 3: Multiply the answer to Step 2 by the numerator (3). 

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Alex's book is 230 pages long. He has read 60% of it. How many pages has he read? 

STEP-BY-STEP ANSWER

To find 60% divide the amount by 10 and multiply the answer by 6.

Step 1: Find 10% of the book by dividing 230 by 10.

Step 2: Multiply the answer to Step 1 by 6.

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Sunil throws a tennis ball 17.4m. Nina throws a tennis ball 16cm further. How far did Nina throw the tennis ball?

STEP-BY-STEP ANSWER

Step 1: Convert 17.4m into cm by multiplying 17.4 by 100 (1740).

Step 2: Add 16 to 1740. The answer is 1756cm.

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The school librarian wants to buy shelves for books. A bookshelf holds 16 books. The librarian has 215 books. How many shelves will she need to buy to hold all the books?

STEP-BY-STEP ANSWER

Step 1: Divide the number of books (215) by the number of books that a shelf holds (16). There is a remainder.

Step 2: Round up the answer since you can't buy part of a shelf.

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At Alpha Sports a Super Score tennis cricket bat costs £55.00

At Beta Sports, a Super Score cricket bat costs £102 but they have a sale at which everything is 40% off. 

At which shop is the cricket bat the cheapest? 

.....

Emily owns a bag of marbles. All the marbles are either red, green or blue. The colours have the ratio 5 red : 3 green: 1 blue.

Emily has a total of 72 marbles.

How many of Emily's marbles are green?

STEP-BY-STEP ANSWER

Step 1: Add up the number of marbles in the ratio (5+3+1 = 8)

Step 2: Divide the number of marbles (72) by the 8 (from Step 1)

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Zara is thinking of a number.

The number is < 40 >90.

The two digits that form it total 9.

The number is a square number.

What number is Zara thinking of?

STEP-BY-STEP ANSWER

The answer is greater than 40 and less than 90.

Work out the square numbers between 40 and 90. A square number is the answer to a number, multiplied by itself. 7x7 = 49, 8x8 = 64, 9x9 = 81.

Check which number is made up of digits that add up to 9. 8+1 = 9 so 81 is the answer.

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STEP-BY-STEP ANSWER

What are the common factors of 36 and 20?

Reminder: Factors are pairs of numbers that, when multiplied together, produce the number of which you are trying to find factors.

Create two factor bugs. Check for factors using a logical method i.e. work out what can be multiplied by 1 to find the given number. Then see if 2 can be multiplied by a number to produce the given number. After that, see if 3 can be multiplied by a number to produce the given number, and-so-on. Repeat this until you have tried all numbers from 1 up to to half of the given number.

The factors of 36 are: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6

The factors of 20 are: 1 and 20, 2 and 10, 4 and 5.

Since 1 and 2 appear in both lists, they are the common factors.

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Put the following numbers in order from largest to smallest:

4.5, -6.8, 4.05, - 6.09, 5.45

STEP-BY-STEP ANSWER

Step 1: Choose a number that has the largest number of digits.

Step 2: Change numbers that have fewer digits than the number you chose in Step 1 so that they have the same number of digits. If a number includes a a decimal point, write a number of zeroes after the number you chose so that your number has the same number of digits as the number you chose in Step 1. I.e. 4.321 and 4 will become 4.321 and 4.000.

Step 3: Put the numbers on a number line. Remember that the larger the number seems (positive or negative) the further it will be from 0.

Negative numbers will always be smaller than 0 or positive numbers.

An alternative good method to the Step 3 is to stack the numbers on top of each other. Then, write next to each number a number that shows their number in order of size.

4.5, -6.8, 4.05, - 6.09, 5.45

4.05 (3)

4.50 (4)

-6.80 (1)

-6.09 (2)

5.45 (5)

The answer is: -6.8, -6.09, 4.05, 4.5, 5.45

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In the Shah family there are 3 adults and Prisha and Saanvi, both aged 10, Umar, age 8, Asher aged 6 and Ranbeer aged 3. They all want to go to the zoo.

Adult tickets are £16.75 each.

Tickets for children (aged 0-16) are £9.50 each.

A family ticket (for 2 adults and 2 people aged 0-16) costs £42.00

What is the cheapest way for the family to go to the zoo? What change would they get from £100?

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How many minutes is 2/3 of 2 hours?

STEP-BY-STEP ANSWER

Step 1: Convert the hours into minutes. There are 60 minutes in one hour.

Step 2: Multiply the number of hours by 60 so 2 x 60 = 120 minutes.

Step 3: To find a fraction of an amount, divide the amount (60) by the denominator (3). The divisor for this question is 40.

Step 4: Multiply the to the previous step by the numerator (2) which produces the answer (80 minutes).

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What fraction of 3 hours is 35 minutes?

Step 1: Convert 3 hours into minutes. There are 60 minutes in one hour.

Step 2: Multiply the number of hours (3) by 60 (180 minutes).

Step 3: The numerator is 35 and the denominator is 180. This can be simplified to 7/36.

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Explain the difference between regular and irregular shapes

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What is the value of 'a' if 4a + 2 = 14?

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Ranbeer bought 3 cakes and bottles of water for £2.05.

Alfie bought 2 cakes and 2 bottles of water for £1.70.

What is the total cost of 1 bottle of water and 1 cake?

STEP-BY-STEP ANSWER

Step 1: Work out what is the same about what each person did. I.e. Ranbeer and Alfie both bought at least 2 cakes and 2 bottles of water. 

Step 2: Subtract all that is the same for both Ranbeer and Alfie. I.e. remove 2 cakes, 2 bottles and £1.70 from both people. All that is left is one cake and 35 p. This means that one cake most cost 35p. 

Step 3: Since we know that Alfie bought 2 cakes, that must have cost him 70p so we can remove that from the £1.70 he spent. This leaves £1.00. We know that 2 bottles of water were bought by Alfie so we can divide the £1.00 by 2, leaving 50p for 1 bottles of water.

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The temperature in Toronto was -4 degrees Celsius. It fell by 3 degrees. What did the temperature become?

STEP-BY-STEP ANSWER

Draw a vertical number line to help you. If the temperature was -4 and fell, it went down by 3 and so the answer becomes -7 degrees Celsius.

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What are the next three numbers in the sequence?

13, 10, 7, 4, ___, ___, ___

STEP-BY-STEP ANSWER

Look at the difference between each of the numbers. At this stage it is to subtract 3 each time so the next three numbers are 1, -2 and -5.

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Complete the gaps in the sequence?

4, ___, 16, 32, ____, 128, 256, ____

STEP-BY-STEP ANSWER

Tickets to go bowling are £4.80 each. £1728 worth of tickets are sold. How many tickets were purchased?

...

QUESTION TOPICS COMING SOON

Simplify the following fractions

Put the following fractions in order of size, smallest to largest.

Write in words the value of the number that is underlined.

Formulae

Symmetry

Translation

How many degrees has X shape been rotated?

Algebra

Proportion

Calendars

Pictographs

Other topics:

How to find the area of a rectlinear (composite) shape

Carroll Diagrams

Venn Diagrams

Algebra

What are the lowest common multiples of X and Y

Write three factors of X and Y

Dice - where would the symbol end up?

Interpret tally charts

4-quadrant coordinates

How much less did X pay than Y.

Number patterns

Speed/distance time

Describe the journey (based on a graph)

What is the missing angle?

Volume of a cube

Nets