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Numeracy: maths in your head - lesson starters and enders

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rters <strong>and</strong> Ender<br />

Essential for numeracy <strong>lesson</strong>s<br />

SMILE<br />

MATHEMATICS<br />

ole class <strong>in</strong>teractive teach<strong>in</strong>g


Maths In Your Head<br />

Maths In Your Head is a collection of whole class activities, usually used as <strong>lesson</strong><br />

<strong>starters</strong> or <strong>enders</strong>, to encourage mental mathematics. Developed by practis<strong>in</strong>g<br />

teachers, these activities are particularly suitable for use with<strong>in</strong> the <strong>lesson</strong> framework<br />

of the National <strong>Numeracy</strong> Strategy. The levels of difficulty can be adapted to address<br />

Key Stages 2 to 4.<br />

Each activity has a brief description. Teachers will need to spend some time<br />

<strong>in</strong>troduc<strong>in</strong>g the basic activity <strong>in</strong> order to familiarise students with it. As students<br />

become more confident, variations can be <strong>in</strong>troduced <strong>and</strong> the level of difficulty<br />

<strong>in</strong>creased.<br />

Photocopiable resource sheets are <strong>in</strong>cluded <strong>and</strong> any equipment required is clearly<br />

<strong>in</strong>dicated.<br />

Some variations are suggested, but there is space on each page for teachers to add<br />

their own variations.<br />

Addition <strong>and</strong> Subtraction 2<br />

Mak<strong>in</strong>g 100 2<br />

Ten Add 3<br />

Mixed number 4<br />

Beat the Clock 4<br />

B<strong>in</strong>go 5<br />

B<strong>in</strong>go, the Hard Way 6<br />

Four Rules Dice 6<br />

Estimat<strong>in</strong>g Game 7<br />

Round the Clock 8<br />

Statistical Dice 9<br />

Today's the Day 10<br />

Percentages, Fractions <strong>and</strong> Decimals 11<br />

Decimal Dice 11<br />

Fraction Dice 12<br />

Hundredth Game 13<br />

Percentage Dice 14<br />

Place Value 15<br />

How many different Scores? 15<br />

Order<strong>in</strong>g 16<br />

What's my Place 17<br />

Types of Number 18<br />

Multiple grid 18<br />

Play Your Cards Right 19<br />

Th<strong>in</strong>k <strong>and</strong> say 20<br />

Resource Sheets 21


Addition <strong>and</strong> Subtraction<br />

Mak<strong>in</strong>g 100<br />

Aim To improve students' facility with speed <strong>in</strong> mental addition.<br />

You will need a dice. Each student needs to make a score sheet.<br />

e.g.<br />

1 0 0<br />

Description The dice is thrown. The students may 'pass' or may write the number <strong>in</strong><br />

any box.<br />

The w<strong>in</strong>ner is the first one to score 100 exactly.<br />

Variations Record the numbers thrown on the dice on a white board. After one<br />

student has made 100 exactly, see if it could have been achieved <strong>in</strong><br />

fewer goes.<br />

Change the target number.<br />

Play four games simultaneously, with a different target number for each.<br />

This gives the option of students plac<strong>in</strong>g the number <strong>in</strong> any of the<br />

boxes.


Ten Add<br />

Aim To develop strategies for mentally add<strong>in</strong>g to 10.<br />

You will need 6 dice.<br />

Description Throw 6 dice. Students must make as many 10's by add<strong>in</strong>g the<br />

numbers on the dice.<br />

e.g.<br />

Dice thrown: 1, 6, 4, 4, 1, 3<br />

Possible to make 5 10's: 6 + 4, 6 + 4, 4 + 4+1+1<br />

6 + 3+1, 6 + 3 + 1<br />

Variation Throw more dice.<br />

F<strong>in</strong>d different totals.<br />

Fix the total as 10 <strong>and</strong> only allow two numbers to be added.<br />

F<strong>in</strong>d fixed products <strong>in</strong>stead of sums.<br />

Give 2 different target numbers.<br />

Use dice with different numbers on.


Mixed number<br />

Beat the Clock<br />

Aim To develop students' facility with mental multiplication <strong>and</strong><br />

division.<br />

You will need sufficient copies of Beat the Clock 1, 2 <strong>and</strong> 3 Resource<br />

Sheets for each student to have the appropriate sheet.<br />

Description This activity is a good <strong>lesson</strong> starter <strong>and</strong> should take no longer than 5<br />

m<strong>in</strong>utes. Each student is given a copy of Beat the Clock 1, 2 or 3<br />

Resource Sheets.<br />

Resource Sheet 1 conta<strong>in</strong>s mixed multiplication up to 12 x 12.<br />

Resource Sheet 2 conta<strong>in</strong>s mixed multiplication <strong>and</strong> division up<br />

to 12 x 12.<br />

Resource Sheet 3 conta<strong>in</strong>s mixed multiplication, division <strong>and</strong> factors.<br />

e.g. 42 = may be answered as 6x7, or 21 x 2, or 84 -f 2 etc.<br />

The teacher tells the students to start <strong>and</strong> times them for three m<strong>in</strong>utes.<br />

Students write the answers to the questions on the sheet as quickly as<br />

possible. As it conta<strong>in</strong>s mixed tables they should be encouraged to<br />

complete the answers that they know <strong>and</strong> then come back to 'work out'<br />

miss<strong>in</strong>g ones. The questions are not arranged <strong>in</strong> order of difficulty<br />

The teacher can record the marks that each student obta<strong>in</strong>s <strong>and</strong><br />

monitor improvement on the same test. When students achieve 38 or<br />

more correct answers they should move on to the next sheet.


B<strong>in</strong>go<br />

Aim To improve students' facility with mental mathematics.<br />

You will need to photocopy the B<strong>in</strong>go A&B Resource Sheets. Teachers<br />

need to cut up the sheet <strong>and</strong> put all the pieces <strong>in</strong> a conta<strong>in</strong>er. A 1 - 100<br />

grid (optional).<br />

Description Each student draws a grid, five columns by three rows.<br />

Students then write down their own choice of fifteen numbers on the<br />

grid <strong>in</strong> <strong>in</strong>k. The first column should conta<strong>in</strong> numbers between 1 - 20,<br />

the second column 21 - 40, ...<br />

The teacher selects <strong>and</strong> reads out one clue. Students put their h<strong>and</strong> up<br />

when they know the answer, confirm the answer, <strong>and</strong> mark off the<br />

number if it appears on their grid.<br />

Teachers can record the answers on a 1 - 100 grid.<br />

Variation The teacher can just call out each question, without students<br />

respond<strong>in</strong>g.<br />

The student who gets the answer correct can make up the next<br />

question.


B<strong>in</strong>go, the Hard Way<br />

Aim To improve students' facility with mental mathematics.<br />

You will need either Number Resource Sheet, photocopied on to card,<br />

or the 0 - 9 cards from SMILE 2226 Number Cards.<br />

Description Each student draws a 5 x 5 grid <strong>and</strong> places the numbers 1 - 25, at<br />

r<strong>and</strong>om, on the grid.<br />

Shuffle the cards <strong>and</strong> turn over the first three cards. These three<br />

numbers are to be used to make a number from 1 - 25.<br />

Each student shades <strong>in</strong> the number on their grid that they have made<br />

<strong>and</strong> writes down the calculation.<br />

1 11 23 21 18<br />

16 2 13 20 10<br />

9 8 3 7 14<br />

25 24 17 4 6<br />

15 2 22 19 5<br />

Variation Students may like to aim for:<br />

• the first row<br />

• the first column<br />

• diagonal<br />

• full house<br />

Four Rules Dice<br />

Aim To improve students' facility with mental mathematics.<br />

You will need 5 dice<br />

Description Each student writes down the numbers 1 - 20 on the left h<strong>and</strong> side of<br />

the page. The five dice are thrown. Each set of 5 numbers can be used<br />

to make just one of the student's numbers, us<strong>in</strong>g any of the operations,<br />

x + <strong>and</strong> - <strong>and</strong> brackets. Cont<strong>in</strong>ue until one student has made all 20<br />

numbers.


Estimat<strong>in</strong>g Game<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of estimation.<br />

Description Divide the class <strong>in</strong>to teams of 3 or 4.<br />

The teacher asks the teams to write down an estimate for the height of<br />

an item <strong>in</strong> the classroom, e.g. a fil<strong>in</strong>g cab<strong>in</strong>et.<br />

Each team's estimate is recorded by the teacher on a white board. The<br />

item is then measured <strong>and</strong> the team with the closest estimate scores 1<br />

po<strong>in</strong>t. The teacher then asks the teams to write down an estimate for<br />

another item, us<strong>in</strong>g the knowledge of the first item's height.<br />

This cont<strong>in</strong>ues with 1 po<strong>in</strong>t be<strong>in</strong>g awarded to the team with the closest<br />

estimate.<br />

Variations Instead of heights of object, try weights.<br />

Use imperial <strong>in</strong>stead of metric units.<br />

Use non-st<strong>and</strong>ard units, i.e. h<strong>and</strong>spans.


Round the Clock<br />

Aim To develop students' facility with <strong>and</strong> underst<strong>and</strong><strong>in</strong>g of number.<br />

You will need 3 dice.<br />

Description Draw the clock face on a white board or on an OHR Divide the class<br />

<strong>in</strong>to two teams. The three dice are rolled together. Us<strong>in</strong>g any operation<br />

<strong>and</strong> the numbers on the dice, make the number 1, followed by the<br />

number 2, then 3 ... <strong>in</strong> consecutive order. Each team must record how<br />

each number was made.<br />

e.g. If team A rolls 1, 2 <strong>and</strong> 4, it can go as far as 10.<br />

1 0) 4 (4) 7 (4 + 2 + 1)<br />

2 (2) 5 (4 + 1) 8 (4x2)<br />

3 (1+2) 6 (4 + 2) 9 (4 x 2) + 1<br />

10 (4+ 1) x2<br />

Then Team B rolls three dice. Teams take it <strong>in</strong> turns to go until one team<br />

reaches 12.<br />

The aim of the game is to go around the clock <strong>in</strong> as few dice rolls as<br />

possible.<br />

Variation This can be played co-operatively as a whole class challenge.<br />

Class discussion such as:<br />

Which is the best dice roll?<br />

Which is the worst?


Statistical Dice<br />

Aim To re<strong>in</strong>force underst<strong>and</strong><strong>in</strong>g of the statistical terms: Mode, Median,<br />

Mean <strong>and</strong> Range.<br />

You will need 3 dice, <strong>and</strong> a pack of play<strong>in</strong>g cards with the Aces, two's<br />

<strong>and</strong> three's removed.<br />

Description One dice is thrown for the code. Here is a suggestion:<br />

1 = Mode 2 = Median 3 = Mean 4 = Range 5 = Mean<br />

6 = Mode<br />

It is important that the four different terms are <strong>in</strong>cluded at least once, but<br />

you could ask the students to decide on the code for numbers 5 <strong>and</strong> 6.<br />

(They are likely to choose mode <strong>and</strong> range if they underst<strong>and</strong> the<br />

concepts.)<br />

A card is chosen from the pack of cards. The number on the card<br />

determ<strong>in</strong>es how many times the dice are thrown.<br />

e.g. A 2 was thrown (median)<br />

A 7 was picked from the pack of cards.<br />

The question is, "What is the median of these 7 numbers?"<br />

The dice is thrown 7 times <strong>and</strong> the scores read out.<br />

Students now have to write down the answer to the question.<br />

Ace's, two's <strong>and</strong> three's are removed from the pack to make the<br />

questions more mean<strong>in</strong>gful. Also 10 is the most likely number (Jacks,<br />

Queens <strong>and</strong> K<strong>in</strong>gs also count as 10) <strong>and</strong> it is relatively easy to f<strong>in</strong>d the<br />

mean of 10 numbers.


Today's the Day<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of <strong>and</strong> facility with number.<br />

Description Write the date <strong>in</strong> the form: 23. 9. 98<br />

Keep<strong>in</strong>g the date digits <strong>in</strong> order <strong>and</strong> us<strong>in</strong>g any operation, or brackets,<br />

make as many numbers as possible.<br />

e.g.<br />

23 + 9 + 98 = 130<br />

23 + 9 + 9 + 8 = 49<br />

2 + 3 + 99 + 8 = 112<br />

2(3 + 9) + (9 - 8) = 25<br />

To create more of a challenge, make the number less than 100.<br />

The whole class's results can then be compiled on a 1 - 100 grid.<br />

The student who f<strong>in</strong>ds a number that no one else has found, can be<br />

asked to show the method used.<br />

Variation Use digits <strong>in</strong> any order <strong>and</strong> record numbers on a 1 - 100 grid.<br />

Students are then asked to try to make those miss<strong>in</strong>g numbers from<br />

the date of the next <strong>maths</strong> <strong>lesson</strong>.


Percentages, Fractions <strong>and</strong> Decimals<br />

Decimal Dice<br />

Aim To develop students' facility with mental multiplication <strong>and</strong><br />

division by 10,100 <strong>and</strong> 1000.<br />

Teachers will need to make up a version of grid below, large enough for<br />

the whole class to see.<br />

Description Divide the whole class <strong>in</strong>to two teams. Team members take it <strong>in</strong> turn to<br />

roll the dice <strong>and</strong> decide whether to multiply or divide the number on the<br />

dice by 10, 100 or 1000 to make one of the numbers on the grid.<br />

1000 0.1 0.001 20 10 0.006 100<br />

0.002 0.06 30 2000 0.01 0.05<br />

0.002<br />

30 4000 40 200 20 0.2 0.6<br />

600 0.06 0.03 6000 500 0.005 4000<br />

0.02 3000 300 0.004 50 0.3 0.001<br />

0.5 0.05 1000 60 500 0.04 0.03<br />

400 0.003 60 0.01 0.4 0.003 5000<br />

That number is then shaded or covered with that team's colour. The<br />

w<strong>in</strong>n<strong>in</strong>g team is the first to make a l<strong>in</strong>e of four.


Fraction Dice<br />

Aim To practise skills of shad<strong>in</strong>g fractions<br />

Each student needs an A5 sheet of pla<strong>in</strong> paper. A dice or sp<strong>in</strong>ner needs<br />

to be marked us<strong>in</strong>g some of these fractions. Alternatively, the Fractions<br />

Resource Sheet can be cut up, the pieces folded <strong>and</strong> put <strong>in</strong> an<br />

envelope to provide a means of r<strong>and</strong>omly select<strong>in</strong>g fractions.<br />

1/16 2/16 3/16 4/16 5/16 8/16<br />

1/8 2/8 3/8 4/8<br />

1/4 1/2<br />

Description Each student folds their paper <strong>in</strong>to sixteenths.<br />

The dice is thrown <strong>and</strong> each student has to shade that fraction on the<br />

sheet. The fraction must make a complete piece.<br />

e.g.<br />

If the dice showed 5/16, it could not be shaded <strong>in</strong> two pieces of 1/16<br />

<strong>and</strong> 4/16.<br />

Variation Fold the sheet <strong>in</strong>to twelfths, or twenty-fourths <strong>and</strong> change the fractions<br />

on the dice.


Hundredth Game<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of <strong>and</strong> facility with decimal<br />

numbers.<br />

You will need one dice <strong>and</strong> sufficient copies of Hundredth Game<br />

Resource Sheet for each student to have a copy of Hundredth Game<br />

Record<strong>in</strong>g Sheet.<br />

Description There are 6 rounds to a game. With<strong>in</strong> a round the dice is thrown four<br />

times for each number.<br />

1st throw This is the target number.<br />

2nd - 4th throw The number on the dice can be used to go <strong>in</strong>to any<br />

box, but once it is placed it cannot be changed.<br />

The game proceeds until all the boxes are filled.<br />

Add up all the Target numbers. Add up all the students' numbers. The<br />

student with the total nearest to their Target Number Total is the w<strong>in</strong>ner.<br />

Variation The students can score po<strong>in</strong>ts accord<strong>in</strong>g to how close each number is.<br />

Less than 0.5 score 10<br />

Between 0.5 <strong>and</strong> less than 1.0 score 5<br />

Between 1.0 <strong>and</strong> less than 1.5 score 3<br />

Between 1.5 <strong>and</strong> less than 2.5 score 1<br />

More than 2.5 score 0


Percentage Dice<br />

Aim To develop students' skills <strong>in</strong> work<strong>in</strong>g out percentages mentally.<br />

You will need a dice.<br />

Description Each student needs to draw a 3 x 5 grid.<br />

PERCENTAGE (x 10) £ Amount<br />

The left h<strong>and</strong> column is used to record the percentages.<br />

The middle column is used to record amounts of money <strong>in</strong> £'s.<br />

A dice is thrown eight times. The number on the dice can be used to<br />

go <strong>in</strong>to any box <strong>in</strong> the first two columns, but once it is placed it cannot<br />

be changed. Once these two columns are filled, the student has to work<br />

out the percentages of the four amounts. The student then adds all four<br />

answers together.<br />

The aim is to get as close to £5 as possible.<br />

PERCENTAGE (x 10) £ Amount<br />

Giv<strong>in</strong>g a total of £3.40<br />

10% £5 0.50<br />

40% £3 1.20<br />

60% £2 1.20<br />

10% £5 0.50<br />

Variation Highest total.<br />

Lowest total.<br />

Different target.<br />

Instead of money, use the numbers on the dice <strong>and</strong> multiply it by 10,<br />

100 ...


Place Value<br />

How many different Scores?<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of place value.<br />

You will need a dice <strong>and</strong> each student needs to make a copy of the<br />

score sheet.<br />

Total<br />

Description The dice is rolled eight times. After each roll, the students choose which<br />

of the top eight boxes to record that number <strong>in</strong>. Once placed the<br />

number cannot be changed. The game proceeds until all the top eight<br />

boxes are filled. The students add up their score. The closest to 120<br />

w<strong>in</strong>s.<br />

A very useful discussion can take place if the teacher records all the<br />

different scores. Some questions to ask are:<br />

How many different scores could there have been with the eight scores<br />

on the dice?<br />

The scores differ by 9. Will this always be true? Why?<br />

Variations Change the target number.<br />

Change from closest to 120 to furthest away.<br />

Use two dice, one for the tens, one for the units.<br />

Change the scor<strong>in</strong>g sheet.<br />

e-g- , , , ,<br />

Total


Order<strong>in</strong>g<br />

Aim To develop an underst<strong>and</strong><strong>in</strong>g of <strong>in</strong>equalities <strong>and</strong> the<br />

notation > <strong>and</strong>


What's my Place<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of place value.<br />

Hundred<br />

(thous<strong>and</strong><br />

You will need a large room <strong>and</strong> sufficient copies of What's my Place<br />

Resource Sheet. Each group of six students will need 1 copy<br />

photocopied on to coloured paper. The teacher will need to make up<br />

1 set of Place Value Cards:<br />

Ten<br />

thous<strong>and</strong><br />

Thous<strong>and</strong> Hundred Ten Unit<br />

Description Put the 6 Place Value Cards <strong>in</strong> a straight l<strong>in</strong>e, at one end of the room.<br />

Divide the class <strong>in</strong>to groups of six. Each group is given one copy of<br />

What's my Place Resource Sheet.<br />

The teachers says, "Take up <strong>your</strong> position accord<strong>in</strong>g to <strong>your</strong> digit '3'."<br />

So the student with 654321 goes to the 'Hundred' label, the student with<br />

the 541263 goes to the 'Unit' label etc. All students by each label should<br />

have the same number.<br />

The students then return to their orig<strong>in</strong>al group <strong>and</strong> the teacher calls out<br />

another digit.<br />

Variation Use numbers written as words.<br />

Change the numbers us<strong>in</strong>g O's.<br />

Increase the labels.


Types of Number<br />

Multiple grid<br />

Aim To develop students' facility with multiples <strong>and</strong> factors.<br />

You will need a dice. Each student will need to make a copy of the<br />

follow<strong>in</strong>g grid.<br />

Score<br />

Score Total<br />

Description A dice is rolled four times. After each roll the number on the dice can be<br />

used to go <strong>in</strong>to any of the four boxes, but once it is placed it cannot be<br />

change. When all four boxes have been filled, this produces four, two<br />

digit numbers, two by rows, <strong>and</strong> two by columns.<br />

Score<br />

Po<strong>in</strong>ts are awarded accord<strong>in</strong>g to the largest factor less than ten.<br />

If the largest factor is a multiple of one, score one.<br />

If the largest factor is a multiple of two, score two.<br />

If the largest factor is a multiple of three, score three etc.<br />

e.g.<br />

Score<br />

Total<br />

35 scores<br />

62 scores<br />

36 scores<br />

52 scores<br />

7<br />

2<br />

9<br />

Total score 22<br />

Variation Change the scor<strong>in</strong>g, so that extra po<strong>in</strong>ts are awarded if the numbers<br />

are:<br />

• square numbers<br />

• prime numbers etc...


Play Your Cards Right<br />

Aim To develop students' underst<strong>and</strong><strong>in</strong>g of different types of numbers.<br />

You will need either Number Resource Sheet, photocopied on to card,<br />

or the 0 - 9 cards from SMILE 2226 Number Cards.<br />

Description The teacher shuffles the cards <strong>and</strong> take out five cards. These cards are<br />

then shown to the class.<br />

Students choose any three digits to create the different types of<br />

numbers which the teacher calls out.<br />

e.g. The five cards were: 2, 6, 1, 5 <strong>and</strong> 9.<br />

The teacher asks questions for a three digit number to make:<br />

• The highest possible even number<br />

• The highest possible odd number<br />

• The smallest possible even number<br />

• The nearest number to 500<br />

• The nearest number to 1000<br />

• The smallest odd number<br />

• The smallest number<br />

• The nearest odd number to 400


Th<strong>in</strong>k <strong>and</strong> say<br />

Aim To revise vocabulary of types of number.<br />

Description Below are 36 statements cover<strong>in</strong>g a range of topics, some open <strong>and</strong><br />

some closed. Choose a question <strong>and</strong> ask a student to f<strong>in</strong>d a number<br />

which matches the statement.<br />

A multiple of eight.<br />

A number less than 46 - 25.<br />

A number greater than 75 + 64.<br />

A square number.<br />

A factor of 24.<br />

A multiple of 7.<br />

A prime number greater than 30.<br />

A square number greater than 30.<br />

A multiple of 9.<br />

A number less than 34 - 21.<br />

3 more than 198.<br />

Double 73.<br />

A multiple of 5.<br />

A number less than 12x8.<br />

A number greater than 97 + 23.<br />

6 more than 27.<br />

A factor of 16.<br />

The sum of this number's digits is 8.<br />

A prime number less than 20.<br />

A square number less than 10.<br />

A number greater than 123 + 67.<br />

The product of this number's digits is 15.<br />

Double 59.<br />

Half of 125.<br />

Double 27.<br />

Half of 75.<br />

Half of 72.<br />

A factor of 40.<br />

The sum of this number's digits is 12.<br />

A prime number between 40 <strong>and</strong> 50.<br />

A square number larger than 60.<br />

A factor of 36.<br />

A number whose two digits are odd.<br />

A number whose two digits are even.<br />

Double 69.


Resource Sheet Section<br />

Beat The Clock 1 - Resource Sheet 22<br />

Beat The Clock 2 - Resource Sheet 23<br />

Beat The Clock 3 - Resource Sheet 24<br />

What's My Place - Resource Sheet 25<br />

B<strong>in</strong>go A - Resource Sheet 26<br />

B<strong>in</strong>go B - Resource Sheet 27<br />

Fraction - Resource Sheet 28<br />

Hundredth Game - Resource Sheet 29<br />

Number - Resource Sheet 30<br />

Order<strong>in</strong>g Game - Resource Sheet 31<br />

Notes 32<br />

21


Name<br />

Question Answer<br />

1. 5x6 —<br />

2. 2x9 —<br />

3. 10x4 —<br />

4. 3x11 —<br />

5. 7x3 —<br />

6. 3x3 —<br />

7. 6x2 —<br />

8. 5x5 —<br />

9. 8x3 —<br />

10. 2x4 —<br />

11. 5x4 —<br />

12. 10x2 —<br />

13. 2x5 —<br />

14. 7x4 —<br />

15. 6x3 —<br />

16. 10x8 —<br />

17. 7x7 —<br />

18. 7x5 —<br />

19. 4x3 —<br />

20. 4x4 —<br />

Question Answer<br />

21. 8x5 —<br />

22. 4x9 =<br />

23. 6x7 =<br />

24. 8x4 —<br />

25. 8x8 —<br />

26. 11x9 =<br />

27. 6x6 —<br />

28. 3x 12 —<br />

29. 6x9 —<br />

30. 10x7 —<br />

31. 9x3 —<br />

32. 12x4 —<br />

33. 11 x 11 —<br />

34. 6x 12 —<br />

35. 10x 10 —<br />

36. 12x11 —<br />

37. 9x9 —<br />

38. 8x9 —<br />

39. 8x6 —<br />

40. 8x7 —


Name<br />

Question Answer<br />

1. 10x6 —<br />

2. 3x5 —<br />

3. 6 + 3 =<br />

4. 6x4 —<br />

5. 30 + 3 =<br />

6. 6x11 —<br />

7. 22-2 =<br />

8. 5x9 —<br />

9. 8x11 =<br />

10. 90-9 —<br />

11. 12x2<br />

12. 10x5 =<br />

13. 8x 12 =<br />

14. 30 + 5 =<br />

15. 11x4 =<br />

16. 10x 12 =<br />

17. 55-5 —<br />

18. 16-2 —<br />

19. 11x7 =<br />

20. 7x7 —<br />

Question Answer<br />

21. 40 + 5 =<br />

22. 9x9 =<br />

23. 110+10 =<br />

24. 8x6 =<br />

25. 63 + 7 =<br />

26. 12x7 =<br />

27. 7x8 —<br />

28. 12 x12 =<br />

29. 6x7 =<br />

30. 70 + 7 —<br />

31. 12x5 =<br />

32. 64 + 8 =<br />

33. 9x6 =<br />

34. 36 + 3 =<br />

35. 36 + 9 =<br />

36. 72 + 12 =<br />

37. 72 + 8 —<br />

38. 8x7<br />

39. 56 + 7 =<br />

40. 108 + 9 =


Name<br />

Question Answer<br />

1. 42 —<br />

2. 27-3 =<br />

3. 7x9 =<br />

4. 36 + 9 =<br />

5. 64 —<br />

6. 10x0 =<br />

7. 12x 12 =<br />

8. 21 —<br />

9. 18-2 =<br />

10. 24-2 =<br />

11. 1 x 11 =<br />

12. 40 —<br />

13. 9x 12 =<br />

14. 6x0 =<br />

15. 45 =<br />

16. 72 —<br />

17. 54 =<br />

18. 99-11 —<br />

19. 108 =<br />

20. 6x6 —<br />

Question Answer<br />

21. 5x5 —<br />

22. 12-4 —<br />

23. 81 =<br />

24. 4x8 =<br />

25. 7x7 —<br />

26. 33 —<br />

27. 132-11 =<br />

28. 8x3 —<br />

29. 6x7 —<br />

30. 48 =<br />

31. 56 =<br />

32. 20-4 =<br />

33. 32-8 =<br />

34. 24 =<br />

35. 0x7 =<br />

36. 3x 10 —<br />

37. 36 —<br />

38. 28 =<br />

39. 12 —<br />

40. 2x7 —


What's My Place - Resource Sheet 25


• 9 times 0<br />

•4 2<br />

-16<br />

• 15 take away 15<br />

• Difference between<br />

60 <strong>and</strong> 5 dozen<br />

• Double 5<br />

•30-3<br />

• 10% of 100<br />

• The square root<br />

of 100<br />

•5x4<br />

•4 2<br />

+ 4<br />

• Half of 40<br />

•A fifth of 100<br />

•5x6<br />

• A third of 90<br />

• Number of days<br />

<strong>in</strong> April<br />

• 5 more than 25<br />

• 5x8<br />

• 50% of 80<br />

• 2 x 20<br />

• Half of 80<br />

• 5 x 10<br />

•50% Of 100<br />

• Double 25<br />

• 20 less than 70<br />

• 10 lots of 6<br />

• 3 lots of 20<br />

•Two thirds of 90<br />

10<br />

• 16 m<strong>in</strong>us 15<br />

• 23 + 23<br />

• 50 take away 49<br />

• 1 2<br />

1<br />

8 plus 3<br />

' A third of 33<br />

1<br />

20 take away 9<br />

•The first two digit<br />

prime number<br />

•40-19<br />

•3x7<br />

• A third of 63<br />

• 4 more than 17<br />

• 3 times 4<br />

• 1 dozen<br />

• Half of 24<br />

12<br />

• The square root<br />

of 144<br />

•2x11<br />

•17 + 5<br />

• Half of 44<br />

• 25 m<strong>in</strong>us 3<br />

22<br />

30 32<br />

50<br />

60<br />

• Number of m<strong>in</strong>utes<br />

<strong>in</strong> an hour<br />

•10 times 7<br />

• 2 lots of 35<br />

• 10 more than 60<br />

• 30 plus 40<br />

• 4 lots of 20<br />

• 10x8<br />

•10 less than 90<br />

80<br />

• Four fifths of 100<br />

•10 times 9<br />

• 2 lots of 45<br />

•10 less than 100<br />

• 90% of 100<br />

90<br />

• 20 plus 21<br />

•82 + 2<br />

• 4 more than 37<br />

• 2 more than 39<br />

• 47 plus 4<br />

• 100-49<br />

•Treble 17<br />

• 30 more than 21<br />

• 57 plus 4<br />

• 100-39<br />

• Number of days <strong>in</strong><br />

June <strong>and</strong> July<br />

•The total of 59<br />

<strong>and</strong> 2<br />

• 40 plus 31<br />

•100-29<br />

• 3 more than 68<br />

•The total of 69<br />

<strong>and</strong> 2<br />

• 100-19<br />

•3 J<br />

• 75 plus 6<br />

•9 2<br />

+ 10<br />

•100-9<br />

• 1 more than 90<br />

•The total of 89<br />

<strong>and</strong> 2<br />

•2x26<br />

• 40 plus 12<br />

42<br />

52<br />

• 2 more than 50<br />

• Number of weeks<br />

<strong>in</strong> a year<br />

>2 x 31<br />

• 40 plus 22<br />

62<br />

« 2 more than 60<br />

> Number of days <strong>in</strong><br />

July <strong>and</strong> August<br />

6x12<br />

9x8<br />

1<br />

6 dozen<br />

1<br />

80 m<strong>in</strong>us 8<br />

•90-8<br />

• Double 41'<br />

82<br />

• 3 more than 79<br />

• 8 less than 90<br />

•4x23<br />

• 90 plus 2<br />

• Double 46<br />

• 100 m<strong>in</strong>us 8<br />

• 2 plus 1<br />

• A third of 9<br />

• 5 take away 2<br />

• A quarter of a<br />

dozen<br />

• 7 plus 6<br />

• Half of 26<br />

• 7 less than 20<br />

13<br />

• Next prime<br />

number after 11<br />

•11 plus 12<br />

• Half of 46<br />

• 30 subtract 7<br />

23<br />

•The next prime<br />

number after 19<br />

•3x11<br />

• Half of 66<br />

• 3 more than 30<br />

• 7 less than 40<br />

•30 plus 13<br />

• Half of 86 "<br />

• 3 more than 40<br />

• 45 m<strong>in</strong>us 2<br />

• 25 plus 28<br />

• 60 m<strong>in</strong>us 7<br />

• 3 more than 50<br />

33<br />

53<br />

•The next prime<br />

number after 47<br />

•Treble 21<br />

•7x9<br />

• 3 more than 60<br />

• 7 less than 70<br />

69 plus 4<br />

Add 23 to 50 _<br />

2 less than 75<br />

73<br />

•The next prime 40 plus 34<br />

number after 71<br />

• 79 plus 4<br />

• 90 m<strong>in</strong>us 6 83 I • Add 33 to 50 .19x7<br />

84<br />

i • 2 less than 85 • 4 more than 80 •<br />

! • The next prime<br />

] number after 79<br />

• 89 plus 4 93 • Add 43 to 50<br />

2 lots of 2<br />

12 + 3<br />

• 40 plus 44 i<br />

• 86 plus 8<br />

• Double 47 94<br />

• 7 less than 100 • 4 more than 90<br />

•3 x 31 • 100 m<strong>in</strong>us 6<br />

2 2<br />

The square root<br />

of 16<br />

2 lots of 7<br />

Half of 28 14<br />

Next even number<br />

after 12<br />

30 take away 16<br />

6 lots of 4<br />

2 dozen<br />

3x8<br />

The mean of 23<br />

<strong>and</strong> 25<br />

34% of 100<br />

Double 17<br />

5 more than 29<br />

40 take away 6<br />

4x11<br />

Double 22<br />

Half of 88<br />

4 more than 40<br />

9 times 6<br />

Double 27<br />

24<br />

54<br />

3 times 3 times 6<br />

60 take away 6<br />

8 times 8<br />

Double 32<br />

8 2<br />

70 take away 6<br />

80 m<strong>in</strong>us 6<br />

Double 37<br />

4 more than 70<br />

64


10% of 50<br />

30-6<br />

A quarter of 20<br />

The third odd<br />

number<br />

15% of 100<br />

3x5<br />

A quarter of 60<br />

20 take away 5<br />

25% of 100<br />

5 2<br />

15<br />

A quarter of 100<br />

A half of 50<br />

35% of 100 %j<br />

7x5 •<br />

5 less than 40<br />

A half of 70<br />

45% of 100<br />

9x5<br />

5 less than 50<br />

A half of 90<br />

55% of 100<br />

11 x5<br />

5 less than 60<br />

25 plus 30<br />

35 plus 30<br />

13x5<br />

5 less than 70<br />

The sum of 61<br />

<strong>and</strong> 4<br />

50 plus 25<br />

3x25<br />

5 more than 70<br />

Three quarters<br />

of 100<br />

50 plus 35<br />

5 x 17<br />

5 more than 80<br />

15 less than 100<br />

50 plus 45 ^1<br />

5x19 M<br />

5 more than 90<br />

5 less than 100<br />

•<br />

2 lots of 8<br />

4 2<br />

20% of 80<br />

Half of 32<br />

13 plus 13<br />

2 x 13<br />

30 take away 4<br />

• 9 plus 8 16 17<br />

•28-11<br />

26<br />

Number of weeks<br />

<strong>in</strong> half a year<br />

Half of 92<br />

20 plus 26<br />

4 less than 50<br />

10 more than 6<br />

8x7 ETj<br />

30 plus 26<br />

4 less than 60<br />

20 more than 6 2<br />

11x6<br />

3 x 22<br />

4 less than 70<br />

Treble 22<br />

80 m<strong>in</strong>us 4 j<br />

2 x 38<br />

66<br />

10 more than 66<br />

10 less than 86<br />

90 m<strong>in</strong>us 4<br />

2x43<br />

10 more than 76<br />

10 less than 96<br />

12x8 £TJ<br />

2 x 48<br />

10 more than 86<br />

100 m<strong>in</strong>us 4<br />

• 2 more than 15<br />

•17% of 100<br />

• 3 3<br />

•9x3<br />

• 30 m<strong>in</strong>us 3<br />

• 5 more than 22<br />

• 40 m<strong>in</strong>us 3<br />

•6 2<br />

+ 1<br />

• Half of 74<br />

27<br />

•The sum of 35<br />

<strong>and</strong> 2<br />

• 50 m<strong>in</strong>us 3 47<br />

• 40 plus 7<br />

• 8 more than 39<br />

• Next prime<br />

number after 43<br />

• 60 m<strong>in</strong>us 3<br />

• 50 plus 7<br />

• 8 more than 49<br />

• Treble 19<br />

• 70 m<strong>in</strong>us 3<br />

• 40 plus 27<br />

• 3 less than 70<br />

1<br />

57<br />

j.<br />

Next prime<br />

number after 61<br />

•15 + 3<br />

3x6<br />

1<br />

7 less than 25<br />

' Double 9<br />

• 2 times 14<br />

• 30 m<strong>in</strong>us 2<br />

• Number,of days<br />

<strong>in</strong> 4 weeks<br />

• The product of<br />

7 <strong>and</strong> 4<br />

•2 times 19 ^<br />

• 40 m<strong>in</strong>us 2 H<br />

• 12 less than 50<br />

• 3 more than 35<br />

4x12<br />

• 50 m<strong>in</strong>us 2<br />

8x6<br />

1<br />

3 more than 45<br />

30 plus 28<br />

1<br />

60 m<strong>in</strong>us 2<br />

Double 29<br />

1<br />

3 more than 55<br />

'2x34<br />

• 70 m<strong>in</strong>us 2<br />

' 8 more than 60<br />

•4 x 17<br />

• 13 plus 6 18 19<br />

•38-2<br />

28<br />

58<br />

•3 2<br />

+ 10<br />

• One less than 20<br />

• Add 8 to 21<br />

• 30 m<strong>in</strong>us 1<br />

• 21 less than 50<br />

•5 2<br />

+ 4<br />

• 25 plus 24<br />

• 50 m<strong>in</strong>us 1 B<br />

• 11 less than 60<br />

•7 2<br />

• 55 plus 4<br />

• 60 m<strong>in</strong>us 1 •<br />

• The sum of 49<br />

<strong>and</strong> 10<br />

• 9 more than 50<br />

29<br />

3x23 68 69<br />

70 m<strong>in</strong>us 1<br />

11 less than 80<br />

• The difference<br />

between 100 <strong>and</strong> 31<br />

f/H •7x -7x11 11 wjjri -Treble •Treble 26 wl»i . 75 plus 4 f7«j<br />

toWMU 50 • plus 50 plus 27 27 HHl 80 ' m<strong>in</strong>us 80 m<strong>in</strong>us 2 2 • 80 m<strong>in</strong>us 1 • • •<br />

3 less than 80<br />

85 subtract 8<br />

m • Treble 29<br />

8X11<br />

• 50 plus 37<br />

• 3 less than 90<br />

• 95 subtract 8<br />

• 44 add 53<br />

• 95 plus 2<br />

• 3 less than 100<br />

• The largest two<br />

digit prime number<br />

i<br />

1<br />

1<br />

8 more than 70<br />

Double 40 then<br />

m<strong>in</strong>us 2<br />

1<br />

90 m<strong>in</strong>us 2 Hi<br />

1<br />

8 more than 80<br />

Double 44<br />

50 add 48 [jl<br />

100 m<strong>in</strong>us 2 Ml<br />

1<br />

8 more than 90<br />

1<br />

Double 49<br />

• 11 less than 90<br />

• The difference<br />

between 100 <strong>and</strong> 21<br />

• 85 plus 4 ^jTjl<br />

• 90 m<strong>in</strong>us 1 fe^Ml<br />

• 9 more than 80<br />

• The difference<br />

between 100 <strong>and</strong> 11<br />

•3x33<br />

• 9x11 to<br />

• 9 more than 90<br />

»The difference<br />

between 100 <strong>and</strong> 1


1 I 2 I 3 \ 4<br />

16 16 16 16<br />

5 8 1 2<br />

16 16 8 8<br />

3 4 1 1<br />

8 8 4 2<br />

1 2 3 4<br />

16 | 16 16 16


Hundredth Game - Resource Sheet 29<br />

Hundreth Game Record<strong>in</strong>g Sheet Hundreth Game Record<strong>in</strong>g Sheet<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score<br />

Hundreth Game Record<strong>in</strong>g Sheet<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score<br />

Hundreth Game Record<strong>in</strong>g Sheet<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score<br />

Hundreth Game Record<strong>in</strong>g Sheet<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score<br />

Hundreth Game Record<strong>in</strong>g Sheet<br />

Target number<br />

(1st throw)<br />

Number<br />

(2nd - 4th throw)<br />

Total<br />

Score


0 1 2 |3|<br />

4 5 6 71<br />

8 9


Order<strong>in</strong>g Game - Resource Sheet 31


Notes


Maths In Your Head<br />

Maths In Your Head is a collection of whole class activities, usually used as <strong>lesson</strong><br />

<strong>starters</strong> or <strong>enders</strong>, to encourage mental mathematics. Developed by practis<strong>in</strong>g<br />

teachers, these activities are particularly suitable for use with<strong>in</strong> the <strong>lesson</strong> framework<br />

of the National <strong>Numeracy</strong> Strategy. The levels of difficulty can be adapted to address<br />

Key Stages 2 to 4.<br />

Each activity has a brief description. Teachers will need to spend some time<br />

<strong>in</strong>troduc<strong>in</strong>g the basic activity <strong>in</strong> order to familiarise students with it. As students<br />

become more confident, variations can be <strong>in</strong>troduced <strong>and</strong> the level of difficulty<br />

<strong>in</strong>creased.<br />

Photocopiable resource sheets are <strong>in</strong>cluded <strong>and</strong> any equipment required is clearly<br />

<strong>in</strong>dicated.<br />

Some variations are suggested, but there is space on each page for teachers to add<br />

their own variations.<br />

SMILE<br />

MATHEMATICS<br />

Isaac Newton Centre<br />

108A Lancaster Road<br />

London W11 1QS<br />

Tel. 020 7598 4841<br />

Fax. 020 7598 4838<br />

Email, <strong>in</strong>fo@smilemathematics.co.uk<br />

Web. www.smilemathematics.co.uk

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