Maths for Learning Inclusion Tasks to Move Students Onovsstaffwiki.wikispaces.com/file/view/Tasks_to_move_students_on.pdf · Maths for Learning Inclusion (M4LI) Tasks to Move Students

Maths for Learning Inclusion (M4LI) Tasks to Move Students On

Numbers 1 – 10 Structuring Number

Maths for Learning Inclusion

Tasks to Move Students On Part 1


Numbers 1 – 20 Addition and Subtraction


Using the Base 10 System


Beginning Multiplication and Division


Multiplication and Division


Saying, Reading and Writing Numerals


Tasks to Move Students On Part 2

Maths for Learning Inclusion Intervention Kit

Tasks To Move Students On


Tasks to Move

Students On

Part 2


Tasks to Move

Students On

Part 1

Maths for Learning Inclusion – Intervention Kit Tasks to Move Students On July 2008

Question 1 COUNTING • Trusting the count • Counting a collection to find out how many

Tasks to move students on:

a) A Scattered Collection (Objects such as counters, shells, teddy bears etc) Show a scattered collection of objects and ask how many? Put objects in a line and ask now how many. Have the student count from each end and from the middle. Make groups, how many in each group, and how many altogether.

b) Counting a collection (Objects such as counters, shells, teddy bears etc) Have students count a small collection of objects. Could we find out how many if we count by 2’s? 3’s? 4’s? etc

c) Making a necklace (Beads and thread) Have the student count out eg. 6 beads to make a necklace (choose other numbers)

d) Children and Ages (Pictures of Children and their Ages) Show student the pictures. Have them group them and count how many in each group.

e) Rearranging a Collection (Objects such as counters, shells, teddy bears etc) Have the student rearrange a collection of objects so its easier to count. For example put the counters into groups of 2 or 5 or 10.

f) Constant Function (Calculator) Use the constant function (1 + 1===) on the calculator to: • Count by one’s, Skip count.

g) Which is Bigger? (Counters) Ask student to say which is bigger 3 or 4. Have the student convince you of this in some way (they can use concrete materials if they want). Do this with other numbers.

h) Counting using MAB (MAB) Arrange MAB eg place out 2 ones then ask students to count on.

i) Numbers Bag (Number bag with numbers appropriate for student) Draw out a number then get the student to write the number sequence that follows the number eg. If they pull out 3 they write 4, 5, 6 etc.

j) Ten New Students (Pencil and paper) Say to the student “imagine that ten new students were coming to school next term”. Draw a picture to show me how many boys and girls could there be.”

k) How Many Now? (Objects to count) Put a selection of items in a circle - number depending on child). Ask “how many objects are there?” If the student doesn’t stop where they started you need to discuss stopping where you started so that you don’t count objects twice. Put out a number of objects in a row and ask ‘how many” move the objects into a different arrangement then ask “how many” again. Repeat this activity a few times putting the objects in different arrangements. The child should recognise that although the objects have moved the number is still the same.

Maths for Learning Inclusion (M4LI) Tasks To Move Students On



Question 2

SUBITISING • Seeing how many at a glance • Thinking of numbers in parts


a) Pick up Blocks (Blocks or counters or objects) Without counting ask the student to pick up 2 blocks, 3 blocks etc.

b) How many…? (Cubes or counters, cloth or large piece of paper, dominoes and dice). Put out counters on the table in a familiar dice pattern, uncover the pattern for a short time and ask the student to identify how many counters there are. As the student gets quicker at recognising the patterns, increase the amount of counters.

c) Dropping Counters (Counters or blocks or objects) Who is the quickest to say how many are dropped?

d) Dice Rolling (Dice) Roll a die, and ask the student “How many dots do you see?” When they can do this quickly, Roll two dice, and ask “How many dots do you see?”

e) What Do You See? (Subitising Cards – non standard and standard) Flash ‘What Do You See Cards’. Rotate the card so that it is in a different direction and ask students to look for different groups. Draw attention to ‘groups of’ in the patterns, example 5 and 2 is 7. Play snap and memory with the cards

f) Making Dot Cards (Cards and dots) Have students make their own pairs of cards with groupings of up to six dots on them, randomly placed. Play snap. Have student use increasingly larger numbers as they become confident.

g) How Many Fingers? (No resources) Have two students face each other, then clap their hands three times before holding up between five and ten fingers. Have them show all the fingers on one hand and some extra fingers on the second hand. Together, students say how many fingers are held up together.

h) Blank Ten Frames (Blank Ten frames and counters) Using 2 different coloured counters, put some counters in groups on a blank 10 frame and state the number sentence for the groups they see e.g. 8 and 2 is 10.

i) Take a Quick Look (Cubes or counters, cloth or large piece of paper, dominoes and dice) Put out counters on the table in a familiar dice pattern, uncover the pattern for a short time and ask the student to identify how many counters there are. As the student gets quicker at recognising the patterns increase the amount of counters. Using dominoes ask the student to show you the patterns they now know.




Question 3 Making finger patterns

Tasks to move students on: The student needs to be able to raise the fingers automatically and not one after the other (i.e. if you asked a student to show you seven fingers you want them to be able to do this automatically and not put up 5 then add on 2) a) Show me using your fingers (Model if necessary)

1 3 5 7 9 2 10 6 b) Show me with fingers (Model if necessary)

Show me 6 fingers. Show me 6 a different way. Continue with other numbers Record eg. 4 is 4 and 0, or 3 and 1 or 2 and 2.

c) Show me using two 2 hands (Model if necessary)

2 3 7 5 8 4 etc fingers




Question 4

Partitioning Five

Tasks to move students on: a) Five Frames (Five frames)

Show student a five frame. If it has, for example 2 dots in it, tell the student you see two dots and three empty squares. Flash the student another Five Frame and ask what did they see? Repeat this with all frames.

b) Empty Five Frames (Blank five frames) Put counters in some of the blank squares and ask the student what do you see?

c) Five Counters (Counters)

Put out 5 counters and ask the student to make groups, for example you can make two groups – 1 group could have one counter in it and the other would have 4.

d) Make 5 (Two sets of five frame cards) Place the cards face up and have the student try to find two cards that together total 5. To challenge the student turn the cards face down.




Question 5

A Five Pattern on a Ten Frame

Tasks to move students on: a) Making 5 (1 – 5 number cards)

Put out a number and have student tell you the other number needed to put with it to make 5.




Question 6

A Pair Pattern on a Ten Frame


a) Double it Using Unifix (Unifix cubes or counters) Put out 1 unifix cube or counter, show student how you can double it by putting the same out again. Do this with other numbers. Have the student count the doubles. Record.

b) Double it Using Arrays (Paper and Pencil, counters) Draw 2 objects in an array and write how many there are. Draw 6 objects in an array and write how many there are. Do this with other numbers. Do this same activity but use counters.

c) Double on a Ten Frame (‘Doubles on a Ten Frame’ Cards) Flash doubles on a ten frame and ask student ‘how many are there?’ When student knows their doubles on the ten frame add one to it. Show them how they can use their knowledge of doubles to work out how many there are.

d) Flashing Doubles (Doubles Cards) Flash the doubles cards and ask student ‘how many are there?’

e) Blank Ten Frames (Blank Ten Frame and Counters) Use ten frames to show doubles. For example, use a blank ten frame, and place 3 counters in one row. Ask the student to place three in the other row (to make 6) and explain that double three is six. Repeat this for other numbers.

f) Doubling Counters (Counters) Repeat the above activity, but use counters to demonstrate doubles for larger numbers that won’t fit on a 10 frame.

g) Memory/Snap (Memory/Snap Double Cards) In this game the ‘pairs’ are doubles (i.e. 4 and 8 match). (Play with either the dot or number cards). Use the cards as flash cards - ask the student to say the double for the number.

h) Doubling Dice (Dice) Use dice to practice doubles. Roll a die - ask the student to say the double of that number.

i) Halve it – Double it (Number cards and counters) Use number cards and ask students to say which number is half of it (i.e. number on card is 10: answer is 5), and double it (number on card is 10: answer is 10 + 10 = 20). (The student might need counters.)




Question 7 & 8

Combining to Make 10 and Missing Addend Problems Tasks to move students on:

a) Number Combinations of 5 (Cards 1-5) Show them all the 2 number combinations that add up to 10. Have them solve them.

b) Number Combinations of 10 (Cards 1-10) Show them all the 2 number combinations that add up to 10. Have them solve them.

c) How Many More To Make 10? (Blocks, straws, counters, objects, or pictures) Put out 2 blocks, straws, counters, objects, or pictures and ask the student how many more to make 10 (do this with other numbers - up to 10). Roll a large dice. Have the student say the number, and then ask “how many more to make ten?”

d) Making 10 (Cards 0-10) Scatter the number cards 0-10 in front of the student and ask the student to put two cards together so they add up to 10. Ask if they know any other 2 numbers that add up to 10. Repeat question but have the student answer it without using cards.

e) Dot Cards (Card) Have students make own dot cards 1-10 and when finished ask them what two cards can they put together to make 10.

f) Unifix Cubes (10 Unifix Cubes) Give the student 10 unifix cubes joined together. Have them break them into parts to discover the different number combinations that make 10. Record.

g) Flip Blocks (‘Flip Block Toss’ Game Board) Using 10 flip blocks of the same colours play “Flip Block Toss”. Rules: Hold 10 flip blocks in the palm of your hand and gently toss the blocks on the table. Students sort them into the two coloured groups and record onto the frame. Have student say and write the number sentence.

h) Part-Part-Whole (Using Part-part-whole grid and 10 unifix cubes) Using the part-part-whole grid separate 10 unifix cubes and place on the grid. Have student say and write the number sentence. Ask if they can write it another way? Explain the concept of the grid to the student. i.e if we know the whole and one part, we can find the other part? How would we do this? What would the number sentence be? What if the other part was missing? What number sentence would we write? After the initial session, ask how many different ways could you say and write this number sentence? Encourage student/s to learn the 4 ways for any number sentence up to 10. Repeat this activity using an Abacus. As student becomes more confident work with combinations to 20.



Question 7 & 8

Number combinations of 5 and 10

i) Number Line 1-10 (Number line) Introduce a number line 0-10 on a stick or floor mat. Jump along eg. Start at 0 and jump two spaces forward, and then 8 more. Ask student “What number do you land on?”

j) Number Bonds to 10 (Using game board) Game board and instructions in resource folder.

k) Birds in a Tree (Birds and Trees Pictures) Show the student five bird pictures and tell the student how many there are. Place out the pictures of trees in front of the student. You put one bird in a small tree and four in a large tree. Say: there are four birds in the first tree and one bird in the second tree. Move one bird so that there are three birds in one tree and two birds in the other. Then ask: Are there still five birds altogether? Repeat the activity for combinations of 2 and 3, 1 and 4 and 0 and 5. Repeat using 10 birds.

l) Combining Two Groups (Beads, two pieces of card or paper, number cards) Ask the students to count ten beads checking the students counting skills. Ask the students to split the beads into two groups then cover each group with a piece of paper. Q: How many beads are there altogether? If the student has difficulty with this let them look under one piece of paper at a time. Q: How can you work out how many altogether? Repeat this activity with different amounts until the student can combine the two groups.



Number Intervention Kit – Resources to support Tasks to Move Students On - July 2008. Numbers 1 – 10 Structuring Number (Yellow)

Children & Their Ages

10 years old

10 years old

10 years old

10 years old

10 years old

7 years old

10 years old

6 years old

9 years old

9 years old

9 years old

5 years old


5 years old

5 years old

7 years old

12 years old

5 years old

5 years old

7 years old

8 years old

6 years old

12 years old

6 years old

8 years old


0

1

2

3

4

5

6

7

8

9

10

11

Number Cards


12

13

14

15

16

17

18

19

20


Subitising Cards – Standard




Subitising Cards – Non-Standard




Subitising Cards – Doubles



Blank 10 Frames


Five Frames with Dots


Blank Five Frames


Double on a Ten Frame Card




Toss 10 flip blocks. Separate the colours on the frame. Say what the number sentence is and write it underneath. Date:

Number Sentence: Date:

Number Sentence:

Flip Block Toss Gameboard


part part

whole

1. Using the part-part-whole grid separate 10 unifix cubes and place on the grid. 2. Say and write the number sentence. 3. Can you write it another way? 4. Explain the concept of the grid to the student. i.e if we know the whole and one part, we

can find the other part? How would we do this? What would the number sentence be? What if the other part was missing? What number sentence would we write?

After the initial session, ask how many different ways could you say and write this

number sentence? Encourage student/s to learn the 4 ways for any number sentence.

Part – Part – Whole Grid


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Number Line


3 4 8 1 9 2 6 5 8 9 6 1 5 3 2 10 2 5

7 6 9 2 3 10 • Each player gets counters of the same colour (about 10). • Player 1 spins a 1-9 spinner and then identifies the number on the grid that needs to be added to the spinner number

to make 10. • When a player gets 4 counters in a row they win.

Number Bonds to 10 Gameboard


Birds and Trees


Question 1

Additive Tasks

Tasks to move students on: a) Flip Tile Toss (Flip tiles)

Give students some flip tiles. Throw them and then count how many red tiles and how many yellow tiles. Create an addition equation for this. Use various amounts of tiles to create equations.

b) Card Game (Deck of cards)

Split a deck of cards into two piles. Turn over one card from each pile. The first person to call out the correct answer to the addition of these numbers takes the cards and adds them to their pile. The winner is the person with the most cards at the end of the game.

c) Dice Roll (Two dice or two ten sided dice)

Alternative: Roll two dice and add the numbers together. The first person to get 10 correct answers is the winner.

d) How Many More? (Spinner)

Roll a dice/spin a number spinner. How many more do you need to add to that number to make 10? (or 15, 20 etc). Use a number line to count on to find the missing addend.

e) Beanbag Toss (Number cards, bean bags)

Have numbers 1 - 20 placed on large cards the floor. Students throw a bean bag onto a card. They must then calculate the number that needs to be added to this number to make 20 (or 10/15 etc). If they are correct, they keep the card, the person with the most cards at the end of the game is the winner.

f) Making 20 (Number cards 1-20)

Have number cards (assorted to 20) face down on the table. Pick up one card. How many more to make 20? If the answer is correct, the student may keep the card. The winner is the person with the most cards at the end of the game.




Question 1 continued Additive Tasks

g) Calculator Adding (Calculator, number cards and symbols, counters or cubes)

Ask the student to put a number sentence into the calculator, checking that the student can identify the + and = keys. Can the student construct a number sentence with the cards to match the one made on the calculator? Encourage the student to experiment with the calculator.

h) Adding Stories (Cubes, hoops and dice) Tell the student you are going to create some stories which include adding. Let the student choose a context which is suitable to them e.g there are 4 children at the party and 3 more arrive. Q: How many are there altogether? Show me how you know that. Let’s make a list of all the words you can think of that we use when we are adding. Some puppies are black and some are brown. Altogether there are 12 puppies. Q: How many black puppies and how many brown puppies could there be?

i) Combining Two Groups (Beads, two pieces of card or paper) Ask the students to count seven beads checking the students counting skills. Ask the students to split the beads into two groups then cover each group with a piece of paper. Q: How many beads are there altogether? If the student has difficulty with this let them look under one piece of paper at a time. Q: How can you work out how many altogether? Repeat this activity with different amounts until the student can combine the two groups.




Question 2

Subtractive Tasks


a) Flip Tile Toss (Flip tiles) Give the students a pile of flip tiles. Ask the student to throw them up into the air and record the number of red and yellow tiles showing when they land. Write two subtraction equations for each.

b) Card Game (Deck of cards)

Shuffle a pack of cards. Turn over two cards and subtract the smaller from the larger. The first person to call out the answer keeps the cards. The winner is the person with the most cards at the end of the game.

c) Subtraction Bingo (Bingo board)

Play bingo. Instead of calling out the number, say a subtraction problem that has the number as the answers. i.e. for 5, say ’12 - 7 =’ etc.

d) Counter Removal (Counters)

Start with a number of counters on the table. Ask the student to look away and remove some. Ask ‘How many counters did I take?’ Ask the student to record a number sentence for this.

e) Winning Equation (Number cards 1-20)

Place the number cards 1 - 20 face down on the table. Ask students to pick two cards. i.e. 10 and 4. Ask students to create a subtraction equation where the answer is known (10 - [ ] = 4) and then answer it. If their answer is correct, they can keep the card. The winner is the person with the most cards at the end of the game.

f) Frogs and Lily Pads (Green cubes to represent frogs, circles of green paper to represent lily pads)

Ask the student to select eight or nine frogs and put each frog on a lily pad. Q: Can you count the frogs? Q: Can you count the lily pads? Q: What can you tell me about these two numbers? (That they are the same). Ask the student to take away some frogs, Q: How many frogs did you start with? Q: How many frogs did you take away? Q: How many frogs are left in the pond? Repeat the activity with a different number of frogs and lily pads. Q: Show me the ones you took away. Q: Show me the ones that are left. How many are left? Q: Let’s write a number sentence about this. How many did we start with?

g) How Many Left? (Cubes and pieces of paper to represent biscuits and plates, number line and felt pens)

Put seven biscuits on a plate. Q: How many biscuits? Q: Take some biscuits away and tell me how many you have taken away. Q: How many are left? On a white board or on a number line or track relate the taking away to counting back on a number line. Encourage the student to verbalise and record some number sentences such as: 5 count back 2 means you land on 3, 5 - 2 = 3




Question 3 Double Dot Cards Tasks to move students on:

a) Double Dice Roll (Dice) Roll a dice. What would double the number be? (Note: Can use a second dice to help student).

b) Domino Add (Dominoes)

Practice with flashcards/dominos. ‘Ask - ‘How many on each side? How many altogether?’

c) Ten Frame Doubles (Blank 10 frames, counters) Use ten frame cards. Put counters in the top row. Ask ‘How many would there be if I put the same amount in the bottom row?’ Write sum to match

i.e.

3 + 3 = 6

d) Observation Walk (No resources) Look for objects that have doubles in the environment. i.e. 1 + 1 = 2 - wheels on a bike, 4 + 4 = 8 - legs on a spider etc

e) Unifix Stacks (Unifix cubes)

Make 2 equal stacks with unifix cubes. How many altogether? Write the equation for this.

f) Number Line Doubles (Number line) Use a number line to show doubles (including large number line on the floor that students can step on)

g) Doubles Snap/Memory (Deck of cards or number cards)

Play snap/memory with number cards. Pairs are numbers and their doubles. i.e. 4 and 8 would be a pair.

h) Two Towers (Cubes and a whiteboard)

Make two columns or towers each of twelve inter locking cubes. Show the student one tower. Q: How many cubes are there in this tower? Show the student the second tower and place the two towers side by side. Q: How many cubes make up the second tower? Establish that the towers are the same height and have the same number of cubes. Repeat with different numbers.



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Question 4

Close to Double


a) Ten Frame Close to Doubles (Ten frames and counters) Use ten frames to explore close to doubles. For example, show students a card with 5 + 6 on it and give them 11 counters. Ask students to place the counters on the ten frames, one on the top/one on the bottom at a time. Discuss that 5 +6 = 5 + 5 + 1 = 11

b) Number Line Demo (Number lines) Use a number line to demonstrate close to doubles. i.e. 4 + 5 = 4 + 4 + 1 and 5 + 5 - 1

3 + 3 + 1 = 3 + 4

3 +3 +1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Note: A number line can also be drawn on the asphalt/floor so that students can actually jump the ‘jumps’ as they count on.



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Question 5

Simple Addition

Tasks to move students on: a) Ten Frame Addition (Ten frames and counters)

Use a ten frame and counters to show counting through ten. For example, 7 + 5 = 7 + 3 + 2

i. 7 + 3 +2 = 12

b) Recording

Ask students to place the counters on the ten frame, and then write the equation showing counting through 10. i.e. 7 + 3 + 2 = 12

c) Five Frame Addition (Five frames, counters)

Use a five frame to show counting through 5, using the same method as for counting through ten.

2 + 4 = 2 + 3 + 1 .

d) Number Line Addition (Number line)

Use a number line to show counting through five or ten. Ask the student to record the equation, showing this strategy.

b. 7 + 3 +2

7 + 5 = 7 + 3 + 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Note: A number line can also be drawn on the asphalt/floor so that students can actually jump the ‘jumps’ as they count on.



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Question 6

Simple Subtraction

Tasks to move students on: a) Ten Frame Subtraction (Ten frames, counters)

Use a ten frame and counters to show subtraction through ten. For example, 11 - 3 = 11 - 1 - 2

11 - 1 - 2 = 8

b) Recording

Ask students to take the counters from the ten frame, and then write the equation showing subtracting through 10 i.e. 11 - 1 - 2 = 8

c) Five Frame Subtraction (Five frames, counters)

Use a five frame to show subtraction through 5, using the same method as for counting through ten.

i. 7 - 4 = 7 - 2 - 2 7 - 2 - 2 = 3 d) Numer Line Subtraction (Number line)


12 – 4 = 12 – 2 – 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21



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Question 6 continued

Simple Subtraction

e) Subtraction Snap/Memory (Set of question and answer cards) Play games such as snap and memory with question and answer cards.

For example,

would be a match

f) Bye Bye Biscuits (Different coloured blocks, number line) Use blocks to represent thirteen biscuits on a plate. Q: How many biscuits? Q: Take some biscuits away and tell me how many you have taken away. Q: How many are left? On a white board or on a number line or track relate the taking away to counting back on a number line. Have the student record the number sentence.



5 - 2 3


Question 7

Addition and Subtraction

Tasks to move students on: a) Flashcard Strategies (Flashcards)

Use flash cards with addition and subtraction number sentences on them. Reinforce/discuss the strategies that can be used to solve these (counting through ten, doubles, close to doubles etc)

b) Ten Frame Addition (Ten frames and counters) Use a ten frame and counters to show counting through ten.

i. For example, 7 + 5 = 7 + 3 + 2

7 + 3 +2 = 12 c) Number Line Addition (Number line)


7 +3 +2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7 + 5 = 7 + 3 + 2



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Addition and Subtraction

d) Snap/Memory (Addition question and answer cards)

Play games such as snap and memory with question and answer cards. ii. For example,

would be a match

e) More Calculator Adding (Cubes, number line, 2 sets of number and symbol cards and a calculator) Ask the student to key in 4+6=10 and ask them what they will have to do to get the answer back to 4? Ask student to make the number sentences with the cards. Encourage student to use cubes or the number line to help them. Repeat this activity with different numbers, then go back to making number sentences with the cards. Can the student check their answers using their calculators? Lay out the number sentence 4-6=10 ask why this isn’t correct, give the student cubes to support their working if needed.



12 + 11 23


Question 8

Number Relationships / Number Facts Tasks to move students on: a) Coummutative Law (Materials such as beans, counters, blocks, straws etc)

Use everyday materials to represent all the combinations of a given number. Discuss Commutative Law - i.e. ‘Is 5 + 6 the same as 6 + 5? How are they the same? How are they different?’

b) Counting Strategy (Unifix cubes)

Use unifix cubes to demonstrate connection between equations (i.e. 2 + 6 = 3 + 5 = 4 + 4). Start with 6 and 2, take 1 from one stack and add it to the other. Write the new equation (5 + 3). Ask ‘How many are there now?’ Discuss how the parts of the equation may be different, but the total is the same (i.e. one up/one down)

6 + 2 5 + 3 4 + 4

c) Inverse Relationship (MAB blocks)

Use MAB Blocks to explore inverse relationships (and Commutative Law). Ask students to write all the number sentences that can be made i.e. 2 + 5 = 7 5 + 2 = 7

7 - 5 = 2 7 - 2 = 5

d) Add and Subtract (Counters) Write a simple addition equation for the student. (i.e. 9 + 5 = ) Provide counters and ask them to show you the equation using the counters. Ask them to write another addition equation using these amounts (5 + 9 = 14). Then ask the student to make a subtraction sum using these amounts. (i.e. 14 - 9 = 5). Ask ‘Is there another subtraction sum that you could make using these amounts?’





Number Relationships / Number Facts e) Calculator Inverse Relationships (Calculator)

Have student 1 enter a number into a calculator without anyone seeing it and then add an agreed number eg. 8. Student 2 then writes the number sentence used.

eg. + 8 = 12 and then rewrites it in a way that can be solved on the calculator. eg. 12 – 8 = f) Making Sentences (Cubes, number and symbol cards)

Tell the student you want them to make 2 different sized rods that make 12 when added together. Explain that you are going to make some addition and subtraction sentences that use 12. Encourage the child to record their sentences e.g. 8+4 = 12 12–4 = 12. Continue with different numbers.

g) On the Number Line (Cubes, number lines or whiteboards and number cards)

Explain you are going to make sensible number sentences that go together, ask the student to choose the numbers and explain you will record the sentences. Ask the student to mark their starting number on the number line, if you close your eyes can you imagine some hops along the number line to get to a number bigger than your number (or smaller). To make that number sentence which cards would you need? Again discuss vocabulary. Can the student explain what it means when we say “addition undoes subtraction.”



Number Intervention Kit – Resources to support Tasks to Move Students On - July 2008. Numbers 1 – 20 (Green)

Numbers 1 – 20 (Large)











Number Cards

0

1

2

3

4

5

6

7

8

9

10

11

Number Cards


12

13

14

15

16

17

18

19

20

+ - =

Symbol Cards


3 9 18 6 7 11

6-3 12-3 20-2 10-4 11-4 16-5

Subtraction Bingo / Subtraction Snap


2 4 6 8 10 12

6-4 12-8 11-5 10-2 20-10 15-3


1 3 5 7 9 11

13-12 8-5 12-7 13-6 17-8 14-3


14 16 18 20 13 15

16-2 18-2 20-2 25-5 16-3 19-4


17 19 2 4 6 8

20-3 22-3 8-6 9-5 9-3 14-6


10 12 14 5 7 9

13-3 16-4 18-4 8-3 13-6 16-7


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Number Line


11+2 17-4

13+6

12+7

16-3

14-1

9+4 12-9

14+5

12+6

16-7

16-5

Flashcard Addition & Subtraction


16+3 15-6

15+3

17+3

14-5

15-5

4+9 14-6

10+2

10+1

13-5

13-4


11+3 12-3

11+5

11+4

17-5

12-4

13+3 17-8

13+5

13+4

18-9

18-8


13+7 18-7

14+6

14+2

19-8

19-9

15+4 19-10

17+2

16+3

11-3

11-2


23 14 10 12 8 19

12+11 9+5 7+3

9+3 6+2 13+6

Addition Question and Answer Cards / Addition Bingo


8 12 4 9 5 7

5+3 7+5 3+1

6+3 3+2 5+2


21 11 17

10 3 15

12+9 7+4 9+8

6+4 2+1 9+6


25 18 11

16 22 6

19+6 11+7 9+2

8+8 18+4 4+2


2 20 13

14 9 19

1+1 13+7 8+5

8+6 7+2 10+9


24 5 15

18 7 12

19+5 3+2 8+7

11+7 5+2 8+4


Blank 10 Frames


Blank Five Frames

Maths for Learning Inclusion – Tasks to Move Students On July 2008.

Maths for Learning Inclusion (M4LI) Tasks To Move Students On Using the Base 10 System

Question 1

Counting by tens using ‘10 Dot Cards’

Tasks to move students on: a) 100 Chart Skip Counting (1 – 100 chart, counters)

Practice counting by tens using a 1 - 100 chart, placing a counter on each number as you say it. What happens to the tens place each time you move forwards?

b) 10 Strip Counting (Ten strips) Practice counting by tens using the 10 strips.

c) Card Count (Decade cards)

Have cards (10, 20, 30 etc). Turn one over (i.e. 60) ask the student to count on in tens (i.e. 70...80..90..100…110...120…130)

d) Ten Jump (Chalk, hardcourt)

Write the numbers 10, 20, 30 …….100 (or starting at another number i.e. 60, 70, 80……..150 etc) on the asphalt with chalk. Ask the student to jump from one number to the next (in order) and say the number aloud as they jump.



Question 2

Counting on by 10 using ‘Dot Cards’


a) Counting On (Die, MAB long, ten strips) Roll a die. Start at this number and count on by tens using MAB ten blocks or ten strips to assist.

b) Number Chart Count On (1 – 100 Number chart) Use a 1 - 100 Chart. Ask student to choose a number and count on by tens.

c) Jumping Tens (Large 1 – 100 chart)

Draw a large 1 - 100 Chart on the asphalt (or on a large piece of paper etc). Ask the student to start at a given number and count on by 10, jumping from one number to the next (in order) and saying the number aloud as they jump.

d) Calculator Skip Count (Calculator) Use a calculator to explore counting by 10s. Start at a number and predict what the answer will be if you count on by tens 5 (or 6, 10 etc) times. Check your answer.

e) Hundreds Chart (Paper strips, calculator)

Give students a strip of paper. Ask them to record any number between 1 and 9 at the top. Enter the chosen starting number on the calculator and add on 10. eg. 8 + 10 = = =. Record numbers on the strip. Ask “What number will be next?”



Question 3

How many do I have now?

Tasks to move students on: a) Counting On (MAB minis and longs, cover card sheet)

Arrange MAB tens and ones in a line. Cover the blocks with some card and uncover as the student counts. Rearrange the blocks and ask the student to recount. Is there the same amount? Reinforce the concept of counting on by 10s to add the ten blocks and then adding on ones for the minis. This can be supported by using a 1 - 100 Chart. i.e.

10 +4 +20 +2 +10 +3 +10 +1

b) Dice Roll (Ten sided dice) Students work in pairs to make addition sums for each other. Person 1 rolls two 10 sided dice, the first one tells how many MAB tens will be used and the second how many MAB ones will be used. This person then organises these blocks in any order under the cover sheet (similar to the activity above). The MAB blocks are then revealed one part at a time (as in activity a) and the second person must then add the amounts as they are uncovered.

NOTE: Discuss with the student the strategies they used to add. If the student is having difficulty, provide a 1 - 100 Chart and suggest the student adds the MAB tens first and then the MAB ones.

Cover Card

10 + 4 = 14 +10 + 10 = 24 + 2 = 26 +10 = 36 + 3 = 39 etc…..



Question 4

Skip Counting by tens of the decade

Tasks to move students on: a) Dice Decades (6 or 9 sided dice)

Roll a die. Start at this number and count on by ten

b) Card Count Off (Number cards 1 – 20) Pick a number card from the 1 - 20 pack. Count on from this number by tens.

c) 100 Chart Count On (1 – 100 chart)

Use a 1 - 100 Chart to practice counting on by 10. Choose any number and ask the student to count on from there by 10s

d) Jump and Count (Large 1 – 100 chart)

Draw a large 1 - 100 Chart on the asphalt (or on a large piece of paper etc). Ask the student to start at a given number (off the decade) and count on by 10, jumping from one number to the next (in order) and saying the number aloud as they jump.

e) Counting Sequences (Line of students or counters)

Ask the class to form a line. Beginning at 10, have students say in turn the next number in the counting sequence, going down the line and then back again.



Question 5

Place value cards Tasks to move students on: a) Highest and Lowest (Dice)

Roll 3 (or four) dice. Arrange them to make the largest number possible. Record this number. What is the value of each numeral? Then arrange the numbers to make the smallest number possible.

b) Rock and Roll (Dice)

Each student rolls 5 dice together. They then arrange their dice to make the largest number possible then call out ‘Rock and Roll’. Every other player must then freeze. The first player to call out then reads out their number, earning 10 points if they read it correctly. The person with the highest number earns 5, everyone else earns no points. The first person to 50 wins.

c) Place Value Snap (Deck of cards)

Play ‘Place Value Snap’. One person turns over a card for Tens column, the other for the Ones column. The player who says the correct number first keeps the cards. If it is a tie, the cards are put to the side, the pile building until one person gives a correct answer. They then keep all the cards in the tie pile. The winner is the person who has the most cards at the end of the game.

d) Record the Number (MAB blocks, dice)

Roll two (or 3, 4) dice. Use the numerals to record a number. Then make this amount using MAB blocks grouping in hundreds, tens and ones. Ask the student to record how many Hundreds, Tens and Ones are in each column.

e) Largest or Smallest (Number cards or deck of cards)

This game can be done making either the largest or smallest number. Each player draws 3 (or 4) cards and reads their numbers aloud. Each player then makes the largest number they can with those cards. The player with the highest number earns a point. The first one to 10 wins.

f) What is the Value? (0 - 9 number cards) Place multiple sets of 0 - 9 cards face down on the desk. Choose 3 cards, turn them over. How many different numbers can you make with these cards? What is the value of each numeral in each number? i.e. in 563 - what is the value of the 3? Of the 5? Of the 6?




Place value cards

Tasks to move students on: g) Three Die Roll (Die)

Roll three die. Use the numbers rolled to make as many different numbers as you can. h) 1 – 100 Chart Tic – Tac – Toe (1 – 100 Chart, dice, counter)

The goal is for a player to get 3 of their counters in a row (any direction). Two dice are rolled and the first player then makes a number using these numerals. They place a counter on that number on the 1 - 100 Chart and say the number aloud. The second player then has their turn. This continues until one player has three counters in a row.

i) Write the Number (MAB blocks)

Place out different blocks and say to the student “Can you write down the number shown by the blocks please?”

j) Place Value Thinkboard (Thinkboard template)

Have the student choose a number to represent in different ways on The Thinkboard. k) Expanded Notation (Paper to record on)

Have students read and record numbers as expanded notation eg. 38 is 3 tens and 8 ones. Have them also write numbers from expanded notation in place value order as well as reversed order eg. 8 ones and 3 tens is 38.

l) Snap (Numeral and Representation Cards)

Play snap with one set of cards that shows the numeral eg. and another set of cards showing the representations of numbers eg.

25

2 tens and 5 ones



Question 6 Horizontal Sentences (using Horizontal Sentence cards)


a) Horizontal +10 (Horizontal +10 addition cards, MAB Blocks/ten strips/unifix cubes) Show the student a card with a + 10 question in it. (i.e. 23 + 10). Use MAB Blocks/ten strips/unifix cubes to solve. Then ask ‘What is 23 + 9?’ Demonstrate with MAB blocks

i.e. 23 + 10 - 1 = 23 + 9. Ask the student to solve other problems using this process.

b) Subtraction Sentences (Practice questions, MAB blocks, number line, 1 -100 number chart).

Use Practice questions. Ask the student to solve using their knowledge of counting by tens. Support the student with MAB blocks, number line and a 1 - 100 Chart to assist with counting backwards.

i.e. 65 - 29 = 65 - 30 + 1. OR 65…55….45….35 + 1

c) Add or Subtract 9 (Number cards, deck of cards) Place a number card (either ending in a 9 or an 8) on the table. Place two cards from a deck of cards next to the other card and Add (or subtract) 9 from it. The first person to say the correct answer earns a point. The first person to 10 wins.

i.e.

subtract = 26 - 10 + 1 = 7

d) Methods (Addition and subtraction number sentence cards) Ask the student to record the different ways that they can solve the problem. i.e. counting by tens, adding tens then adding units, number line, 1- 100 chart etc

e) Memory (Number sentence and answer cards)

Play memory with questions and their answers as pairs. i.e. and

16 34 - 18

6 9 2

Number Intervention Kit – Resources to support Tasks to Move Students On - July 2008. Using the Base 10 System (Orange)

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 – 100 Chart


101 102 103 104 105 106 107 108 109 110

111 112 113 114 115 116 117 118 119 120

121 122 123 124 125 126 127 128 129 130

131 132 133 134 135 136 137 138 139 140

141 142 143 144 145 146 147 148 149 150

151 152 153 154 155 156 157 158 159 160

161 162 163 164 165 166 167 168 169 170

171 172 173 174 175 176 177 178 179 180

181 182 183 184 185 186 187 188 189 190

191 192 193 194 195 196 197 198 199 200


201 202 203 204 205 206 207 208 209 210

211 212 213 214 215 216 217 218 219 220

221 222 223 224 225 226 227 228 229 230

231 232 233 234 235 236 237 238 239 240

241 242 243 244 245 246 247 248 249 250

251 252 253 254 255 256 257 258 259 260

261 262 263 264 265 266 267 268 269 270

271 272 273 274 275 276 277 278 279 280

281 282 283 284 285 286 287 288 289 290

291 292 293 294 295 296 297 298 299 300


301 302 303 304 305 306 307 308 309 310

311 312 313 314 315 316 317 318 319 320

321 322 323 324 325 326 327 328 329 330

331 332 333 334 335 336 337 338 339 340

341 342 343 344 345 346 347 348 349 350

351 352 353 354 355 356 357 358 359 360

361 362 363 364 365 366 367 368 369 370

371 372 373 374 375 376 377 378 379 380

381 382 383 384 385 386 387 388 389 390

391 392 393 394 395 396 397 398 399 400


401 402 403 404 405 406 407 408 409 410

411 412 413 414 415 416 417 418 419 420

421 422 423 424 425 426 427 428 429 430

431 432 433 434 435 436 437 438 439 440

441 442 443 444 445 446 447 448 449 450

451 452 453 454 455 456 457 458 459 460

461 462 463 464 465 466 467 468 469 470

471 472 473 474 475 476 477 478 479 480

481 482 483 484 485 486 487 488 489 490

491 492 493 494 495 496 497 498 499 500


501 502 503 504 505 506 507 508 509 510

511 512 513 514 515 516 517 518 519 520

521 522 523 524 525 526 527 528 529 530

531 532 533 534 535 536 537 538 539 540

541 542 543 544 545 546 547 548 549 550

551 552 553 554 555 556 557 558 559 560

561 562 563 564 565 566 567 568 569 570

571 572 573 574 575 576 577 578 579 580

581 582 583 584 585 586 587 588 589 590

591 592 593 594 595 596 597 598 599 600


601 602 603 604 605 606 607 608 609 610

611 612 613 614 615 616 617 618 619 620

621 622 623 624 625 626 627 628 629 630

631 632 633 634 635 636 637 638 639 640

641 642 643 644 645 646 647 648 649 650

651 652 653 654 655 656 657 658 659 660

661 662 663 664 665 666 667 668 669 670

671 672 673 674 675 676 677 678 679 680

681 682 683 684 685 686 687 688 689 690

691 692 693 694 695 696 697 698 699 700


701 702 703 704 705 706 707 708 709 710

711 712 713 714 715 716 717 718 719 720

721 722 723 724 725 726 727 728 729 730

731 732 733 734 735 736 737 738 739 740

741 742 743 744 745 746 747 748 749 750

751 752 753 754 755 756 757 758 759 760

761 762 763 764 765 766 767 768 769 770

771 772 773 774 775 776 777 778 779 780

781 782 783 784 785 786 787 788 789 790

791 792 793 794 795 796 797 798 799 800


801 802 803 804 805 806 807 808 809 810

811 812 813 814 815 816 817 818 819 820

821 822 823 824 825 826 827 828 829 830

831 832 833 834 835 836 837 838 839 840

841 842 843 844 845 846 847 848 849 850

851 852 853 854 855 856 857 858 859 860

861 862 863 864 865 866 867 868 869 870

871 872 873 874 875 876 877 878 879 880

881 882 883 884 885 886 887 888 889 890

891 892 893 894 895 896 897 898 899 900


901 902 903 904 905 906 907 908 909 910

911 912 913 914 915 916 917 918 919 920

921 922 923 924 925 926 927 928 929 930

931 932 933 934 935 936 937 938 939 940

941 942 943 944 945 946 947 948 949 950

951 952 953 954 955 956 957 958 959 960

961 962 963 964 965 966 967 968 969 970

971 972 973 974 975 976 977 978 979 980

981 982 983 984 985 986 987 988 989 990

991 992 993 994 995 996 997 998 999 1000


1001 1002 1003 1004 1005 1006 1007 1008 1009 1010

1011 1012 1013 1014 1015 1016 1017 1018 1019 1020

1021 1022 1023 1024 1025 1026 1027 1028 1029 1030

1031 1032 1033 1034 1035 1036 1037 1038 1039 1040

1041 1042 1043 1044 1045 1046 1047 1048 1049 1050

1051 1052 1053 1054 1055 1056 1057 1058 1059 1060

1061 1062 1063 1064 1065 1066 1067 1068 1069 1070

1071 1072 1073 1074 1075 1076 1077 1078 1079 1080

1081 1082 1083 1084 1085 1086 1087 1088 1089 1090

1091 1092 1093 1094 1095 1096 1097 1098 1099 1100


1101 1102 1103 1104 1105 1106 1107 1108 1109 1110

1111 1112 1113 1114 1115 1116 1117 1118 1119 1120

1121 1122 1123 1124 1125 1126 1127 1128 1129 1130

1131 1132 1133 1134 1135 1136 1137 1138 1139 1140

1141 1142 1143 1144 1145 1146 1147 1148 1149 1150

1151 1152 1153 1154 1155 1156 1157 1158 1159 1160

1161 1162 1163 1164 1165 1166 1167 1168 1169 1170

1171 1172 1173 1174 1175 1176 1177 1178 1179 1180

1181 1182 1183 1184 1185 1186 1187 1188 1189 1190

1191 1192 1193 1194 1195 1196 1197 1198 1199 1200


1201 1202 1203 1204 1205 1206 1207 1208 1209 1210

1211 1212 1213 1214 1215 1216 1217 1218 1219 1220

1221 1222 1223 1224 1225 1226 1227 1228 1229 1230

1231 1232 1233 1234 1235 1236 1237 1238 1239 1240

1241 1242 1243 1244 1245 1246 1247 1248 1249 1250

1251 1252 1253 1254 1255 1256 1257 1258 1259 1260

1261 1262 1263 1264 1265 1266 1267 1268 1269 1270

1271 1272 1273 1274 1275 1276 1277 1278 1279 1280

1281 1282 1283 1284 1285 1286 1287 1288 1289 1290

1291 1292 1293 1294 1295 1296 1297 1298 1299 1300


1301 1302 1303 1304 1305 1306 1307 1308 1309 1310

1311 1312 1313 1314 1315 1316 1317 1318 1319 1320

1321 1322 1323 1324 1325 1326 1327 1328 1329 1330

1331 1332 1333 1334 1335 1336 1337 1338 1339 1340

1341 1342 1343 1344 1345 1346 1347 1348 1349 1350

1351 1352 1353 1354 1355 1356 1357 1358 1359 1360

1361 1362 1363 1364 1365 1366 1367 1368 1369 1370

1371 1372 1373 1374 1375 1376 1377 1378 1379 1380

1381 1382 1383 1384 1385 1386 1387 1388 1389 1390

1391 1392 1393 1394 1395 1396 1397 1398 1399 1400


1401 1402 1403 1404 1405 1406 1407 1408 1409 1410

1411 1412 1413 1414 1415 1416 1417 1418 1419 1420

1421 1422 1423 1424 1425 1426 1427 1428 1429 1430

1431 1432 1433 1434 1435 1436 1437 1438 1439 1440

1441 1442 1443 1444 1445 1446 1447 1448 1449 1450

1451 1452 1453 1454 1455 1456 1457 1458 1459 1460

1461 1462 1463 1464 1465 1466 1467 1468 1469 1470

1471 1472 1473 1474 1475 1476 1477 1478 1479 1480

1481 1482 1483 1484 1485 1486 1487 1488 1489 1490

1491 1492 1493 1494 1495 1496 1497 1498 1499 1500


1501 1502 1503 1504 1505 1506 1507 1508 1509 1510

1511 1512 1513 1514 1515 1516 1517 1518 1519 1520

1521 1522 1523 1524 1525 1526 1527 1528 1529 1530

1531 1532 1533 1534 1535 1536 1537 1538 1539 1540

1541 1542 1543 1544 1545 1546 1547 1548 1549 1550

1551 1552 1553 1554 1555 1556 1557 1558 1559 1560

1561 1562 1563 1564 1565 1566 1567 1568 1569 1570

1571 1572 1573 1574 1575 1576 1577 1578 1579 1580

1581 1582 1583 1584 1585 1586 1587 1588 1589 1590

1591 1592 1593 1594 1595 1596 1597 1598 1599 1600


1601 1602 1603 1604 1605 1606 1607 1608 1609 1610

1611 1612 1613 1614 1615 1616 1617 1618 1619 1620

1621 1622 1623 1624 1625 1626 1627 1628 1629 1630

1631 1632 1633 1634 1635 1636 1637 1638 1639 1640

1641 1642 1643 1644 1645 1646 1647 1648 1649 1650

1651 1652 1653 1654 1655 1656 1657 1658 1659 1660

1661 1662 1663 1664 1665 1666 1667 1668 1669 1670

1671 1672 1673 1674 1675 1676 1677 1678 1679 1680

1681 1682 1683 1684 1685 1686 1687 1688 1689 1690

1691 1692 1693 1694 1695 1696 1697 1698 1699 1700


1701 1702 1703 1704 1705 1706 1707 1708 1709 1710

1711 1712 1713 1714 1715 1716 1717 1718 1719 1720

1721 1722 1723 1724 1725 1726 1727 1728 1729 1730

1731 1732 1733 1734 1735 1736 1737 1738 1739 1740

1741 1742 1743 1744 1745 1746 1747 1748 1749 1750

1751 1752 1753 1754 1755 1756 1757 1758 1759 1760

1761 1762 1763 1764 1765 1766 1767 1768 1769 1770

1771 1772 1773 1774 1775 1776 1777 1778 1779 1780

1781 1782 1783 1784 1785 1786 1787 1788 1789 1790

1791 1792 1793 1794 1795 1796 1797 1798 1799 1800


1801 1802 1803 1804 1805 1806 1807 1808 1809 1810

1811 1812 1813 1814 1815 1816 1817 1818 1819 1820

1821 1822 1823 1824 1825 1826 1827 1828 1829 1830

1831 1832 1833 1834 1835 1836 1837 1838 1839 1840

1841 1842 1843 1844 1845 1846 1847 1848 1849 1850

1851 1852 1853 1854 1855 1856 1857 1858 1859 1860

1861 1862 1863 1864 1865 1866 1867 1868 1869 1870

1871 1872 1873 1874 1875 1876 1877 1878 1879 1880

1881 1882 1883 1884 1885 1886 1887 1888 1889 1890

1891 1892 1893 1894 1895 1896 1897 1898 1899 1900


1901 1902 1903 1904 1905 1906 1907 1908 1909 1910

1911 1912 1913 1914 1915 1916 1917 1918 1919 1920

1921 1922 1923 1924 1925 1926 1927 1928 1929 1930

1931 1932 1933 1934 1935 1936 1937 1938 1939 1940

1941 1942 1943 1944 1945 1946 1947 1948 1949 1950

1951 1952 1953 1954 1955 1956 1957 1958 1959 1960

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

1971 1972 1973 1974 1975 1976 1977 1978 1979 1980

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000


0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

0 – 99 Chart


10 20 30 40

50 60 70 80

90 100 110 120

130 140 150 160

170 180 190 200

Decade Cards


Place Value Thinkboards

Number

Expanded Notation

Pic

ture

H

undred/tens/ones


25 2 tens and 5 ones

19 1 ten and 9 ones



51 5 tens and 1 one




Place Value Numeral and Representation Cards





16 1 ten and 6 ones



11 1 ten and 1 ones



23 + 10 31 + 10

39 + 10

64 + 10

15 + 10

42 + 10

54 + 10

67 + 10

71 + 10

84 + 10

Horizontal +10 Addition Cards


92 + 10

12 + 10

27 + 10

33 + 10

47 + 10

51 + 10

62 + 10

74 + 10

85 + 10

56 + 10


65 - 29 94 - 19

31 - 11

72 - 21

89 - 51

99 - 19

46 - 29

53 - 31

78 - 19

98 - 59

Subtraction Sentences


23 - 11

64 - 9

46 - 21

85 - 31

58 - 39

75 - 19


0

1

2

3

4

5

6

7

8

9

10

11

0 – 20 Cards


12

13

14

15

16

17

18

19

20


40-19

21

34 - 18

16

30 – 15 15

26 - 8

18

35 - 9

26

Number Sentence and Answer Card


22 - 12

10

36 - 18

18

28 - 14

14

31 - 20

11

27 - 19

8


Ten Dot Strips

Maths for Learning Inclusion – Tasks To Move Students On July 2008

Question 1

Counting Forward Tasks to move students on:

a) Count On (1 – 100 chart)

Use a 1 - 100 chart. Block out random numbers or groups of numbers. Ask students to identify the missing numbers and count on from there.

b) Digit Count On (Deck of cards, 1 – 100 chart)

Ask the student to take 2 (or 3) cards from a deck of cards and make a 2 (or 3) digit number from them. Ask the student to count on from this number. (1 - 100 chart may need to be used to scaffold learner). Variation: Have one student to clap once to count forward, or clap twice to count backwards.

c) Line Up (No resources)

Have students stand in a line and count forward from a set number.

d) Calculator Count On (Calculator) Investigate counting forwards from large numbers using a calculator. Ask the student to read the numbers aloud as they go. (e.g. 224 +1, 225 + 1 etc)

e) How Far Can You Count? (Objects to count, number line, number cards and 100 square)

On a number line or track ask the student to select a number and stand or put their finger on it. Ask student to tell you which number will come next, which would come before. Ask the student to count on as far as they can go and back. Encourage the student to start from a given number and count on rather than always starting at one. With a variety of objects model moving objects to count them. Ask a student to estimate how many objects they think there are and then count to check their answers.

f) Counting Sequences (No resources)

Have the class form a line. Have students say in turn the next number in the counting sequence. Begin at different numbers e.g. 9, 31, 43, 89

g) Counting Fish (Magnetic Fishing Set)

Put ten fish shapes on the table with paper clips on their noses, let the student catch a fish with a magnet and put it alongside the number 1 on the number track. Q: How many fish have you caught? Q: If you catch another fish, how many fish will you have? Q: What is one more than one? If the student predicts wrongly, catch another fish and count the number of fish the check the answer. Make sure you say ‘one more than one is two.’




Question 1 continued Counting Forward h) Bean Bags (Number track, beanbags, hoops)

Put out a number track and make sure the student can count along it forwards and backwards. Explain that the game is to throw beanbags into a hoop and every time a beanbag lands in the hoop a point is scored. The score is marked with tallies and also a marker is moved along the number track. Q: If I throw one more beanbag into the hoop what will the score be now? What is one more than six? Can you find that number card? Progress on to larger numbers when the child is ready.

i) Cross the Boundary (2 sets 0-9 cards, 100 chart)

Give the students 2 sets of number cards from 0 -9 and a 100 chart ask them to identify particular numbers on the chart. Put the 0 card on the table and ask Q: What number comes after zero when we count up? Q: Find the correct card and put it on top of zero. Keep counting with the cards, Q: What happens when we get to 39? With 2 cards display 40. Q: What is this number? Q: What comes after 40? Cover the zero to make 41. Q: Can you count on using the cards?

j) The Penny Has Dropped (Number track or line, number cards, count on cards, a tin and counters)

Let the students take a number and place a counter on that number, then take a count on card, the student counts on the amount on the card moving the counter for each move. When the student moves the counter the teacher drops a counter into the tin. Emphasise the match between one move and one counter dropping. Encourage the student to draw a picture showing what they have done during this activity.

k) Don’t Count Where You Stand! (large foam numbers or A4 sheets with numbers on, count on cards

and number cards or dice) Make a number track on the floor with the paper. Q: Can you remember what it is that you might be having trouble with when you count on? Q: What is the special thing about the number you count on? (remind student that they must take a step when they count on one). Ask the student to throw a dice to see which number they start on then choose a ‘count on card’ and ask them to do what the card says. Q: How much more than forty five is forty eight? Q: How could you check that forty five count on three is forty eight? Carry on with this using other ‘count on cards”.

l) Land on 10 (Floor number line or track and count on cards)

Ask the student to take a face down ‘count on card’ and tell the student to stand on which ever number will make 30 when they count on. e.g. number 27 if their count on card is 3. Encourage the student to jump along the number line until they reach 30. Q: How do I know which number to tell you to stand on to make sure you always reach 30? Q: If you take a ‘count on 2 card, where will I tell you to stand? Q: How do you know that?




Question 2

What number comes after? Tasks to move students on:

a) Before and After (1 – 100 chart, counters)

Use a 1 - 100 Chart to investigate numbers. The student rolls two dice, makes a number and places a counter on it on the chart. Ask ‘Which numbers come before and after it?’

b) Guess My Number (No resources)

Play ‘Guess my number”. One person thinks of a number. The others must ask questions ‘Is it before/after …?’ to determine the number.

c) Turn Over (Deck of cards)

Turn over two cards from a deck of cards and make a number with them i.e. 1 and 3, 13 or 31. Say the number that comes before and after this number.

d) Musical Number Plates (Numbered paper plates)

Have numbers written on paper plates and have the plates face down on the floor in a circle. When the music stops, students pick up a plate and say the number before and after it.

e) Two Things (Number cards 1 – 20)

Place the set of number cards from 1 – 20 on a table face up. Choose one card and ask the student to select a card that is one less than that card. If the student is successful move on to taking 2 cards and ask the children to tell you two things about them. If the student is still finding this difficult use the dot cards and ask them to match each dot card with the number that is one more or one less than.

f) Number After (Paper, pencil)

Choose a 2-3 digit number to record. Ask the student “What is one more?” Have the student write the next number in the sequence. Add to the sequence daily.




Question 3

Identification of Numerals

Tasks to move students on: a) Identifying Numbers (Number cards 0 – 20)

Using the number cards 0-20, ask the students to put the cards in order from 0 to 20. Ask the children to say the number names as they put the cards out. This needs to be practised before the child is likely to be able to understand one more and one less.

b) Read the Number (No resources)

Write a 3 (or 4) digit number. Ask the student to read the number aloud. c) Two Card Turnover (Deck of cards, 1 – 100 number chart, counters)

Turn over two cards from a deck of cards i.e. 4 and 6. Ask the student to make a two digit number from them and say it aloud. They can then put a counter on a 1 - 100 Chart. The aim is to be the first person to have 3 counters in a row (in any direction).

d) Digits and Dice (10 sided dice)

Roll 3 10 sided dice. Ask the student to make as many 3 digit numbers as possible and read them aloud.




Question 4

Recognising Numerals

Tasks to move students on: a) Say the Number (Flash cards)

Use flash cards (or write numerals on an individual whiteboard). Ask the student to say the number aloud.

b) Number War (Deck of cards)

Play ‘Number War’. A pack of cards is divided evenly amongst the players. Each player turns over two cards (the first being the tens and the second being the ones). All players call their number out, and the person with the largest number keeps all the cards. If there is a tie, both players then turn over a third card and use this to make a three-digit number. The person with the highest number keeps the cards. The winner is the person with the most cards at the end of the game.

c) Write and Cross Extension (1 – 100 chart, ten sided dice)

Use two 10 sided dice and ask the student to make a 2 digit number. These numbers can then be recorded on a 1 - 100 Chart. The first person to get three numbers in a row crossed off is the winner.




Question 5

Putting Numerals in order


a) Greater Than / Less Than (Deck of cards, greater than and less than cards) A pile of greater than/less than symbols are placed face down on the table. Each student has two cards (no picture cards) and must make a number with those cards (i.e. 19 or 91). Students establish whether their number is greater or less than their opponent’s number. The top card from the </> pile is turned over. The winner is the student whose number matches the card. i.e. 19 and 45, if the card is >, 45 is the winner.

b) Biggest Domino (Dominoes, number line) Show the student a domino. Ask them to write a numeral for the dots on each side. Which is the bigger number? Show the numbers on a number line

i.e. ‘2 is less than 4’ c) Two Dice Roll (Dice)

Roll two dice and make a number with the numerals. Repeat several times, then ask the student to place the numbers from smallest to largest.

d) Smallest to Largest (Deck of cards, number line, 1 – 100 chart) Choose 3 cards from a deck of cards. Make as many (1, 2 , 3 digit) numbers as you can. Place these numbers in order from smallest to largest. (A number line or 1 - 100 Chart can be used to scaffold the learning).

e) In Betweens (100 chart) This game involves thinking about what happens when the digit is nine. Start with asking the students to say all the numbers that end in 9 eg. 9, 19, 29 etc. Give the student a 100 square for support. “Can you show me a number that is bigger than forty nine but smaller than fifty nine?” Repeat this activity gradually building up speed. When the child is confident, just point between two numbers and ask the child to call out a number that goes between those two numbers.



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Putting Numerals in order

f) Run in the Gap (Enlarged number cards ending in 9) You will need enlarged number cards ending in 9 and at least eleven children or a whole class. Ten children hold a large number card each and stand in a horse shoe shape. Someone calls out a number e.g. forty five and one or more students must run between the gap where 45 would come (ie. Between the child holding 39 and the child holding 49). Everyone who runs between the right numbers wins ten points. As an extension, extend the numbers up to two hundred or further.

g) Teen Numbers (1-100 chart, number cards) Support the child to read and name the teen numbers and make them with number cards. Ask students to show you on the 100 chart what comes after 9? 19? 29 etc and read the numbers in the second row on the number chart. Q: Can you make me 10, 15, 18 etc with the number cards? Put out all the number cards to 20 and ask the students to pick them up in order from smallest to largest and vice versa and say the names.




Question 6

Writing Numbers


a) Roll and Write (Dice) Roll the dice 4 times. Students have 1 min to write as many different number combinations from the four numbers as possible. Students then receive a point for every number they read aloud correctly. Extension: Order the numbers

b) Turn and Tell (Deck of cards, grid paper) Turn over three playing cards (No picture cards). Ask the student to make a number from these and then write the next 10 (or 20 etc) numbers. Ask the student to then read the numbers aloud. (Use a 1 - 100 Chart for support if needed) Discuss patterns that can be seen in the numbers.

c) Calculator Task (Calculator) Type these numbers on the calculator e.g. 7, 47, 724. Check that each number has been entered correctly. Make sure calculator is cleared between numbers.

d) Read the Number (Calculator) Pick any number from 2 to 9 and type it on the calculator. Read the number. Type in a different number from 2 to 9 (forming a 2 digit number). Read the number. Continue to higher numbers.

e) Up to Fifty Five (Number strips – up to 55) Show the number strip 26-35. Q: What comes before twenty seven? What comes after twenty seven? Emphasise the change in the ones digit but not the tens digit. Then move on to Q: What number comes after thirty nine? Ensure the child is aware of the tens and ones digit changing. Repeat with other number strips.




Question 7

What numbers come before?

Tasks to move students on: a) Before and After (1 – 100 chart, dice, counters)

Use a 1 - 100 Chart to investigate numbers. The student rolls two dice, makes a number and places a counter on it on the chart. Ask ‘Which numbers come before it?’

b) Guess My Number (No resources)

Play ‘Guess my number”. One person thinks of a number. The others must ask questions ‘Is it before/after ….?’ to determine the number.

c) Turn Over (Deck of cards)

Turn over two cards from a deck of cards and make a number with them i.e. 1 and 3, 13 or 31. Say the number that comes before and after this number.

d) Musical Number Plates (Numbered paper plates)

Have numbers written on paper plates and have the plates face down on the floor in a circle. When the music stops, students pick up a plate and say the number before and after it.

e) Possibilities (Dice)

Roll three (or four) dice. Make all the possible three (or four) digit numbers. Say them aloud. Ask ‘Which number comes before it?’

f) Number Before (Paper, pencil)

Choose a 2 – 3 digit number to record. Ask the student “What is one less?” Have the student write the number that comes before it. Have the student add to the before sequence daily.

g) What Number Comes Before (Number cards 1 – 20)

Place the set of number cards from 1 – 20 on a table face up. Choose one card and ask the student to select a card that is one less than that card.

h) Ten Counter Race (Number track, coin, counters)

Each student lays their counters along a self numbered track eg 35-58. They take turns to toss a coin, if the coin lands on heads they take one of their counters away and must say the right number sentence for example ‘fifty seven is one less than 58’ if the player tosses tails they do nothing. The winner is the first person to get rid of all their coins.




Question 8

Counting Backwards


a) Go Back (1 – 100 chart) Use a 1 - 100 Chart to support students counting backwards. Say a number and ask them to count backwards from that number.

b) Jump Back (Number line) Use a number line to support students counting backwards. Say a number and ask them to count backwards from that number.

c) Flash Back (1 – 100 flashcards) Use flash cards with numbers 1 to 100 on them. Turn one card over and ask the student to count backwards from this number (for 10 or so numbers).



Number Intervention Kit – Resources to support Tasks to Move Students On - July 2008. Saying, Reading & Writing Numerals (Pink)

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31 32 33 34 35 36 37 38 39 40

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51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

1 – 100 Chart


Ten Fish


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Number Line – Blank


Count on 1

Count on 2

Count on 3

Count on 4

Count on 5

Count on 6

Count on 7

Count on 8

Count on 9

Count on 10

Count On Cards


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Flashcard Numbers


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Greater Than / Less Than Cards


Large Cards Ending in 9











14 15 16 17 18 19 20 21 22 23 24 25

26 27 28 29 30 31 32 33 34 35

36 37 38 39 40 41 42 43

44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

59 60 61 62 63 64 65 66 67 68 69 70 71

72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

Number Strips


89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105

106 107 108 109 110 111 112 113 114 115 116 117 118 119

120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

147 148 149 150 151 152 153 154 155 156 157 158 159 160

Maths for Learning Inclusion – Tasks To Move Students On July 2008.

Question 1

Making Equal Groups


a) Equal Groups (Counters, calculator) Ask the student to make __ groups of __ . Ask ‘How many altogether?’ Discuss link between multiplication and addition (i.e. use a calculator, 4, + 4, + 4 and compare with 3 x 4). Encourage student to use summaries to describe their groupings eg. 3 fours, 3 lots of four, 3 groups of four, 3 sets of four and record them as 4 + 4 + 4 and later as 3 fours then 3 x 4.

b) Groups Of (Counters) Ask the student to make 4 groups of 5 counters. Ask them to work out how many counters they used without counting. Draw attention to ‘groups of’, counting by 5s, addition ( 5 + 5 + 5 + 5). Ask the student to write a description of the groups (4 groups of 5 is 20) and then a number sentence (4 x 5 = 20), when they have understood the ‘groups of’ concepts. Repeat with different amounts.

c) Dice Groups (Dice, counters) Roll two dice. Ask the student to make groups of using these numbers (i.e. 3 and 4 – student makes 3 groups of four). Ask ‘How many counters altogether?’ (Reinforce ‘groups of’ and skip counting as strategies for working this out)

d) Planning (Counters or other materials, calculator) Have student use a predetermined number of counters and ask them to make equal groups e.g. 15 could be 5 threes. If the student counts by ones, ask them to count by threes. If the student skip counts, ask them how many threes they need. Ask student to write a number sentence and use a calculator to check the result.




Question 2

Skip counting Tasks to move students on:

a) Number Skip (Number line) Practice skip-counting with a number line. i.e. 3 x 3 = 3 + 3 + 3 = 9

b) Skip and Mark (1-100 chart, counters) Practice skip-counting with a 1 - 100 Chart, placing a counter on each number as it is said.

c) Dice and Skip (Dice, number line, 1-100 chart) Roll two dice. Skip count using the first number, the second number tells how many skips the person must count (Number line, 1 - 100 Chart for support). i.e. if a 2 then a 5 is rolled, the student would count 2, 4, 6, 8, 10. The student earns a point for every correct number. The first person to 30 points is the winner. Extension: Ask the student to write a multiplication equation for the skip count i.e. 2, 4, 6, 8, 10 = 2 x 5

d) Skip-counting (Chalk number line) Draw a chalk number line on the floor (mark in numbers starting at zero and mark at regular intervals to number of your choice eg 20). It needs to be big enough for student to use to jump/hop along. Ask them to skip count by twos, threes etc.

e) Frog Jump (Toy frog or substitute, number line)

A frog jumps on the number line. Each jump is worth 2. Start at zero. What numbers will the frog land on? (A toy plastic frog can be used on a card number line strip). Variations can be to have a different starting number, have a different jump number, record the numbers you land on or ask “If you do four jumps, what is your finish number?” etc.

f) Quick Count (Counters)

Tip out a quantity of counters and ask student to count them as quickly as possible. If the student counts by ones, model counting by twos.

g) Large Collection Skip Count (No resources)

Ask the student to select a number to use when skip counting a large collection. Ask them why they chose the number.

h) How Many? (Counters)

Say “I’m interested in how people count by threes. If you count to twelve by threes how many threes would you count?” Use counters to make an array.




Question 3

Arrays Tasks to move students on: a) Roll Two (Dice, counters or grid paper and coloured pencils)

Roll two dice. Make an array using these numbers. i.e. 3 and 4 - make three rows of four AND four rows of three. Are they similar? How many in each array?

b) Array Questions (No resources)

Make various arrays and ask the following questions: “How many dots are there altogether? How many rows? How many dots in each row?”. Turn the array 90° and ask “How many dots altogether?”

c) Two Cards (Deck of cards)

Turn over two cards from a deck of cards. i.e. 5 and 3. Make an array using these numbers and record as 5 threes. Turn the array 90° and record as 3 fives. Discuss the connection between the two.

d) Recording (Practice arrays)

Show the Practice Arrays and ask the student to write multiplication equations for them. e) Styro Arrays (Styrofoam, matchsticks)

Student uses coloured pins/matchsticks to make arrays on a Styrofoam block eg make 4 lots of 3, (arranged in rows and columns) turn block around so that representation is now 3 lots of 4. ‘What do you notice?’ How many altogether in each array? Do with other numbers/arrays.

f) Magnetic Arrays (Magnets, magnetic whiteboard)

Use a magnetic whiteboard (small) and magnets to make a variety of arrays. Label the arrays made. Whiteboards can be turned to show the two arrays.

g) Observation Arrays (Muffin tins, egg cartons)

Provide different arrays found around the home/school/environment etc e.g. muffin tins, glue stick holders, egg cartons, patty pan tins, sheets of stickers and so on. Record the multiplication fact represented by the array.





Arrays h) Kid Pix Arrays (Kid Pix Program)

Use Kid Pix to create arrays using the stamp tool. Write matching multiplication fact or story. Print up to make an ‘Arrays’ book.

i) Make It (Counters) I have 12 dots arranged in array. What might my array look like? Use other numbers.

j) Word Problems (Printout of word problems, counters, pen, paper)

Give students a written problem and have them create an array to represent it. Students can then record e.g. 4 sixes or 4 x 6. - There are four rows of tables in the puppet theatre. Each row seats 6 people. How many people can sit down? - I have a slab of chocolate. There are 5 rows and each row has 6 pieces. How many pieces of chocolate are there? - Fred planted 3 rows of seeds. There are 7 seeds in each row, how many seeds altogether? - If there 9 rows on the bus. Each row seats 4 people, how many people can sit on the bus? - The cup cake tin has 5 rows. Each row has 3 cup cake holders. How many cup cakes can I make? - I planted 30 plants. If each row has to have the same number of plants, what different combinations of rows could I plant them in?

k) Rectangular Arrays (Arrays)

Show students “Rectangular Arrays” and ask: How many equal groups do you see? How many in each group? How many altogether? Rotate the card and repeat. Ask: Do you see different groups?




Question 4

Equal Groupings - Visible Tasks to move students on:

Multiplication

a) Unifix Groups (Unifix cubes or MAB blocks) Use Unifix cubes or MAB blocks to show equal groups .i.e. show 6 as 6 x 1, 1 x 6, 2 x 3, 3 x 2.

b) Tins and Pencil Sort (Tins, pencils) Put 4 pencil tins on the table. Ask ‘If each tin has 5 pencils in it, how many pencils altogether?’ (provide pencils for students to put into the tins). Repeat using different amounts.

c) Equal Groups (Counting Materials) Ask student to solve problems using equal groups e.g. How many straws will be needed to make five pentagons, five hexagons. Ask student to write an addition number sentence and a multiplication number sentence. Talk about how each sentence shows the same situation.

d) Number Line Skip (Number line) Ask students to skip count along a number line, recording as they go (i.e. to 15 by 5s and 3s)

3 + 3 + 3 + 3 + 3 = 5 + 5 + 5 = 3 x 5 = 5 x 3

e) Dice Show (Dice) Using six dice ask student to show five lots of 2 using the dice, six lots of 1, 3 lots of 4 and so on.

f) Counters in Containers (Counters, containers) Using counters. Put 10 counters each in 2 containers. (Put 6 counters each in 3 containers. Put 4 counters each in 6 containers and so on.) For each one ask:

o How many groups are there? o How many in each group? o How many altogether? o Write a number sentence to match this.





Equal Groupings - Visible

Multiplication continued

g) Word Problems (Variety of counting materials, pen, paper) Emphasise that this activity is to practice making equal groups of objects. Students may use materials or draw objects to represent their mathematical thinking. - One bike has two wheels. How many wheels would 7 bikes have? 2 x 7 = - One car has four wheels. How many wheels would 8 cars have? 4 x 8 = - One spider has 8 legs. How many legs would 5 spiders have? 8 x 5 = - One ant has six legs. How many legs would two ants have? 6 x 2 =

Partitioning with Division

h) Partition It (Counters) Give the student an amount of counters (i.e. 15), then ask ‘If I divided them into __ equal groups, how many counters would be in each group?’ Draw the link to division equations and discuss strategies for sharing equally.

i) Straw Shapes (Straws) Provide the student with an amount of straws. Ask ‘If a triangle has three sides, how many triangles can I make?’. Make the connection with multiplication (ask student to write a multiplication equation for the problem as an extension) NOTE: At first, ensure that there are no ‘left over’ straws i.e. for triangles, have 12 or 15 straws ready. Use other shapes e.g. squares, pentagon, hexagon, octagon etc.

j) Tomato Pizza (Paper, counters) Draw a pizza that has been cut up into 4 (or 5 or 8 etc) slices. Give the student 12 (or 15, 24 etc) counters and Ask ‘You have 12 pieces of tomato, can you put them on the pizza so that all slices have the same amount of tomato pieces? Repeat with different amounts.

Division A (Counters)

k) Scatter (Counters) Give the student an amount of counters. Say “Here are ___ counters. If I wanted to share them among people so that each person got ___, how many people could I share them with?’





Equal Groupings - Visible

l) Word Problems (Pens, paper) Have the student write some word problems where they start with the total amount and know the size of the portions e.g. There are 30 students in our class. Each table seats 6 children. How many tables will we fill? There are 16 chocolate squares. If I wanted to share them equally amongst people so that each person got 4 squares, how many people could I share them with?

Division B (Counters)

m) Unifix Towers (Unifix cubes) Give students a tower of 12 unifix cubes. Ask them to break it (divide) into 3 equal towers. How many cubes in each tower? Write a division equation for it e.g. 12 ÷ 3 = 4. Then divide the tower into 4 groups and write the equation e.g. 12 ÷ 4 = 3. Discuss the connection between these equations. Repeat with other amounts.

n) Drawing Arrays (Grid paper or plain paper) Have the student draw various arrays. Ask the student to circle groups of ___. Construct a division equation for this together. i.e. 3 x 4 Array - 12 ÷ 3 = 4.

o) Question Relationship (Counters) Ask student “If I have 20 lollies to share amongst 4 people, how many lollies each?” THEN ask “If I had 20 lollies to share amongst 5 people, how many lollies each?” and show the connection between the two.

p) Word Problems (Variety of counting materials, pen, paper) Emphasise that this activity is to practice making equal groups of objects. Students may use materials or draw objects to represent their mathematical thinking. - If I need 4 straws to make a square, how many squares could I make with 24 straws? - Jim had 15 Smarties. His Mum told him to share them equally between himself and his two brothers. How many Smarties did they each get? - Mary was making party bags for her birthday. She had 21 Freddo Frogs to share equally among the 7 party bags. How many Freddos could she put in each bag? - There are 6 fish bowls and 36 fish. Each fish bowl has an equal number of fish. How many fish in each fish bowl? - There were 24 students in the class. If 4 students sit at each table, how many tables are there?




Question 5

Equal Groupings - Hidden


Multiplication

a) Make it with MAB (MAB blocks, 1-100 chart, number line) Use MAB blocks to make equal groups, cover them and say ‘I have __ groups, each group has ___. How many altogether? Then show the MAB blocks and count through the groups with the student. Write a multiplication equation for the problem. Discuss the strategies used. If the student is having difficulty, use a 1 - 100 chart or number line to help the student skip count to get the answer.

b) Pencils and Tins (Pencils, tins) Cover 4 pencil tins on the table. Ask ‘If each tin has 5 pencils in it, how many pencils altogether?’ Provide pencils for the student to check their answer with. Ask the student to write a multiplication equation for the problem. Repeat using different amounts.

Partitioning with Division

c) Groups (Counters) Tell the student that you have an amount of counters (i.e. 15), then ask ‘If I divided them into __ equal groups, how many counters would be in each group?’ Draw the link to division equations and discuss strategies for counting equally. Provide counters for the student to check their answer.

d) Envelopes (Counters, envelopes) Provide the student with 5 (or another amount) of envelopes. Say ‘I have put ___ counters in each envelope, how many counters altogether?’ Allow students to check that their answer with counters.

e) Straws (Straws) Tell the student that you have an amount of straws. Ask ‘If a triangle has three sides, how many triangles can I make?’. Make the connection with multiplication (ask student to write a multiplication equation for the problem as an extension). Provide straws for the student to check their answers. NOTE: At first, ensure that there are no ‘left over’ straws i.e. for triangles, have 12 or 15 straws ready.






f) Draw a pizza that has been cut up into 4 (or 5 or 8 etc) slices. Say that you have 12 (or 15, 24 etc) counters and Ask ‘You have 12 pieces of tomato, can you put them on the pizza so that all slices have the same amount of tomato pieces? Repeat with different amounts. Provide counters for the student to check their answer.

Division A

g) Share the Counters (Counters) Give the student an amount of counters. Say “Here are ___ counters. If I wanted to share them among people so that each person got ___, how many people could I share them with?’

h) Word Problems (Printout) Ask students to solve the word problems. Emphasise the importance of equal shares. Students may need counters to support their learning at first. Make clear the connection with the multiplication or division equation. After the problem has been solved, encourage students to write a number equation/s to represent the problem e.g. 36÷12=3 or 12x3=36 - If you had 36 Freddo frogs and 12 party bags, how many Freddos would you put in each bag so that they are shared equally? - I have 3 plates and 15 chocolates. If I share them equally, how many chocolates on each plate? - I have 30 tennis balls that need to be shared equally amongst 5 of my friends. How many tennis balls will each person get? - I have 24 flower seeds. I need to plant them so that there are 6 seeds in each row. How many rows can I make? - There are 18 slices of toast and 9 people. How many slices can each person have if it is shared equally? - I have 48 crayons that need to be shared equally amongst 4 tins. How many crayons will be in each tin? - There are 30 students in the class and 5 tables. If each table has the same number of students sitting on it, how many students will be at each table? - There are 28 kids who want to play netball. Each team needs seven players. How many teams can be made? - I have a pack of 40 cards. We are playing a game where each person needs 8 cards. How many people can play?






Multiplication Using an Array

i) Altogether Array (Practice arrays, counters) Use the Practice Arrays or make your own using counters. Cover the array, leaving only the top row (or top two rows) visible. Ask ‘How many dots in this row?’ then “if there are __ more rows. How many dots altogether?’. Encourage the student to draw a diagram or use counters to solve the problem. Discuss the multiplication equation used to solve this. Use different arrays, following the same sequence.

i.e.

Division B Using an Array

j) Covered Arrays (Practice arrays, counters) Use the practice arrays or make your own using counters. Cover the array, leaving only the top row (or top two rows) visible. Ask ‘How many dots are there in this row?’ then ‘If there are ___ dots altogether, how many more rows are there?’. Encourage the student to draw a diagram or use counters to help them solve the problem. Discuss the strategies used to solve this problem and encourage the student to create a multiplication equation to represent this problem.



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(Only top row uncovered) Say ‘How many dots in this row? There are another two rows hidden, how many dots altogether?

Number Intervention Kit – Resources to support Tasks to Move Students On – July 2008 Beginning Multiplication and Division (Purple)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21



Frog Jump


Practice Arrays








There are four rows of tables in the

puppet theatre. Each row seats 6 people. How many people can sit down?

I have a slab of chocolate. There are 5 rows and each row has 6 pieces. How many pieces of chocolate are there?

Fred planted 3 rows of seeds. There are

7 seeds in each row, how many seeds altogether?

If there 9 rows on the bus. Each row

seats 4 people, how many people can sit on the bus?

The cup cake tin has 5 rows. Each row has 3 cup cake holders. How many cup

cakes can I make?

I planted 30 plants. If each row has to have the same number of plants, what different combinations of rows could I

plant them in?

Arrays Word Problems


One bike has two wheels. How many

wheels would 7 bikes have?

One car has four wheels. How many

wheels would 8 cars have?

One spider has 8 legs. How many legs

would 5 spiders have?

One ant has six legs. How many legs

would two ants have?

Multiplication Word Problems


If I need 4 straws to make a square, how many individual squares could I

make with 24 straws?

Jim had 15 Smarties. His Mum told him to share them equally between himself

and his two brothers. How many Smarties did they each get?

Mary was making party bags for her

birthday. She had 21 Freddo Frogs to share equally among the 7 party bags.

How many Freddos could she put in each bag?

There are 6 fish bowls and 36 fish.

Each fish bowl has an equal number of fish. How many fish in each fish bowl?

There were 24 students in the class. If 4 students sit at each table, how many

tables are there?

Division Word Problems


If you had 36 Freddo frogs and 12 party bags, how many Freddos would you put in

each bag so that they are shared equally?

I have 3 plates and 15 chocolates. If I

share them equally, how many chocolates on each plate?

I have 30 tennis balls that need to be

shared equally amongst 5 of my friends. How many tennis balls will each person

get?

I have 24 flower seeds. I need to plant them so that there are 6 seeds in each

row. How many rows can I make?

There are 18 slices of toast and 9

people. How many slices can each person have if it is shared equally?

I have 48 crayons that need to be

shared equally amongst 4 tins. How many crayons will be in each tin?

Equal Groupings Division


There are 30 students in the class and 5

tables. If each table has the same number of students sitting on it, how many students will be at each table?

There are 28 kids who want to play

netball. Each team needs seven players. How many teams can be made?

I have a pack of 40 cards. We are

playing a game where each person needs 8 cards. How many people can play?

Maths for Learning Inclusion – Intervention Kit 2008. Maths for Learning Inclusion – Intervention Kit 2008.


Maths for Learning Inclusion (M4LI) Tasks To Move Students On Multiplication and Division

Question 1

Verbal Multiplication and Division Calculating Tasks

Tasks to move students on: a) Calculation Strategies (Practice questions, counters)

Use the following questions to practice strategies for multiplication and division. Provide counters etc for students to use. Reinforce the concept of ‘groups of’ and make the link with multiplication equations and division equations clear (i.e. help the student to write an equation to express the problem). Have students work through the following questions:

• If there are 3 piles of books and 4 books in each pile, how many books are there altogether? • I have 4 coins and each coin is worth $2.00. How much money do I have altogether? • Twenty books were put on 4 shelves, with an equal number on each shelf. How many books are on

each shelf? • There are 18 apricots and each child is given 3 apricots. How many children are there? • If we share 12 biscuits among 4 children, how many biscuits would each child get? • There are 17 plums and each child is given 5. How many children are there and how many plums

are left? • If we shared 13 oranges equally among 3 children, how many oranges would each child get and how

many would be left over?

• There are 15 pieces of paper and each child is given 3 pieces of paper. How many children are there?

• Four children have 5 apples each. How many apples altogether? • There are 6 dogs. Each dog has 4 legs, how many legs altogether? • There are 3 butterflies. Each butterfly has 6 legs, how many legs altogether? • Five students have 4 books each. How many books altogether?




Question 1 (continued)


• Three students each have 7 crayons. How many crayons altogether?

• There are 14 stickers. Each child is given 2 stickers, how many children are there?

• There are 18 basketballs. Each student is given 3, how many students are there?

• I have 28 pencils. If I put 8 in each pencil case, how many pencil cases are there?

• There are 25 fingers (including thumbs!) how many hands?

• There are 35 pens. Each student has 7 pens. How many students?

• There are 20 slices of orange. If there are 5 people, how many pieces of orange will they each get?

• I have 18 marbles. I want to share them equally amongst my 3 friends. How many marbles will each friend get?

• There are 36 fish. If I share them equally among 6 fishbowls, how many fish in each fishbowl?

• There are 24 biscuits. If there are 8 people, how many biscuits will each person get?

• I have 12 cherries. If I share them equally between my sister and myself, how many cherries will we each get?

• There are 20 pears. If each person gets 3 pears, how many people are there and how many pears will be left over?

• There are 26 pencils. If each person gets 6 pencils, how many people are there and how many left

over?

• There are 11 cat biscuits. If each cat gets 3 biscuits, how many cats are there and how many biscuits will be left over?

• There are 21 blocks. If each person gets 5 blocks, how many people are there and how many blocks will be left over?




Question 1 (continued)


• There are 44 buttons. If each person gets 8 buttons, how many people are there and how many buttons are left over?

• If we shared 9 bananas equally between 2 people, how many bananas would they each get and how many would be left over?

• There are 30 flowers. If I shared them equally among 7 people, how many would each person get and how many flowers would be left over?

• If we shared 15 balloons equally among 4 people, how many would each person get and how many would be left over?

• There are 28 shells. If we shared them equally among 5 students, how many would each student get and how many shells would be left over?




Question 2

Multiplication Tasks to move students on:

a) Create an Array (Counters) Have students create an array for multiplication equations (i.e. 3 x 4 = 12). Then count or circle ‘groups of’ to emphasise multiplication. Discuss strategies for finding out the answer i.e. counting by 4s, using known multiplication facts.

b) Number Line Skip (Number line) Use a number line to skip count to answer multiplication tables (i.e. 5 x 7 is the same as 5 + 5 + 5 + 5 + 5 + 5 + 5)

c) Multiplication Bingo (Grid paper) Play multiplication bingo. Each player rules up a 3 x 3 grid and writes 9 products (answers to times tables) in it. Two dice are rolled and the numbers multiplied (4 and 6 - 4 x 6 = 24), players may then cross off 24, if it is on their grid. The first person to have all their numbers crossed off is the winner. Note: Discuss with students how they are solving the equations and provide counters, pencil and paper etc to help them solve them).

d) Memory/Snap (Multiplication cards) Play Memory or Snap with multiplication cards, where the equation and its product are the pair. i.e.

and are a pair

e) Multiplication Snap (Deck of cards) Two cards from a deck of cards are turned over and the first person who can correctly say the equation and the answer keeps the cards. This continues until all cards are gone, with the winner being the person with the most cards. Note: This game can be simplified by placing cards 1 - 5 in one pile, and cards 6 - 10 (picture cards) in the other which will make the highest equation 5 x 10 = 50.

f) Dice Products (10 sided dice) Roll two 10 sided dice. Ask students to write the multiplication equation of these two numbers and call out the answer. If it is correct, the player earns a point. The first player to 10 points is the winner.

g) Card Products (Deck of cards) Students play in pairs. Divide deck into halves. Player 1 turns over 2 cards e.g. 6 fives 30. Player 2 turns over 2 cards e.g. 5 eights 40. The player with highest number puts the cards at the bottom of their pile. The player with the most cards wins.

●●●● ●●●●●●●●

7 x 8 56




Question 3

Commutative Law

Tasks to move students on: a) Rotate the Array (Practice arrays, counters)

Demonstrate Commutative Law using arrays. Either use the Practice Arrays (from Test 5) or make arrays using everyday objects (i.e. counters, MAB blocks etc). Show the student the array and assist in writing an equation for it

i.e. 3 x 5 = 15

Then, rotate the array, and ask the student to write an equation for it. Highlight the connection between the two equations. Repeat this using a range of arrays.

b) Grid Arrays (Regions) (Grid paper)

Use grid paper to show multiplication equations. Ask the student to draw 2 x 4 using grid paper. Ask ‘How many altogether?’

Then, ask the student to draw a 4 x 2 grid. Ask ‘How many altogether?

Discuss the connection between the two equations. c) Memory (Arrays)

Play memory with arrays. Students need to find matching arrays to make a pair. i.e. a 3 x 4 array and 4 x 3 array would be a pair. To keep the pair, the student needs to say how many dots in the array altogether (i.e. for 3 x 4, 12)

d) Array Problems (Counters)

Have students explore arrays to discover that e.g. 4 x 3 = 3 x 4. e.g. Kelly said we planted corn in rows of 3. Tracy said they were in rows of 4. Could they both be right? Have students use materials or diagrams to solve the problem.

●●●●● ●●●●● ●●●●●

●●● ●●● ●●● ●●● ●●●

5 x 3 = 15 Then…




Question 4

Inverse Relationships


a) Multiply and Divide (Counting Materials) Provide students with everyday objects (i.e. counters etc). Ask them to make a multiplication equation using the objects and record it on paper. i.e.

Then…. Ask ‘If I had 21 counters and I divided them into 3 equal groups, how many counters would be in each group?’ Support the student to write a division equation for this. Highlight the connection between the two equations. Repeat using different amounts.

b) Arrays (Counting materials) Undertake the same process. Ask the student to first identify the multiplication equation and then ask them to think about the division equation. Highlight the connection between the two (turn the array 90°).

c) Card Array (Deck of cards, counters) Turn over two cards from a deck of cards. Create and array using these numbers. e.g. 3 x 4 then write two division equations for this array

( 12 ÷ 4 = 3 and 12 ÷ 3 = 4 )

3 x 7 ●●●●●●● ●●●●●●● ●●●●●●● = 21

3 4 ●●●● ●●●● ●●●●




Question 5

Area Multiplication


a) Area Multiplication (Practice Multiplication Task) Use the practice Area multiplication task. Make links between rows and columns and the multiplication table.

b) Area Grids (Grid Paper) Use grid paper to discuss area multiplication. Demonstrate that if there are 5 rows and each row has 4 squares in it, 5 x 4 = 20 can be written to describe it. Practice with grids of varying sizes.

c) Multiplication Toss (Ten sided dice, grid paper) Players take turns to toss 2 ten sided dice. They colour in a region on their grid paper and record e.g. 5 threes or 5 x 3. The player to colour in the grid paper first wins.

Number Intervention Kit – Resources to support Tasks to Move Students On – July 2008 Multiplication and Division (Blue)

If there are 3 piles of books and 4 books in each pile, how many books are

there altogether?

I have 4 coins and each coin is worth $2.00. How much money do I have

altogether?

Twenty books were put on 4 shelves, with an equal number on each shelf. How

many books are on each shelf?

There are 18 apricots and each child is given 3 apricots. How many children are

there?

If we share 12 biscuits among 4 children, how many biscuits would each

child get?

There are 17 plums and each child is given 5. How many children are there

and how many plums are left?

If we shared 13 oranges equally among 3 children, how many oranges would each child get and how many would be left

over?

There are 15 pieces of paper and each child is given 3 pieces of paper. How

many children are there?

Verbal Multiplication and Division Calculating Tools


Four children have 5 apples each. How many apples altogether?

There are 6 dogs. Each dog has 4 legs, how many legs altogether?

There are 3 butterflies. Each butterfly has 6 legs, how many legs altogether?

Five students have 4 books each. How many books altogether?

Three students each have 7 crayons. How many crayons altogether?

There are 14 stickers. Each child is given 2 stickers, how many children are

there?

There are 18 basketballs. Each student is given 3, how many students are there?

I have 28 pencils. If I put 8 in each pencil case, how many pencil cases are

there?


There are 25 fingers (including thumbs!) how many hands?

There are 35 pens. Each student has 7 pens. How many students?

There are 20 slices of orange. If there are 5 people, how many pieces of orange

will they each get?

I have 18 marbles. I want to share them equally amongst my 3 friends. How many

marbles will each friend get?

There are 36 fish. If I share them equally among 6 fishbowls, how many

fish in each fishbowl?

There are 24 biscuits. If there are 8 people, how many biscuits will each

person get?

I have 12 cherries. If I share them equally between my sister and myself, how many cherries will we each get?

There are 20 pears. If each person gets 3 pears, how many people are there and

how many pears will be left over?


There are 26 pencils. If each person gets 6 pencils, how many people are

there and how many left over?

There are 11 cat biscuits. If each cat gets 3 biscuits, how many cats are there and how many biscuits will be left over?

There are 21 blocks. If each person gets 5 blocks, how many people are there and

how many blocks will be left over?

There are 44 buttons. If each person gets 8 buttons, how many people are

there and how many left over?

If we shared 9 bananas equally between 2 people, how many bananas would they each get and how many would be left

over?

There are 30 flowers. If I shared them equally among 7 people, how many would each person get and how many flowers

would be left over?

If we shared 15 balloons equally among 4 people, how many would each person get

and how many would be left over?

There are 28 shells. If we shared them equally among 5 students, how many

would each student get and how many shells would be left over?


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21



56 15 48 36 12 24 30 63 27

7x8 5x3 8x6 9x4 6x2 4x6 6x5 9x7 9x3

Multiplication Question and Answer Cards


8 20 18 28 40 54 14 21 24

4x2 5x4 6x3 7x4 8x5 9x6 2x7 3x7 3x8


12 27 12 25 42 35 32 27 16

2x6 3x9 4x3 5x5 6x7 7x5 8x4 9x3 8x2


Area Multiplication

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Maths for Learning Inclusion Tasks to Move Students Onovsstaffwiki.wikispaces.com/file/view/Tasks_to_move_students_on.pdf · Maths for Learning Inclusion (M4LI) Tasks to Move Students