Students need to simultaneously develop proficiency with number sequences forward and backwards by one, and their capacity to apply those sequences to counting tasks. Ideally students’ ability to say word sequences develops either ahead of, or synchronous to, their need to apply it. So students who can count collections up to ten should be learning number sequences beyond ten.
Session 1: Hundreds board
Count by ones on a hundreds board, both forwards and backwards, and ask questions which help students connect numerals to spoken words. For example,
Can you find the number 8 without counting up or down?
What number comes after eight?
What number comes before eight?
Variations
Have students work in pairs. They take turns drawing a numeral card out of a container, then work together to find the number on a hundreds board and make a set which contains the number they have drawn, for example a set of eight counters.
First work with numbers 1–10, and extend the range as needed to increase the challenge.
Session 2: Slavonic abacus
Count by ones on a Slavonic abacus, both forwards and backwards. While you count, say the numbers out loud with students as you move the beads. This supports them to connect the spoken word and the quantity.
Can you find the bead for number 7?
What number comes after seven?
What number comes before seven?
Note that when practising the backward number sequence it is the amount that remains, not the bead removed, that is counted. Zero is an important number to say at the end, as the expression of the absence of quantity (no beads).
Variations
Have students work in pairs. They take turns to draw a numeral card out of a container, and challenge their partner to find the number on the Slavonic abacus. If needed, they can count the beads together to check that the right bead has been identified.
First work with numbers 1–10, and extend the range as needed to increase the challenge.
Session 3: Frogs in a bucket
 Link the number after and before a given number, to adding one and subtracting one from a given collection. Use toy animals or other objects and a plastic container so there is a loud ‘plunk’ as objects go into the container. The frog animation gives an example of this with frogs in a bucket.
We had 15 frogs and one jumped out.
How many frogs are in the bucket now?
 Increase the number of objects in the container beyond ten so that students attend to the one more/one less principle rather than image actions inside the container. Avoid putting in the objects one at a time after ten. Throw them in as imaginary groups. For example, a nice sequence is…
17 frogs and one more… 29 frogs and one more… 99 frogs and one more
7 frogs and one less… 15 frogs and one less… 27 frogs and one less…
Variations
If needed, link explicitly to the number sequence by referring to a hundreds board.
Extend the problems to two more/less, three more/less and beyond as students’ understanding and control of sequences grows.
Have students work in pairs, with one student putting objects into a container, and the other student listening and counting how many.
Session 4: What’s changed?
 Begin with a set of objects in a readily subitised arrangement. For example, begin with a set of six cars.
 Tell the students: Take a photograph of the collection and stash it in your mind.
Now close your eyes, and I’m going to change something.
Try to hold the picture in your mind.

Change the objects for a different kind – vary shape, colour and size to add more challenge. For example, change the cars for teddies.

Now open your eyes. How many things can you see now?
Look for students to recognise that the number of items is unchanged. though the items vary from the original ones. Aim for acceptance that the number is unchanged by means other than onebyone counting, though use counting as a ‘fall back’ strategy if needed.
Variations
Students may begin to say the number is invariant because it has been the last few times, without necessarily accepting that number is conserved. Introduce the one more/one less principle with this activity. Vary the number of new objects by one while still retaining the original layout and see if the students detect the change and trust invariance enough to build on it.
Make the variations more significant such as adding or subtracting more than one and changing some parts of the arrangement.
Have the students work on the activity Odd one out in pairs, using Copymaster One.
Students work with sets of three cards, and identify one difference between each card and the other two cards in the set. For example, possible answers for the cards with teddies are: the top card is different from the other two because the teddies are sitting down; the middle card is different from the other two because there are different amounts of teddies in each row, and the bottom card is different from the other two because there are 9 teddies.
Session 5: Is there the same number?
 Lay out two collections one above the other, with items aligned.
Have a look at this collection. Are there more blue teddies, more green teddies or are there the same number? Most young children will equate the length of a collection with number.
 Tell the students: Take a photograph of this collection and stash it in your mind.
Now close your eyes, and I’m going to change something.
 Change the spatial layout of the objects, by spreading out one of the collections.
 Now open your eyes. Are there more blue teddies, more green teddies or are there the same number?
Variations
Vary the spatial arrangement of sets. Begin with a set of objects with some similar characteristics so that students can easily recall the objects that are present. For example, Take a photograph in your mind of the collection. Close your eyes and tell me what you see. Encourage students to pay attention to structure and the organisation of the set, with responses such as “There were two of each animal”, “The animals were on a hexagon”, and “Two on the top, two in the middle, two on the bottom.”
Now I’m going to change something. Vary the spatial layout of the objects, particularly expanding or contracting the length or area of the collection, or rearranging the layout.
Now open your eyes. Are there are still the same number of objects? How do you know?
Make minor variations to the total number as well as the spatial layout so that students are required to trust the invariance of the count and build with it or take from it.
Have students work on the activity Domino Count in pairs. This task encourages students to trust the count in the face of different spatial arrangements.
Working with at least one set of dominoes, students sort the dominoes into groups that have the same number of dots, in total. Each group can be labelled with a numeral card, or students could make their own labels. For example:
Once the dominoes have all been grouped, students can arrange the dominoes in a pattern and write the number fact for each domino. For example,
Session 6: Counting dots
The abstraction principle involves the idea that nontangible items such as sounds, touches, and ideas can be counted. Developing students’ capacity to count items they cannot see and feel is important because it helps them to realise that numbers are ideas.
Messages
Play the game Messages as a class. Students sit in pairs, back to back, with one student from each pair facing the teacher. The teacher shows a pattern card from Copymaster Two for a short time. The students turn around and gently tap the number of dots they saw on their partner’s back. The partner shows how many taps they felt by holding up that many fingers. Both players turn around to check whether the number of fingers matches the number of dots on the pattern card. Alternatively, a digit card can be held up instead of a pattern card.
Pattern memory match
Students play pattern match in groups of three or four. Each group needs a set of pattern cards (Copymaster Two) and a set of digit cards.
The pattern cards are spread out individually, face down on. The digit cards are shuffled and put in a pack, face down, in the centre. Players take turns to turn over the top digit card then turn over one of the pattern cards. If the cards match the player keeps both cards and has another turn. Once all of the cards are matched the player with the most pairs wins.
After the game, talk with students about how they recognised some patterns instantly. Look for students to use combinations of smaller groupings, e.g. “I know it’s seven because four and three are seven.”
No way Jose
In this unit we develop the language of probability by considering events which are likely or unlikely. We do this using the context of children's stories.
This unit is about developing the language of probability. The words that are introduced and explored in this unit are always, perhaps, no way Jose, certain, possible, impossible, will, might, won’t, will, maybe, never, yes, maybe, no. These are informal, everyday words that denote chance or probability. By using these words, that have some familiarity for the students, they should start to get a better idea of the overall concept of probability. As students progress through the primary years they will gradually learn to assign fractions or decimals to given probabilities using both a theoretical and experimental approach.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:
The contexts for this unit can be adapted to suit the interests and experiences of your students. For example:
Getting Started
Today we follow Red Riding Hood on her journey to Grandma’s house and look at the characters she is likely to meet.
Discuss with the students the setting of Red Riding Hood’s journey. Encourage the students to share their ideas about the objects that could be found in the forest.
Peg the picture of the tree beneath the word card will.
Display the picture beneath the word card won’t.
Display the picture beneath the word card might.
Exploring
Over the next 2 to 3 days the students can look at the journeys of other fairytale characters and make decisions about who or what they might meet.
Remind the students to peg the pictures beneath the word cards.
Tell me why you have put that there?
Why do you think that …….. is impossible?
Could you have put it with one of the other words? Why/Why not?
Reflecting
Dear Parents and whānau,
This week in maths we have been exploring the everyday language of probability. We have used words to describe the chance that an event will or won’t occur. We have used story packs to explore this idea. Your child has brought home to share with you a story pack which contains 3 word cards and pictures of objects for the children to classify. It also includes 3 blank cards for the children to draw their own pictures.
As the children are linking the word cards to the pictures you can help by asking questions that encourage the children to explain their thinking.
Tell me why you have put that there?
Why do you think that …….. is impossible?
Could you have put with one of the other words? Why/Why not?
Thank you for helping your child understand important aspects of probability.
Numerals and expressions
The purpose of this unit is to develop understanding of a numeral as a symbol to represent an amount or number, and of the symbols for the operations of addition and subtraction.
This sequence of lessons lays a fundamental and important foundation for students to recognise, read and write symbols to record and communicate mathematical ideas. As the symbols become well understood, they also become tools for processing thinking. This process begins with the introduction of numerals as symbols that represent amounts or numbers of objects. Students hear and see words that are associated with the amounts, and so need to come to understand that a single symbol is representative of all forms of that number, written and spoken.
Being able to quantify and record amounts is just the beginning. We work on and with numbers. We say we operate on them, and these operations change them. As the symbols that represent the number operations of addition and subtraction are introduced, the students should ‘operate’ on items in real contexts. The language associated with addition and subtraction can be confusing. Students do not always connect addition, adding, and, plus, or subtraction, minus, takeaway, less. As many adults use this language interchangeably, students must be supported to connect these operation words with the symbol that represents them.
An expression in mathematics is a combination of symbols (e.g. 4 + 5). An equation is a statement asserting the equality of two expressions (e.g. 4 + 5 = 9). The focus in this unit of work is to have students record expressions, using symbols correctly and with confidence.
In this unit of work, subitising is given an emphasis. The early numeracy stages are defined by a student’s ability to count items, but the ability to subitise or partition an instantly recognised small group of objects into its parts is also important.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
Many of the activities in this unit suggest ways to adapt them to engage with the interests and experiences of your students. Other adaptations include:
This unit includes several activities for each session. Choose 23 activities for a single session or spread each session over more than one day.
Session 1
SLOs:
Activity 1
Play Number Eye Spy.
(Purpose: To identify numbers of items in groups up to five.)
Explain that in the classroom, some things we see might be in groups of two, three, four or five. Give an example, such as a group of three computers at the back of the classroom. Explain that you could give a clue about them by saying, “I spy with my little eye, three of something.”
Pose the problem for them to solve, this time changing the number in the group from three. Have students look about the classroom to identify the group of items you have seen. The person who guesses correctly has the next turn.
Activity 2
(Purpose: To subitise different groups of dots up to five in number.)
Shuffle the cards. Hold them up one at a time, so that the students can all see them. As each card is held up, have the students show how many dots they see, by holding up the same number of fingers.
Activity 3
Do explain that together you will be writing numerals which are symbols for numbers of things.
Emphasise the correct directionality when forming 2, 3 and 5 in particular.
Activity 4
Hold up the word cards in order and read them aloud together several times. Show them out of order, having the students quickly reading them aloud.
Activity 5
Have students work in pairs, or groups of three, to play One, Two, Three, Snap.
(Purpose: To correctly match words, numerals and images of numbers 1 to 5)
Make available to each group, two sets of word cards to five (Copymaster 2), 2 sets of numeral cards to 5 (Material Master 41) and one set of coloured or black dot images to 5 (Copymaster 1). Alternatively, the picture card images from Copymaster 3 can be used instead of the dots.
Each pile is shuffled and placed face down in front of the group.
Explain that students in the group each take turns to take one card from each pile, placing them face up in front of themselves as they do so. If all cards show the same amount (symbol, word and image) they say “Snap!” and keep the set.
If not, they are returned to the bottom of each pile.
The winner is the person with the most sets of three at the end of the game.
Activity 6
Conclude the session with a game of Get Together.
(Purpose: To form groups of up to five in response to hearing a number word, a written number word, or to seeing a numeral or a number word.)
Have students stand. Explain that they are to move about the room in time to music. When the music stops, the teacher will either say a number or show numeral or word cards up to five. Students are to look at the teacher, listen for a number or look for a numeral and, as quickly as possible, make a group of that number with another person, or with other people and to sit down when the group is formed.
Session 2
SLOs:
Activity 1
Ensure that numerals 1 to 5 can be seen by the students. Read them together. Begin by playing Spot the Spots from Session 1, Activity 2. Instead of holding up the same number of fingers, have students write numerals in the air and on the mat with their finger.
Activity 2
(Purpose: To accurately write numerals 1 to 5 in response to hearing number words within a story context.)
Activity 3
Make a think board template (Copymaster 5) and pencil available to each student. Have the students write their favourite number (between 1 and 5) in the centre of their think board. Have them draw a picture, write their own number “story” that includes their favourite number, show any numbers by drawing dots or pictures of equipment, and write any number words.
Activity 4
Make the cards from One, Two, Three, Snap (See Session 1, Activity 5) available to the students so they can play a Memory game as they finish their thinkboard. To play memory they should turn all the cards from three sets face down, mix them up and take turns to find matching trios.
Activity 5
Conclude the session with class sharing of thinkboards.
Session 3
SLOs:
Activity 1
“I can see five and one.”
“I can see five (across) and two (in the corners).”
“I can see four and four.”
Guide the students to shared recording on the class chart:
“I can see five and one” → 5 and 1 → 5 plus 1 → 5 + 1
“I can see five and two” → 5 and 2 → 5 plus 2 → 5 + 2
“I can see four and four” → 4 and 4 → 4 plus 4 → 4 + 4
Activity 2
Together, make a chart, or class dictionary page, about addition and its symbol, + , asking and recording what the students already know.
Included in the ideas recorded, should be:
+ is a symbol or sign, + shows that we are joining together two amounts or numbers; + is an addition symbol; when we see this sign we can read it as “and”, “plus” and “add”; + is a short way of writing “and”, “plus” and “add”.
Activity 3
For example:
Write 5 + 3 and together read: ‘five plus three’, five and three’, ‘five add three’, ‘five and three more’.
Distribute to each child at least four dot cards that show numbers of dots greater than 1.
Have students write about their cards, modeling their recording on what was recorded on the class chart in Activity 1, Step 4 above.
Activity 4
Using the cards from Copymaster 6, have the students work in pairs to play Read and Draw.
(Purpose: To read a mathematical expression in at least two ways and to respond to a mathematical expression with a drawing.)
Tell the students the purpose of the Read and Draw task. Explain that they take turns to be the Reader and the Quick Draw person.
The Reader’s task is to read the mathematical expression in at least two ways to their partner. They should check their partner’s drawing before showing them the task card on which the expression is written. Their task is to check the accuracy of the drawing.
The Quick Draw person’s task is to listen carefully to the expression that is read, and to draw a diagram of what they hear, using circle dots, square boxes or triangle shapes. For example: The Reader reads, 4 + 2: “four and two, four plus two,” and the Quick Draw person draws:
Students should have at least four turns each.
Activity 5
Conclude by playing the Hands Together game.
Each Student makes a number of choice on one hand by showing that many fingers. For example:
Have them show their ‘number’ to a friend. (This is to avoid students changing the number of fingers when they see the expression.)
The teacher uses two sets of expression cards (Copymaster 6). She shows an expression, for example 5 + 3. Children who have made these numbers on their fingers must move to pair up, one student showing 5 fingers and the other showing three. The first pair to form and to show 5 + 3 collects a 5 + 3 expression card each. The game begins again. The game finishes when all cards are used up. Students take turns to read aloud to the class the cards they have ‘won’. Each student should read their cards in a different way from the student before them.
Have students bring favourite small soft toys for Session 4. Bring a small blanket.
Session 4
SLOs:
Activity 1
Write this symbol on the class chart: + Have students tell you addition words and give examples of how to use them. For example, “plus”, “I have five fingers on this hand plus five fingers on this hand.” Record these.
Activity 2
Arrange ten of the students’ soft toys in bed, using the blanket.
For example 1 + 1, 2 + 1, 3 + 1, reading these together. As you do so, focus on modeling the correct formation of numerals 6 to 9.
Read the expressions and words again and highlight the different ways we can read the subtraction symbol.
Activity 3
Have them put their teddies to bed under the tissue, say the rhyme to themselves and each time a teddy falls out, record the expression, for example, 5 – 1. Those who complete this quickly can write the addition expressions as they return the teddies to bed, or take more teddies and record expressions for 6 to 10.
Activity 4
Conclude the session with a game of Musical Chairs (or cushions).
Set out the number of chairs for students in the group. Record the number on the chart. Play a favourite piece of music. When it stops all students sit down. Have them stand and ask a student to remove one chair then come to record the expression and read aloud what they have written.
For example 10 – 1, “ten chairs minus one chair.”
Explain that one student will not have a seat this time and that this person will get to write and read the next mathematical expression on the chart.
Continue the game till no chairs remain and subtraction expressions have been written for each action.
Session 5
SLO:
Activity 1
Activity 2
Make available to the students pencils, paper, felt pens or crayons. Have the students write at least two of their own scenarios and record the mathematical expressions that represent what is happening. Their illustrations should show what is happening in the scenario and expression.
Activity 3
Conclude the session by having the students pair share, then class share their work. Emphasise the importance of having them read their mathematical expressions in at least two ways.
Dear family and whānau,
In class this week the students have been learning how to write numerals correctly. They have also been learning to write and read the symbols for addition and subtraction.
Please find attached a popular rhyme, Ten in the Bed that we have enjoyed in class. With some toys from home, you could read and act out the rhyme, supporting your child to write maths expressions such as 10 – 1, (‘ten minus one’) and 9 – 1 (‘nine takeaway one’), as the toys fall out of bed and expressions such as 1 + 1 (‘one plus one’) and 2 + 1 (‘two and one’) as the toys are put back in bed.
The focus is on writing symbols correctly and on reading these aloud, using “add, plus, and” for addition, and “takeaway, minus, subtract, less” for subtraction.
Please note, we have not yet focused on writing full equations using the = symbol.
Enjoy Ten in the Bed.
Worms and more
This unit comprises 5 stations, which involve the students in developing an awareness of the attributes of length and area. The focus is on the development of appropriate measuring language for length and area.
Early length experiences must develop an awareness of what length is, and develop a vocabulary for discussing length. Young students usually begin by describing the size of objects as big and small. They gradually learn to discriminate in what way an object is big or small and use more specific terms. The use of words such as long, short, wide, close, near, far, deep, shallow, high, low and close, focus attention on the attribute of length. Early area experiences develop an awareness of what area is, and of the range of words that can be used to discuss it. Awareness of area as the "amount of surface" can be developed by "covering" activities such as wrapping parcels, colouring in, and covering tables with paper. The use of words such as greater, larger and smaller, focus attention on the attribute of area.
The stations may be taken as whole class activities or they may be set up as "centres" for the students to use. We expect that many students will already be aware of the attributes of length and area. For them these may be useful maintenance activities.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The contexts for activities can be adapted to suit the interests and experiences of your students. For example:
Station 1: Worms
In this activity we roll play dough to make long and short worms.
My worm is long
My worm is fat
My worm is tiny
How do you know that your worm is short?
Is your worm the same as everyone elses? Why?
Station Two: Near and Far
In this activity we build a town with blocks and then "drive" our cars around it.
Station Three: Shaping Ourselves
In this activity we make ourselves tall, short, wide, narrow, close and far.
As tall as they can
As short as they can
As wide as they can
As close to a table as they can be
As far from the door as they can be
Take up loads of space covering the mat (lie down)
Station Four: Wrapping Paper
In this activity we follow directions and colourin large and small objects on our "wrapping" paper (Copymaster 1). We then find an object to wrap in our paper.
How did you decide which were small?
How did you decide which were large?
Which took the longest to colour? Why?
Which were the quickest to colour? Why?
Whose didn’t?
Why not?
Station Five: Muddy footprints
In this activity we look at some footprints and decide who they could belong to. In our discussion we focus on the use of language associated with area.
Who could this belong to?
Why do you think that?
Is your foot as big as the bear's? How do you know? How could you check?
Dear family and whānau,
This week we have been exploring activities which develop an awareness of length and area. We have been using words like: long, short, tall, big and small to describe objects.
Longs and Shorts
This week we ask your child to look around at home and find objects that are short. Choose 4 objects and draw a picture of them. Once they have a collection of "shorts" you could ask them to find 4 objects that are long and draw a picture of those.
Turns
In this unit we look at the beginning of the concept of angle. As students come to understand quarter and half turns, they also begin to see that ‘angle’ is something involving ‘an amount of turn’. These ideas are explored by using students’ bodies, toys, games and art.
Angle can be seen as and thought of in at least three ways. These are as:
Angle in the New Zealand Curriculum develops over the following progression:
Level 1: quarter and half turns as angles
Level 2: quarter and half turns in either a clockwise or anticlockwise direction; angle as an amount of turning
Level 3: sharp (acute) angles and blunt (obtuse) angles; right angles; degrees applied to simple angles – 90°, 180°, 360°, 45°, 30°, 60°
Level 4: degrees applied to all acute angles; degrees applied to all angles; angles applied in simple practical situations
Level 5: angles applied in more complex practical situations
Outside school and university, angle is something that is used regularly by surveyors and engineers both as an immediate practical tool and as a means to solve mathematics that arises from practical situations. So angle is important in many applications in the ‘real’ world as well as an ‘abstract’ tool. This all means that angles have a fundamental role to play in mathematics and its application.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The contexts for this unit can be adapted to suit the interests and experiences of your students. For example, the contexts for identifying shapes with quarter turns could be a local playground or building of particular interest. This could involve a trip to visit it, or photos could be used.
Session 1
In the three sessions that follow, students produce artwork that they can collect in their own ‘Turns Book'.
Session 2
Prior to this session tie pieces of string to enough crayons for each child to have one, with a few spares to avoid arguments about colours.
Session 3
This session is similar to that of the last session except that here the quarter turns are made using ‘combs’ the students make for themselves. As an alternative, you may prefer to have students use crayons lying flat to create the same effect.
Session 4
Corners of shapes can also be thought of as quarter and half turns. The object of this session is to find corners of shapes that are equivalent to quarter and half turns.
Repeat for other examples.
Does this triangle (right angled) have any quarter turns? (yes)
Are all the corners quarter turns? (no)
Do all triangles have quarter turns (no, provide examples that don't)
Session 5
What kinds of turns have we been talking about this week?
How would you describe a quarter turn? A half turn?
What objects do you know that have quarter turns?
How many quarter turns make a half turn? How many half turns make a full turn?
Family and whānau,
This week we have been thinking about full, quarter and half turns. We have seen how they can be produced by turning our bodies and moving objects. We have also seen that certain objects have quarter turn corners. Could you please help your child look through old newspapers and magazines and cut out two objects that have quarter turn corners and two objects that don’t have quarter turn corners? They should bring the pictures they find to school to glue into their Turns Book.
Learning to count: Counting onetoone
This unit develops students’ understanding of, and proficiency in, counting onetoone.
Gelman and Gallistel (1978) provided five principles that young students need to generalise when learning to count. These principles are:
Just like in reading when one spoken word is matched to one written word, counting involves onetoone correspondence. One item in a collection is matched to one spoken or written word in the whole number counting sequence.
The spoken and written names that are said and read have a fixed order. If that order is altered, e.g. “One, two, four, five,…”, the count will not work.
Assuming the onetoone and stable order principles are applied then the last number in a count tells how many items are in the whole collection.
The first three principles are about how to count. The final two principles are about what can be counted.
Items to count can be tangible, like physical objects or pictures, or they can be imaginary, like words, sounds, or ideas, e.g. Five types of animal.
The order in which the items are counted does not alter the cardinality of the collection. This is particularly challenging for students who think that counting is about assigning number names to the items, e.g. “This counter is number three.”
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
The contexts for activities can be adapted to suit the interests and experiences of your students. For example, use Māori counting numbers.
Students need to simultaneously develop proficiency with number sequences forward and backwards by one, and their capacity to apply those sequences to counting tasks. Ideally students’ ability to say word sequences develops either ahead of, or synchronous to, their need to apply it. So students who can count collections up to ten should be learning number sequences beyond ten.
Session 1: Hundreds board
Count by ones on a hundreds board, both forwards and backwards, and ask questions which help students connect numerals to spoken words. For example,
Can you find the number 8 without counting up or down?
What number comes after eight?
What number comes before eight?
Variations
Have students work in pairs. They take turns drawing a numeral card out of a container, then work together to find the number on a hundreds board and make a set which contains the number they have drawn, for example a set of eight counters.
First work with numbers 1–10, and extend the range as needed to increase the challenge.
Session 2: Slavonic abacus
Count by ones on a Slavonic abacus, both forwards and backwards. While you count, say the numbers out loud with students as you move the beads. This supports them to connect the spoken word and the quantity.
Can you find the bead for number 7?
What number comes after seven?
What number comes before seven?
Note that when practising the backward number sequence it is the amount that remains, not the bead removed, that is counted. Zero is an important number to say at the end, as the expression of the absence of quantity (no beads).
Variations
Have students work in pairs. They take turns to draw a numeral card out of a container, and challenge their partner to find the number on the Slavonic abacus. If needed, they can count the beads together to check that the right bead has been identified.
First work with numbers 1–10, and extend the range as needed to increase the challenge.
Session 3: Frogs in a bucket
We had 15 frogs and one jumped out.
How many frogs are in the bucket now?
17 frogs and one more… 29 frogs and one more… 99 frogs and one more
7 frogs and one less… 15 frogs and one less… 27 frogs and one less…
Variations
If needed, link explicitly to the number sequence by referring to a hundreds board.
Extend the problems to two more/less, three more/less and beyond as students’ understanding and control of sequences grows.
Have students work in pairs, with one student putting objects into a container, and the other student listening and counting how many.
Session 4: What’s changed?
Now close your eyes, and I’m going to change something.
Try to hold the picture in your mind.
Change the objects for a different kind – vary shape, colour and size to add more challenge. For example, change the cars for teddies.
Now open your eyes. How many things can you see now?
Look for students to recognise that the number of items is unchanged. though the items vary from the original ones. Aim for acceptance that the number is unchanged by means other than onebyone counting, though use counting as a ‘fall back’ strategy if needed.
Variations
Students may begin to say the number is invariant because it has been the last few times, without necessarily accepting that number is conserved. Introduce the one more/one less principle with this activity. Vary the number of new objects by one while still retaining the original layout and see if the students detect the change and trust invariance enough to build on it.
Make the variations more significant such as adding or subtracting more than one and changing some parts of the arrangement.
Have the students work on the activity Odd one out in pairs, using Copymaster One.
Students work with sets of three cards, and identify one difference between each card and the other two cards in the set. For example, possible answers for the cards with teddies are: the top card is different from the other two because the teddies are sitting down; the middle card is different from the other two because there are different amounts of teddies in each row, and the bottom card is different from the other two because there are 9 teddies.
Session 5: Is there the same number?
Have a look at this collection. Are there more blue teddies, more green teddies or are there the same number? Most young children will equate the length of a collection with number.
Now close your eyes, and I’m going to change something.
Variations
Vary the spatial arrangement of sets. Begin with a set of objects with some similar characteristics so that students can easily recall the objects that are present. For example, Take a photograph in your mind of the collection. Close your eyes and tell me what you see. Encourage students to pay attention to structure and the organisation of the set, with responses such as “There were two of each animal”, “The animals were on a hexagon”, and “Two on the top, two in the middle, two on the bottom.”
Now I’m going to change something. Vary the spatial layout of the objects, particularly expanding or contracting the length or area of the collection, or rearranging the layout.
Now open your eyes. Are there are still the same number of objects? How do you know?
Make minor variations to the total number as well as the spatial layout so that students are required to trust the invariance of the count and build with it or take from it.
Have students work on the activity Domino Count in pairs. This task encourages students to trust the count in the face of different spatial arrangements.
Working with at least one set of dominoes, students sort the dominoes into groups that have the same number of dots, in total. Each group can be labelled with a numeral card, or students could make their own labels. For example:
Once the dominoes have all been grouped, students can arrange the dominoes in a pattern and write the number fact for each domino. For example,
Session 6: Counting dots
The abstraction principle involves the idea that nontangible items such as sounds, touches, and ideas can be counted. Developing students’ capacity to count items they cannot see and feel is important because it helps them to realise that numbers are ideas.
Messages
Play the game Messages as a class. Students sit in pairs, back to back, with one student from each pair facing the teacher. The teacher shows a pattern card from Copymaster Two for a short time. The students turn around and gently tap the number of dots they saw on their partner’s back. The partner shows how many taps they felt by holding up that many fingers. Both players turn around to check whether the number of fingers matches the number of dots on the pattern card. Alternatively, a digit card can be held up instead of a pattern card.
Pattern memory match
Students play pattern match in groups of three or four. Each group needs a set of pattern cards (Copymaster Two) and a set of digit cards.
The pattern cards are spread out individually, face down on. The digit cards are shuffled and put in a pack, face down, in the centre. Players take turns to turn over the top digit card then turn over one of the pattern cards. If the cards match the player keeps both cards and has another turn. Once all of the cards are matched the player with the most pairs wins.
After the game, talk with students about how they recognised some patterns instantly. Look for students to use combinations of smaller groupings, e.g. “I know it’s seven because four and three are seven.”