The purpose of this unit is to lay the foundation for an understanding of grouping and to make connections between the different grouping arrangements for five and the symbolic recording associated with these.
- Quickly recognise patterns within and for five.
- Record an expression, using ‘and’, the symbol +, and 0.
- Use the equals = symbol and understand that is means ‘is the same as’.
- Record word stories and equations that describe a situation.
- Record an unknown using ☐ in addition equations.
- Record word stories and equations which describe a subtraction situation.
This sequence of lessons lays a fundamental and important foundation for early formal recording of equations. Do not view these lessons with their focus on ‘numbers to five only’ as trivial, as there are many key understandings being established here such as how numbers work and how we talk about and record them.
The focus in these lessons is not on counting but is on instantly recognising or subitising combinations to five. The ability of some young children to recognise small quantities without counting has been somewhat overlooked in the emphasis we have recently given to counting. These lessons are a combination of recognising and just knowing groupings to five, and recording these combinations and separations in multiple ways, and in so doing establishing a base for continued strategy development.
Key concepts underpin these lessons. Students should understand that the number of objects remains the same regardless of their spatial arrangement. They should see and accept that there are many different representations for the combination or separation of sets of objects, both in terms of their physical manifestation and in terms of the symbolic representation of the operation.
Early formal recording of equations builds on a student’s developing numeral recognition and introduces symbols for operations: + - and =. Understanding the meanings of and principle use of these symbols is essential to making sense of our symbolic recording in mathematics. Showing written equations in a number of ways emphasises the meaning of the equals sign as ‘the same as’ rather than students developing the incorrect understanding that it signals that an answer follows the sign.
In communicating maths ideas, students learn to understand and use mathematical language, symbols, text and diagrams to express their thinking and record concepts in a range of contexts and in a variety of ways. Teachers have a key role in developing the students’ ability to communicate their mathematical understandings orally and in writing.
The activities suggested in this series of lessons can form the basis of independent practice tasks.
Links to the Number Framework
One to one counting
Counting from one on materials.
NB. The names of these stages both emphasise counting. However, counting is not the focus of these lessons.
It is important to note that the focus of this unit is on instantly recognising (subitising) collections to five and not on counting the collection. While many students may be able to count five objects they may not be as proficient at subitising small collections. Ways to support students include:
- providing multiple opportunities to subitise with collections up to five before moving onto recognising how many more are needed to make five (session 2). Vary the arrangements of the objects (e.g.in a line, in a dice pattern, closely grouped, randomly spread) and the objects (counters, toys, pencils, pebbles).
- Removing the need for them to identify the numeral or the written number words until they can confidently state the number of objects in the set.
The context for this unit can be adapted to suit the interests and experiences of your students by using collections that are part of the classroom or school environment (e.g. blocks, counters, plastic animals, pens, pebbles, leaves, seeds).
- Large dice with dots
- Dice (enough for 1 for each pair of children)
- Fives frames
- Sets of numeral cards 1-5
- Packs of playing cards
- Plastic coloured bears (or similar)
- Cards with pictures of groupings of objects (1-5)
- Egg cartons
A reminder; these activities emphasise quick recognition of amounts, rather than counting, and develop and model a number of ways of recording combinations (+) and separations (-). Each session includes several activities in which an idea is developed.
SLO: To quickly recognise patterns within and for five.
- Have the students show five fingers. Ask “How many fingers?” and have the students ‘write’ the numeral 5 with their finger in the air and on the mat.
- Show a large dice with dots. Ask the students to hold up five fingers when they can see five dots on the dice. Show faces of the dice to the students in a random order.
- Show the numeral 5 on a card and ask what number it is? Show the word ‘five’ and explain that the symbol 5 is a quick way to write ‘five’. Point out they mean the same thing. Connect “five”, what we say, and 5, what we write. Explain that you have a pile of cards with 5 on them.
- Pass the large dice around the group for individuals to roll. Students hold up five fingers when they spot five dots rolled. The teacher takes a 5 numeral card each time 5 is rolled. How many fives did the class/group roll? Count the cards together when everyone has had a turn.
- Set a time (eg. play a short favourite tune) and have the students work in pairs with one dice and a set of numeral cards showing 5. Students add a numeral card to a pile each time 5 is rolled and see which pair rolls the most fives in the given time. Check and compare ‘results’.
- Provide 3 sets of numeral cards 1-5 and 3 sets of picture cards, and a dice to each pair of students.
Set a short time limit and have the students take turns to roll the dice, find the numeral card and picture card to match. The first student to complete a complete set of numeral and picture cards 1 – 5 OR all three ‘five’ numeral cards and pictures is the winner.
- Introduce fives frames cards. Discuss with the students that a full card shows five dots. Establish their understanding that the whole line is full. There is no need to count them.
- Set a short time limit. Have the students collect recording materials and work in pairs with one pile of five frames that show dots to five. They turn their pile upside down then take turns to turn over the five frames. Each student records the numeral for the number of dots shown. Encourage the students to support their partner in the task. The next card is turned when both have recorded their numeral. Conclude with each student circling the fives they recorded and by reporting the total to the class.
- The teacher models putting her hand in the bag and drawing out between one and five counters. She quickly lays them on the mat and asks, “Is it five?”
- Pass around (at least) one bag of counters of one colour. Ask the question, who can get five? Each student puts their hand in the bag, quickly takes a small handful without counting them and places them in one action on the mat, ensuring none overlays another. Ask, “Is it five?” Encourage the student to recognise the number without counting
- To quickly recognise how many more are needed to make five.
- To record an expression, using ‘and’, the symbol + and 0.
Have students play Snap in pairs with five frames cards. Each student has their own pile of cards upside-down in front of them. As they turn over each card they say the number of dots they can see and say snap if it’s the same number that their partner has just laid down.
- Show the fives frames cards. Discuss with the students the empty spaces and how many more counters are needed to make five. Show five frames in a random order to the class. Have the students show with their fingers how many more counters are needed to make five and write the numeral with their finger on the mat in front of them.
- The teacher models recording the combinations, using ‘and’ and introducing the + symbol, for example 2 and 3, 1 + 4. Introduce 0 and model the example of 5 and 0 and 5 + 0. Write the meaning and synonyms, ‘plus’, and ‘and’.
- Students work in pairs with fives frames, counters and recording materials. A time limit is set (eg. while a favourite piece of music is played or an egg timer is used) and students record combinations as they turn over the five frames cards, adding counters as appropriate.
This can be varied and made a little more abstract with the use of a dice. If a six is rolled, the student just writes 6. For every other roll the student records combinations to five.
For example if a three is rolled the student writes 3 (the dots seen) and 2 (the number of dots needed) or 3 + 2.
- Playing cards 1 (ace) – 5 are introduced or large digit cards 1-5 are used. Discuss that the queen will be used as zero (she has no number) and model how a 5 and a queen is another way to show 5 + 0 = 5. Students work in pairs and play Memory Pairs to five. (Note: you could also use Material Master 4-1 to make a set of digit cards for this game.)
The students spread out the cards between them face down and take turns to find matching pairs of cards which together make five.
The students keep the digit pairs (for example 4 + 1, 2 + 3, 5 + 0) that make five and count these at the end of the game.
- To use the equals (=) symbol and understand that is means ‘is the same as.’
- To record word stories that describe a situation. To record equations using + and = that match the word stories.
- Have students form themselves into groups of five as they sit on the mat. If there is an incomplete group have these students help to record equations. Ask for 2 students in the first group to stand while 3 remain seated.
- Write, for example: “In Molly’s group two children are standing and three children are sitting down. There are five children in Molly’s group.” Underline the number words in the story.
- Ask who can write this in another way. Accept all suggestions, including ‘two and three is the same as five.’ This should result finally in recording 2 + 3 = 5. Emphasise the connection between the words and the symbols. Highlight the fact that the group has five, so 2 + 3 is another way of showing 5. It is the same as five. Use both ‘is the same as’ and ‘equals’ as the equations are read together. Repeat this with other combinations to five using the other groups of students sitting and standing.
- Have the students work in pairs to draw pictures different combinations of bears sitting on fives frames and record equations for these.
Have the students read what they have written and display their work.
- To connect word stories with mathematical equations involving unknowns.
- To record an unknown using ☐ in addition equations.
- Show picture cards of numbers of items up to five.
Discuss stories that could be written about these. For example: “There are three dinosaurs. How many more do I need to make five? Three and what is the same as five?”
- Model recording “three and what is the same as five”: 3 + ☐ = 5. Read this together aloud.
- Distribute assorted picture cards to the students. Have them record their own ‘and what’ equations, show the pictures and read their equations to a buddy. Have their buddies answer the ‘and what?’ question.
- Model writing equations with the unknown in different places, for example ☐ + 1 = 5, 5 + ☐= 5, 2 + 3 = ☐. Write these in word sentences and read aloud both the word sentences and the equations together. Together, answer what would go in the box, identify the unknown quantity.
- Have the students draw pictures and write words and equations using equations with unknowns.
- To record word stories which describe a subtraction situation.
- To record equations using - and = that match the word stories.
- Ask five students to stand in front of the class. Tell four students from the group to return to their place on the mat, while one student remains standing. Record a word story for this. “Five children were standing. Four went away and sat down. One person is still standing.” Read the word story together and ask how this might be recorded just using numerals and symbols. Accept all suggestions and discuss.
- Ask the five students to return and repeat the actions, recording the equation 5 – 4 = 1 as they do so. Emphasise the words ‘went away’. Introduce and write the words ‘subtract’ and ‘minus’. Read the equation several times, substituting the words and emphasising that they mean the same thing.
- Model with students again, writing the word story and recording and reading and the equation in different ways.
- Make "buses" by cutting compartments from a standard egg carton. Have students work in pairs with a fives egg carton bus and 5 plastic teddies. One student puts up to five teddies in the bus, drives it a little way and has some teddies "get off". Their partner writes a word story and an equation to describe what has happened. Have them complete 2 word stories and equations each then read what they have written with another pair of students.
- Write equations using an unknown and read these together. 5 - 3 = ☐ , 5 - ☐ = 0. Together talk about what will ‘go in the box’ and complete these together.