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Numerals and expressions

Keywords:
Achievement Objectives:

Achievement Objective: NA1-4: Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
AO elaboration and other teaching resources

Purpose: 

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.

Specific Learning Outcomes: 
  • Understand that an amount or number of items can be represented with a single unique symbol.
  • To correctly write numerals.
  • Understand that written words and oral words can also be represented with numeral symbols.
  • Recognise numbers within story contexts.
  • Understand and use the addition and subtraction symbols.
  • Recognise and write addition and subtraction expressions from story contexts.
Description of mathematics: 

Algebra is the area of mathematics that uses letters and symbols to represent numbers, points and other objects, as well as the relationships between them. Its value is that it enables general statements to be made simply, it enables a wide range of problems to be solved efficiently, and it even enables some problems to be solved that can’t be solved in any other way.

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. Mathematics is part of our everyday conversation about events in our lives. Students must therefore also be supported to recognise and use numbers and numerals within meaningful contexts.

Being able to quantify amounts and record this, 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 finite combination of symbols. An equation is a statement asserting the equality of two expressions. The focus in this unit of work is to have students record expressions, using symbols correctly and with confidence. That the equals sign is a relationship symbol stating the equal value of two expressions is a more complex concept, and accordingly, this is the focus of the next unit.

In this unit of work, subitising is given an emphasis. The ability of some young children to recognise small quantities without counting, can be overlooked. The early numeracy stages are defined by a student’s ability to count items, rather than to subitise or partition an instantly recognised small group of objects into its parts. Both are important.

The activities suggested in this series of lessons can form the basis of independent practice tasks. It is also assumed that throughout the school day, all class members, students and teacher alike, will look for and take opportunities to apply learning included in this unit of work.

These teaching and learning activities, focusing on numerals and expressions, parallel some of the activities in the Place Value unit Knowing Five.

Links to the Number Framework
Emergent
One to one counting
Counting from one on materials.
NB. The names of these stages both emphasise counting. However, subitising is also highlighted in these lessons.

Required Resource Materials: 
Numeral cards (Material Master 4-1)
Number fans or Fan Numbers (Material Master 4-10)
A CD player and favourite music discs
Favourite soft toys
One small blanket
Plastic teddies
Activity: 

Note: Sessions 1 and 2 focus on numbers and numerals to five. If these are already very well known and understood, extend the tasks to nine as appropriate.

Session 1

SLOs:

  • To understand that an amount or number of items can be represented with a single unique symbol.
  • To correctly write numerals to five.
  • To understand that written words and oral words can be represented with a single symbol.
  • To recognise and match words and symbols with the amounts they represent.

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

  1. Play Spot the Spots, using the red and green 1 to 5 cards from Attachment 1 pages 1-4, or the black and white 1 to 5 cards from pages 7-10.
    (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.
  2. Shuffle the cards and distribute (at least) one to each student. Going around the mat circle, have the students take turns to hold up their card for the others to see. The other students who have a card with the same number of dots hold up their cards too.
  3. Distribute numeral cards to 5, or a number fan to each student. Repeat Step 2 above, but this time the students show the numeral (card) that matches each student’s dot card as it is shown.

Activity 3

  1. On the class chart revise together how to correctly write numerals 1 to 5.
    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.
  2. As numerals are formed on the chart, have students practice forming them in the air, and on the mat in front of them. Have them feel and describe that correct form.
  3. Have students return their dot cards from Step 2 by, one at a time, coming to the chart, showing their dot card, saying the number and forming the numeral. Watch for correct numeral formation, noting those who need further practice.

Activity 4

  1. Write numerals 1 to 5 on the class chart. Ask the students what you have written (numerals). Explain that there are words for these. Show word cards, one to five, Attachment 2.
    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.
  2. (Using Blue Tac or similar), with assistance from the students, arrange the word cards correctly beside the numerals on the chart. Together check that they match.

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 (Attachment 2), 2 sets of numeral cards to 5 (Material Master 4-1) and one set of coloured or black dot images to 5 (Attachment 1). Alternatively, the picture card images from Attachment 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 to 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:

  • To recognise and match sets of items with written and spoken words and their symbols.
  • To correctly write numerals to five.
  • To recognise numbers within story contexts.

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 student write numerals in the air and on the mat with their finger.

Activity 2

  1. Make paper and pencils available to the students. Explain that you are going to read them a story (Attachment 4) and they are to listen very carefully and write down any numbers that they hear in the story. They should write these in order across the page. Alternatively, you could tell them a made up story that includes members of the class.
    (Purpose: To accurately write numerals 1 to 5 in response to hearing number words within a story context.)
  2. Introduce the task by reading the italicised part of the story, show the dog pictures, explain and model what to do.
  3. Read the story, having them complete the task.
  4. Read the story again together, having students actively identifying the number words as they are read, and writing the numerals on the class chart. Emphasise correct formation of the numerals.
  5. Have students check each other’s recording.
  6. Ask if students know of other stories with numbers and record their ideas. For example, The Three Little Pigs. Suggest that students listen for numbers spoken during the day.

Activity 3

  1. Ensure that students can see number words and numerals.
    Make a think board template (Attachment 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.
  2. Once completed, have student pairs share their thinkboards.

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:

  • To understand and use the addition symbol.
  • To recognise and use the written and spoken words for addition, with the addition symbol.

Activity 1

  1. Ask the students which numerals they have been learning to write. Record these on the class chart. Have students take turns to come and write on the class chart other numerals that they know. As they do so, discuss them, highlighting their correct formation, particularly numerals 6, 7 and 9.
  2. Show a selection of dot cards from 6 to 10 (Attachment 1), asking students to say what they can see. The focus here is on seeing familiar groups of 1 to 5 dots within the larger group. Some may readily recognise immediately the larger (complete) groups, but this is not the purpose of this task.
  3. Record in words what they can see. For example:
    “I can see five and one.”
    “I can see five (across) and two (in the corners).”
    “I can see four and four.”
  4. Ask, “Is there another way to write this, using numerals?”
    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

  1. Together write a mathematics expression about at least two other dot cards and model several ways of reading what has been written:
    For example: 
    Write 5 + 3 and together read: ‘five plus three’, five and three’, ‘five add three’, ‘five and three more’.
  2. Make paper and pencils, or, whiteboards and pens, available to the students.
    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 Attachment 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 expression is written. Their task is the 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 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 (Attachment 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:

  • To understand and use the subtraction symbol.
  • To recognise and use subtraction written and spoken words, with the subtraction symbol.

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

  1. Together, read the rhyme, “Ten in the Bed.” (Attachment 7).
    Arrange ten of the students’ soft toys in bed, using the blanket.
       
  2. Read the rhyme a second time and have the students ‘act out’ one toy falling out each time. Have students take turns to return the toys to the bed, one at a time, and as they do so record addition expressions.
    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.
  3. Write 10 and ten (symbol and word) on the class chart and discuss. Read the first verse of the rhyme once more. This time discuss how to use symbols to record what has happened. Write 10 – 1, introducing and recording this as ‘ten takeaway one.’ Continue to read the rhyme, verse by verse, writing each mathematical expression and recording the words each time. Introduce the alternative words for the subtraction symbol as you do so. For example 9 – 1, “nine minus one”; 8 – 1, “eight less one”; 7 – 1, “seven subtract one”.
  4. Ask, “What was happening to the number of toys in the bed?” (The number was getting less). Discuss that subtraction symbol, brainstorm and record the student’s ideas of what it is telling us.
    Read the expressions and words again and highlight the different ways we can read the subtraction symbol.

Activity 3

  1. Make available to each student, paper, pencils, five plastic teddies and a tissue.

    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.
  2. Have students pair share, reading aloud their mathematical expressions. As they take turns, encourage the students to use the different language of subtraction.

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:

  • To recognise and write addition and subtraction expressions from story contexts.

Activity 1

  1. Using class charts from sessions 3 and 4, review the symbols for addition and subtraction.
  2. Either read the short scenarios from Attachment 8, exchanging the names of students in the class for those in the scenarios, or create your own. Have the students identify if the story tells of an addition or subtraction ‘event’ and together record these on the class chart as mathematical expressions.

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.

AttachmentSize
NumeralsAndExpressionscm1.pdf116.83 KB
NumeralsAndExpressionscm2.pdf10.9 KB
NumeralsAndExpressionscm3.pdf1.44 MB
NumeralsAndExpressionscm4.pdf223.57 KB
NumeralsAndExpressionscm5.pdf160.8 KB
NumeralsAndExpressionscm6.pdf26.06 KB
NumeralsAndExpressionscm7.pdf23.27 KB
NumeralsAndExpressionscm8.pdf28.85 KB