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 2-3 activities for a single session or spread each session over more than one day.
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.
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 4-1) 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.
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.
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.
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.
Conclude the session with class sharing of thinkboards.
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”.
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.
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.
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.
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.
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.
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.
Printed from https://nzmaths.co.nz/resource/numerals-and-expressions at 7:14am on the 23rd May 2022