**Curriculum – **Number Sense and Numeration

*Kindergarten*

Begin to make use of one-to-one correspondence in counting objects and matching groups of objects.

Use, read, and represent whole numbers to 10 in a variety of meaningful contexts.

Investigate addition and subtraction in everyday activities through the use of manipulatives.

*Grade 1*

Compose and decompose numbers up to 20 in a variety of ways, using concrete materials.

Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies.

Grade 2

Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies.

**Context**

Educator working with at least two children at a table or on the carpet.

**Materials**

- Deck of cards with face cards removed

**Summary**

The children are presented with a deck of cards laid out in a 5 by 8 square. There are two goals of the game, depending on the developmental level of the students. For students who are working on recognizing whole numbers, the goal is to collect the matching number pair in the cards laid out. For students working on addition and subtraction, the goal is to collect the two cards that either add or subtract to the predetermined sum/difference.

**Instructions**

- Lay the cards randomly in a 5 by 8 rectangle. Explain to the students that for this game, Ace will count as the number 1.
- Start the game by explaining to the students that the goal is to find the matching number in the cards (i.e. 4 of diamonds matched with a 4 of clubs). Let the students know that the colour or suit of the cards are not what we are trying to match. The objective of the first part of the game is to match the numbers.
- After the children have played and become familiarized with the matching numbers game, introduce the second version if appropriate. Let the students know that the goal of the second game is to find the numbers that add/subtract to a certain sum/difference. One player gets to choose a number from 2-20 which becomes the sum/difference the students need to achieve.
- Ask the children before they start playing what number pairs they should be finding for the particular sum/difference. For example, if the player chooses a sum of 5, then the players must find numbers that can add to 5 (e.g. Ace and 4, two and 3). If the player chooses a difference of 3, then the payers must find numbers that can subtract to 3 (e.g. 6 and 3, 7 and 4)
- When all of the cards for the predetermined sum/difference have been found, facilitate a discussion with the kids about which pairs they found. Ask the students how they knew those pairs were the correct ones. Facilitate a discussion examining how quantities can be composed and decomposed.
- Shuffle the cards and lay the out randomly in the 5 by 8 rectangle. Repeat steps 5 – 7.

**Questions to Extend Student’s Thinking**

- How many pairs did you find for this sum? How many pairs were found with another sum?
- Why would there be more pairs found for a bigger sum (i.e. 10 versus 5)?
- What strategies did you use to add the two cards together? What techniques did you use to remember where the cards were?
- How would you play this game with subtraction? What pairs would you need to look for then?

**Look Fors**

- Do the children select the exact card that they were missing? Being able to hold the desired number in their mind and knowing the exact location of the missing card demonstrates a strong visual-spatial working memory. Moreover, knowing the missing card demonstrates strong understanding of what the missing addend is (Losq, 2005).
- Do they need to count the number of symbols on the card? If so, are they using one to one correspondence? Are the students recognizing the numbers on the card? Griffin (2005) noted that typically by the age of four, the children should be able to use one to one correspondence and understand the cardinality rule. If some students are having difficulty recognizing the numbers, then teachers can guide their lessons to increase the students’ knowledge about the number sequence.
- Are the children using their fingers to count? Are the children counting up or counting on when they choose their pairs? Griffin (2003) noted that at Level 3, children are often using their fingers to represent the numbers on each hand. The more sophisticated strategy reflective of Level 4 is the counting on strategy. Counting on allows the child to be quicker at math because they are using a simpler and more efficient strategy. By examining which technique the student is using, teachers can determine what the student’s developmental level is.
- Do the children use certain memory strategies to determine if the pairs create the predetermined sum? This activity can highlight the individual strategies that the students are using to play the game. If children are able to play this game with automaticity, then this demonstrates a strong understanding of the basic and/or derived facts (Issacs & Carroll, 1999).
- Do the children use mathematical language to talk about the cards? The more the students are able to use the mathematical language during the game, the more familiar they will become with these mathematic concepts.