# Numeracy at the end of Year 2

By the end of Year 2 a student should be able to **at least count-on-and-back and apply facile strategies**. He or she should also have an understanding of the meaning of place value with two- or three-digit numbers.

By the end of Year 2 a student should be able to **at least count-on-and-back and apply facile strategies**. He or she should also have an understanding of the meaning of place value with two- or three-digit numbers.

*I have 15 grapes and I eat 3 grapes. How many grapes do I have remaining? [Without materials] Can you write your answer here?*

A student not achieving grade expectations may 'make' (or attempt to make) the 15 by counting up from 1 and then attempt to 'take off 3'. A key characteristic of a child who is able to count-on-and-back is that for this task, the number word 'fifteen' stands in place of a completed count. He or she does not need to make the 15 by counting. The student can coordinate a backward count to remove 3 from the total or use knowledge of number combinations to determine the answer.

Different problem contexts and target numbers of objects may be used but the first number should typically be in the range from 14 to 20, and the second number typically 3 or 4.

Place 23 counters in front of the student.

*I have some counters here. Can you count how many there are?*

If the student makes a mistake, ask him or her to check the answer. Place a piece of paper and a pencil in front of the student.

*Can you write down how many counters you have?*

If correct: *Twenty-three, yes, that's right and you wrote a two and a three. Can you show me with the counters what the 3 means when you write 3 in a number like this? You can use the counters because there are twenty-three counters and this is the number twenty-three.*

If the student counts out 3 counters:

*Put them here next to the three.*

*This is just 3 counters. When you wrote the number 23 you wrote a 2 and a 3. Can you show me with the counters what the 2 means?*

If the student needs further prompting, say:

*I am interested in how you knew to write a 2 and a 3 to mean 23. So could you tell me what the 3 means and what the 2 means, and how together they mean 23?*

If the student puts out 2 counters and 3 counters:

*When you counted 23 there were all these counters. So if this is 2 and this is 3, where do all of the rest fit?*

Cover all of the counters with the paper.

*There are 23 counters under here. How many would be there if I took away 4 counters?*

A student who can coordinate a backward count to remove 4 from the total or use knowledge of number combinations to determine the answer is considered to have achieved a basic expectation of Stage 1.

**Note:** Counting-on-and-back is a precursor to place value knowledge, which is an expectation of MA1-4NA. Even if a student cannot use place value knowledge, he or she should be at least able to count-on-or-back. A student who does not link the representation of 23 to '20 counters and 3 counters' but can still deal with count-based operations with quantity by counting-on-and-back has met grade expectations 2.

Syllabus: MA1-4NA

Counts, orders, reads and represents two- and three-digit numbers.

2 For example, Kamii (1986) found that only half of the children in fourth grade understand the 1 in 16 to mean 10. In Canada, Bednarz and Janvier (1982) concluded that place value remains very difficult in third and fourth grade.

Kamii, C. (1986). Place value: An explanation of its difficulty and educational implications for the primary grades. Journal of Research in Childhood Education, 1, 75-86.

Bednarz, N., & Janvier, B. (1982). The Understanding of Numeration in Primary School. Educational Studies in Mathematics, 13, 33-57.