New Zealand Curriculum: Level 2
Learning Progression Frameworks: Additive thinking, Signpost 4 to Signpost 4
Target students
These activities are intended for students who currently use a count on and back strategy to solve addition and subtraction problems with whole numbers to 20.
Target students should have already developed a degree of part-whole understanding in addition and subtraction contexts (joining and separating). They should have some number facts to call on, particularly number bonds to ten. Understanding of two-digit place value, including the structure of ‘teen’ numbers will support many of the activities described in this intervention. (show diagnostic questions)
The questions should be presented orally and in a written form so that the student can refer to them. Present the basic facts by progressively uncovering the problems using a masking card. Half of an A4 sheet is ideal. If appropriate to the knowledge of your students, you could incorporate te reo Māori kupu for numbers (e.g. tahi - one).
- I will show you some addition problems. I am looking to see if you know the answers. Don’t worry if you need to work them out.
2 + 3 = 1 + 4 = 6 + 2 = 5 + 4 =
Signs of fluency and understanding:
Instantly recalls each fact with no obvious signs of calculation.
What to notice if your student does not solve the problem fluently:
Counting on in ones from the first number. This indicates that the student needs to learn their basic addition facts to ten. Solving 1 + 4 by counting on 2, 3, 4, 5 also indicates that the student has yet to understand the commutative property, e.g. 1 + 4 = 4 + 1
Supporting activity:
Addition facts to ten
- I will show you some addition problems. I am looking to see if you know the answers. Don’t worry if you need to work them out.
3 + ___ = 5 (Say “Three and what equals five?”) 2 + ___ = 6 4 + ___ = 9 5 + __ = 8
Signs of fluency and understanding:
Instantly names the missing addend with no obvious counting on strategy. The student may pause slightly as they mentally search for the related fact.
What to notice if your student does not solve the problem fluently:
Counting on in ones while tracking the counts (possibly on fingers), e.g. Finds 2 + __ = 6 by counting 3, 4, 5, 6, and tracking the counts, possibly using their fingers. This indicates that the student needs to learn the basic addition facts to ten.
Long pauses without obvious counting may indicate that the student is scanning available facts to find the required addends. This demonstrates a need for support in organizing basic addition facts, such as listing all the addend pairs that make eight.
Supporting activity:
Missing addends to ten
- I will show you some addition problems. I am looking to see if you know the answers. Don’t worry if you need to work them out.
4 + 4 = ____ 7 + 7 = ___ 9 + 9 = ___ 6 + 6 = ___
Signs of fluency and understanding:
Instantly recalls the doubles facts without any obvious signs of calculation. This indicates that the student has a strong knowledge base of basic facts beyond ten that they can use to derive unknown facts such as 8 + 7 = 15.
What to notice if your student does not solve the problem fluently:
Counting on, in ones, indicates the student needs to learn their doubles facts to 20.
Supporting activity:
Doubles facts
- I will show you some addition problems. I am looking to see if you know the answers. Don’t worry if you need to work them out.
9 + 6 = ____ 9 + 8 = ___ 9 + 5 = ___ 9 + 7 = ___
Signs of fluency and understanding:
Instantly recalls the ‘nine plus’ facts without any obvious signs of calculation. This indicates that the student has a strong knowledge base of basic facts to 20 that they can use to derive unknown facts, such as 8 + 7 = 15.
What to notice if your student does not solve the problem fluently:
Deriving ‘nine plus’ facts using teen number knowledge, e.g. 9 + 6 = 10 + 5 = 15. The strategy shows the student has part-whole thinking but needs to develop fluency of recall. Continuing to derive these facts adds memory load which might prohibit more complex calculations.
Counting on in ones to find the sums, possibly supported by use of fingers to track the count. This indicates a need to develop part-whole thinking using teen facts and progress to fluent recall.
Supporting activity:
Nine plus facts
- I will show you some addition problems. I am looking to see if you know the answers. Don’t worry if you need to work them out.
6 + 7 = ____ 8 + 6 = ___ 5 + 7 = ___ 7 + 8 = ___
Signs of fluency and understanding:
Instantly recalls the facts without any obvious signs of calculation. This indicates the student has a strong knowledge base of basic addition facts to 20.
What to notice if your student does not solve the problem fluently:
Deriving facts using teen number knowledge or doubles, e.g. 7 + 8 = 7 + 7 + 1 = 15. The strategy shows the student has part-whole thinking but needs to develop fluency of recall. Continuing to derive these facts adds memory load which might prohibit more complex calculations.
Counting on in ones to find the sums, possibly supported by use of fingers to track the count. This indicates the student needs to develop part-whole thinking using teen facts and progress to fluent recall.
Supporting activity:
Harder addition facts to 20
Teaching activities
