Numeracy Project Assessment (NumPA) Form C

Green

Materials

• You will need 12 bean counters.

• This sheet

These fraction cards

These fraction cards

Multiplication and Division

Here is a forest of trees.There are 5 trees in each row, and there are 8 rows.How many trees are there in the forest altogether?

If I planted 15 moretrees, how many rows of 5 would I have then altogether?

What is 3 X 20?

Does the student derive 3 X18 by 60 – 6 = 54?

What is 5 X 8?

Does the student derive 5 x 16 = 80 by doubling 40?If the student does not derive the answers to questions (2) and (3), rate him/her at either stage 4 or 5 and proceed to the questions on proportions and ratios.

Does the student use a part-whole strategy such as place value partitioning, for example, 6 x 20 = 120, 6 x 4 = 24, 120 + 24 = 144; tidy numbers, for example, 6 x25 = 150, 150 – 6 = 144;or proportional reasoning, for example, 6 x24 = 12x12 = 144 (doubling and halving)?

If the student solves any of questions (4) or (5) successfully using at least two different advancedstrategies, rate him/her at stage 7 for multiplication and division and proceed to questions (6)and (7). Otherwise rate the student at stage 6.

Does the student use a mental part-whole strategy such as doubling?reversing with rounding and place value?

Does the student use mental part-whole strategies such as:standard place value?converting equivalent fractions to decimals?

Stage and Behaviour

Proportions and RatiosIf the student responds incorrectly, point to the thirds.

Here are 12 jelly beans to spread out evenly on top of the cake. You eat one-third of the cake. How many jellybeans do you get?

Proportions and Ratios

Does the student use a part-whole strategy based on addition and/ormultiplication?

If the student cannot answer the question, allow them to manipulatethe beans or counters to solve it. If the student needs to manipulate the materials to solvequestion (4), rate them at stage 1 or 2–4, as appropriate, and proceed to the knowledgequestions.

For students who are unsuccessful at question (10), rate them at either stage 5 or 6, whatever is appropriate from their response to question (9), and proceed to the knowledge questions.

Does the student use apart-whole strategy based on equivalent fractions such as finding relationships between different units?

Does the student use a part-wholestrategy based on equivalent fractions such as finding relationships between different units?

Stage and Behaviour

• For each number I show you, tell me the number that comes just after it, the number that is one more. Also tell me the number that comes just before it, the number that is one less.

Forwards and Backwards

Fractional Numbers

Here are some fractions. Say each fraction as I show it.

Put these fractions in order from smallest to largest

(If correct) explain why one-quarter is less than one-third?If the student can recognise the unit fractions but cannot order them, rate him/her at stage 4.

Explain how you know this.If the student orders unit fractions but cannot recognise that is equivalent to 1 or 1 , rate him/her at stage 5.

Here are some fractions. Put them in order from smallest to largest.

Does the student recognise the equivalence of two-thirds and six-ninths? If so, ratethem at stage 7 at least, if not rate them at stage 6. Rate a student who successfully ordersall the fractions in question (20) at stage 8.

Stage and Behaviour

Place ValueFor the following questions, students should be rated by their fluent recall. Prolonged use of strategising suggests the student does not know the answer, and must work it out.The student must correctly answer all of questions...(21) and (22) to be rated at stage 5, otherwise rate them at stage 4.(23) and (24) to be rated at stage 6,(25) and (26) to be rated at stage 7,(27) to (30) to be rated at stage 8.Where the student shows knowledge gaps, rate him/her at the previous stage.

6 7 8

Stage and Behaviour

Basic FactsFor the following questions, students should be rated by their fluent recall. Prolonged use of strategising suggests the student does not know the answer, and must work it out.

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