Exam Questions

Question 1

1. Explain how can simple materials be used to help students understand pattern structure?

Answer 1

Use two or more visually different materials to create a repeating pattern. Some examples of these materials are blocks, buttons, straws, paperclips and shapes. Students need to identify the part that repeats. Ensure students can extend the pattern to the right and to the left and identify ‘missing’ sections of a pattern. They should also be able to make the same pattern using different materials.

Question 2

2. Explain how the following repeating pattern can be used to show repeated addition?
   X X O X X X O X X X O X X X O X.

Answer 2

a. Identify the repeating part of a repeating pattern. For example, the repeating part of X X O X X X O X X X O X is X X O X.
Ask: How many in 1 part or group? (4) How many in 2 parts or groups? (8) How many in 3 parts or groups? (12)

Question 3

3. How can generalising patterns assist with developing algebraic thinking?

Answer 3

Students look across a number of cases to identify common structure. They apply these generalisations and rules to other cases and show that a generalisation works in all cases.
Creating and describing patterns supports the development of early number concepts, the understanding of algebra and students’ ability to compute.

Question 4

4. What is important to consider when helping young children to recognise the word and symbol for each of the numbers to 10?

Answer 4

. They need to be exposed to many different visual representations and embodiments of each number to build a mental object for that number. These concepts need to be experienced.

Question 5

5. What does it mean to ‘trust the count’?

Answer 5

It is the ability to access mental objects for numbers to 10 without having to make, model or record the number.

Question 6

6. Describe at least five skills young children should have to work confidently with numbers to 10.

Answer 6

identify which of two quantities (collections) is bigger or smaller
• recognise small collections to five without counting (subitise)
• match collections to number names and symbols (and vice versa)
• demonstrate knowledge of the number naming sequence
• identify one more, one less, what comes after, what comes before a given number
recognise that counting words and objects need to be in one-to-one correspondence, the last number says ‘how many’, and that the count remains the same even if the objects are rearranged
• recognise numbers as composite units and name the numbers to 10 in terms of their parts
• demonstrate a sense of numbers beyond 10 in terms of ‘1 ten and so many more’.

Question 7

7. Describe at least four skills young children should have before meeting ‘place value’.

Answer 7

Any four or more of these skills:
• accurately count to 20 and beyond
• model, read and write numbers to 10 using materials, representations, words and symbols
• recognise collections to 10 without counting (subitise)
• trust the count for each of the numbers to 10 without having to model or count by ones
• recognise numbers beyond 10 in terms of 1 ten and some more
• count larger collections by twos, fives and tens (recognise 2, 5 and 10 as countable units).

Question 8

8. Why might a young child hear ‘seventeen’ but write 71?

Answer 8

Seven is heard first so it is written first. The teen numbers are more challenging because of their inconsistent number names.

Question 9

9. How can you consolidate two-digit numeration?

Answer 9

comparing (e.g. compare measures to determine which of two objects is longer or heavier)
• ordering a set of numbers (e.g. list age of family members from youngest to oldest)
• counting forwards and backwards in place-value parts (e.g. 2 tens more than 631)
• renaming numbers in terms of their parts (e.g. recognise 85 as 85 ones or 8 tens and 5 ones or 7 tens and 15 ones).

Question 10

10. Describe three strategies for adding and subtracting two-digit numbers?

Answer 10

the ‘split’ or ‘by parts’ strategy which involves dealing with the place-value parts separately; e.g. for 52 + 29, add tens with tens (70), ones with ones (11), then add 70 and 11
• the ‘jump’ strategy which involves counting on or counting back from one of the given numbers; e.g. for 52 + 29, add 5 tens to 29 (79) then add 2 more to get 81
• a ‘compensation’ strategy in which the numbers are reconfigured to make the calculation easier but maintain equivalence; e.g. for 52 + 29, rename as 52 + 30  1.

Question 11

11. What learning activities can be used to develop strategies for counting large collections efficiently?

Answer 11

To recognise numbers to ten as composite units, use regular subitising activities and opportunities to physically count large collections. Children will realise that counting by fives or tens is useful, and that arranging the stacks in an ordered way is a useful means of keeping track of the count and avoiding counting the same pile twice.

Question 12

12. What do children need to demonstrate before they can engage with array-based mental strategies for multiplication?

Answer 12

trust the count and recognise the numbers to ten in terms of their parts
• recognise numbers to ten and beyond as composite units
• have a sound knowledge of two-digit place value and can rename two-digit numbers in terms of their parts
• know their doubles facts to twenty and are developing effective strategies for doubling two-digit numbers
• have access to meaningful, efficient additive strategies, particularly the ‘make to 10’ strategy
• are comfortable with the ‘array/region (times as many)’ idea for multiplication, the making and renaming of arrays/regions, and the commutative property for multiplication.

Question 13

13. List at least three key steps involved in building fraction knowledge and confidence.

Answer 13

provide plenty of experiences in sharing recognised quantities and collections in ways that emphasise the two variables involved (that is, the amount to be shared and the number of shares)
• consider examples and non-examples of fractions and discuss the fact that ordinal number names are used to indicate fractional parts
• investigate what happens as the number of sharers increases or decreases
• recognise and record key generalisations such as the parts are equal, the number of parts increase as the parts get smaller, the number of parts names the part, and the size of the part depends on the size of the whole
• explore partitioning strategies and the ways they can be used to construct fraction diagrams and line models to represent and name proper and mixed fractions
• introduce fraction language and symbols to emphasise the distinction between how many (numerator) and how much (denominator) and link to different interpretations
• informally compare and order fractions in relation to known benchmarks (such as half, quarter, close to one, proximity to whole number) and explore the use of diagrams and line models in this process.

Question 14

14. What are some geometrical concepts that children need to develop during the early primary school years?

Answer 14

spatial objects, including geometric classification and language
• relationships between spatial objects, including seeing the parts and the whole
• developing dynamic imagery, including transformations
• location.

Question 15

15. What are three main types of common misconceptions about decimals? Provide one example for each.

Answer 15

longer-is-larger misconceptions; e.g. 4.63 would be thought larger than 4.8 (longer string length)
• shorter-is-larger misconceptions; e.g. 0.2 would be thought larger than 0.54 (tenths larger than hundredths)
• apparent expert behaviour; e.g. 15.348 would be seen as 15.35 (rounding to two decimal places).

Question 16

What do we mean by ‘open-ended’ problems? How are these used to cater for a
diverse range of abilities?

Answer 16

An ‘open-ended’ problem is a problem that has multiple solutions. An example might be that
I have $2 worth of coins in my pocket, what possible coins might I have? Open problems
cater for diverse range of abilities because children who struggle should be able to produce
a solution (in this example 1 + 1 = 2), while more able children can produce a greater
number of solutions, some of which are more complex (eg. 0.2 + 0. 2 + 0.2 + 0.2 + 0.2 + 1).

Question 17

2. When children are working mathematically (as defined in the syllabus), what sorts of
   things would they be doing? (Hint: describe the sub-strands that comprise the working
   mathematically strand).

Answer 17

When working mathematically, children should be problem-solving, reasoning and
communicating. Reasoning involves having them provide reasons for their working/answers
and they need to be able to do this through oral and/or written communication. Often this
occurs when children are problem-solving.

Question 18

3. What are the three content strands in the new draft syllabus? What are the sub-strands
   in each?

Answer 18

The syllabus has three content strands: Number and Algebra; Measurement and Geometry;
and Statistics and Probability. In the NA strand there are ………

Question 19

4. Define and explain the terms of the acronym ELPSARA.

Answer 19

The acronym ELPSARA refers to:
a. E – experience (drawing on the experience of the child)
b. L – language (taking care to articulate the language that is being used and being
mindful of the child’s current language)
c. P – pictorial (providing the child with a pictorial (visual or concrete) representation
of the mathematical concept)
d. S – symbolic (introducing the child to the symbolic aspects of mathematics)
e. A – application ……elaborate
f. R – reflection …. elaborate
g. A – assessment….elaborate

Question 20

5. One of the big ideas associated with number is place value. How do we introduce
   children to place value, that is, describe an activity we would have them do?

Answer 20

Children are introduced to place value through counting in tens, for example bundling
straws in groups of 10. Children then see that 10 separate straws is the same as one lot of
ten. Children would then be introduced to the symbolic representation

Question 21

6. In what order would you teach the multiplication facts?

Answer 21

The multiplication facts (tables) usually commence with the twos (two times table) because
children have already learnt doubles as a part of their addition facts. We would also start
with the tens facts and fives facts, again because children have learnt to count in 10s and 5s.

Question 22

7. A child tells you that one third is bigger than one half. What misconception do you
   think he/she has about fractions? How would you help them?

Answer 22

. They see the fraction as being two numbers (eg. ½ as 1 over 2). Therefore because 3 is
bigger than 2, they think that 1/3 is bigger than ½ . Get them to fold some paper in to half
and then into thirds, eg. (make sure paper is same size):

Question 23

8. What (pictorial or concrete) representation could you use to help children understand
   the concept of decimals?

Answer 23

I would use the linear arithmetic blocks to show children representations of decimals. Or
use a ruler to show 0.1m and 0.01m (provided that they understand length). Or an area
model that would be a 10cm by 10cm grid (children would then shade in the decimal
fraction).

Question 24

9. What ICT tool could you use in the teaching of data? How would you use it in a
   lesson?

Answer 24

TinkerPlots is a software tool suitable for teaching data. Teaching with this might involve
getting children to construct a person graph (ie physically involving the children) and then
showing them this on TinkerPlots itself. We could collect some data (a simple survey) and
then make a plot of boys/girls (using the children), then a plot on TinkerPlots. The children
could then explore their own (ie tinker with) data

Question 25

10. Why are Van Hiele’s levels of geometric thought useful for teachers?

Answer 25

The Van Hiele levels describe how children develop their geometric thinking. They are useful
for teachers because they guide the types of activities we might use at different levels of
development. For example, we would have children play with shapes in the early years so
that they can start describing properties of shapes (that is move to the description/analysis
stage).

Question 26

11. Describe an activity that stage 2 children might do when learning about position.

Answer 26

In order to teach children the grid reference system, I would use masking tape to mark out a
grid on the floor of our classroom (place in a corner or use entire room). The lines would be
against key features of the room, such as smartboard, door (see diagram below). I would
discuss with children how they could describe their position in the class and use this to
introduce the concept that they describe position against one wall and then against the
other. Eg. I’m in line with the door on the side wall and also the smart-board on the front
wall.

Question 27

12. How would you introduce children to the concept of angle? At what stage would this
    occur?

Answer 27

Angles are not introduced until stage 2. I would show children an analogue clock and discuss
the amount of turn between the two hands. We could then have children identify other
angles that are in the class. We would discuss what it means to have a bigger angle and then
develop activities where children identify angles in the classroom and then order them from
smallest to largest

Question 28

13. What would be the first thing we would introduce children to when we start teaching
    chance? Describe an activity that you would use

Answer 28

Children are introduced to the language of chance first and this starts in Stage 1. I would
discuss terms such as ‘certain’, ‘possible’, and ‘impossible’. What do these mean? Is it
certain that we will have big lunch today? Suggest a number of similar situations and ask
children to decide whether the situation is certain, possible or impossible.

Question 29

14. What kind of response would children give to a question involving chance, if it was
    deemed to be at a numerical level?

Answer 29

When children provide a numerical response to probability, they (as the name suggests) give
a numeric value. For example, they might say that in a jar containing 3 blue and 7 red
marbles, the likelihood of getting a red is greater because there is a 0.7 chance associated
with this.

Question 30

.15. Describe the teaching sequence associated with the development of measurement. In
other words, where do we start and how do we build on this?

Answer 30

The suggested teaching sequence for measurement is:
a. Attribute: provide activities that allow children to understand the nature of the
attribute (eg. what do we mean by area?)
b. Comparing and ordering:
c. Quantifying by counting non-standard units.
d. Quantifying by counting standard units
e. Applications

Question 31

16. One of the concepts associated with measurement is that of the measurement scale.
    What exactly does this mean? That is, what do students need to know about scale?

Answer 31

. The concept of scale refers to the understanding needed to read a measurement scale.
Children need to understand when reading (for example) a ruler that the marks on the ruler
are located at the ENDS of the units not in the middle. They also need to understand that
while a ruler has a zero point, we can measure length from any point on the ruler. Finally,
they need to understand that the scale has different levels of precision. For example, a ruler
might have both cm and mm increments on it.

Question 32

17. Describe an activity that stage 3 children might use when learning about
    measurement?

Answer 32

Children in Stage 3 would be applying their knowledge in measurement. So an activity might
be that they calculate the area of turf needed for the sports field. Children would be
provided with trundle wheels and working in groups would make measurements and
probably then use a formula for calculating the area.

Question 33

18. In early stage 1, children learn to describe, continue and translate patterns. Give
    examples of questions (or activities) that you would use to assess whether children
    could do each of these.

Answer 33

I would ask them to describe the pattern (some would say triangle, square, square,
others by colour).
b. I would ask them to make the same pattern using pattern blocks and then to guess
what comes next.
c. I would ask them to clap every time they see the triangle and stomp when they see
the square. Hopefully the could translate this into clap, stomp, stomp, clap, stomp,
stomp,….

Question 34

19. A child gave an answer of 17 to the question: 12 + 5 = ? + 7. What misconception do
    they have and how would you overcome this?

Answer 34

The child mistakenly thinks that the equals sign means ‘gives the answer’. So they have done
just this and given the answer to 12 + 5. Depending on the child I might use some concrete
support. Example: use some toy scales and show them 12 blue teddy bears and 5 red teddies
on one side. How many teddies do we have on this side? Place 7 teddies on the other side?
How many do we need to ‘balance’ the two sides? How can we write this down? If older,
then explain that the equals sign means the same as. Is 12 + 5 the same as 17 + 7? Obviously
not. What do we need to add to make the two sides have the same value? Try some more
questions.

Question 35

20. How would you use patterns to help children learn their number facts?

Answer 35

Children can see patterns in the hundreds chart when learning their multiplication facts. For
example, multiples of 4 form diagonal patterns on the hundreds chart. Children can also see
that multiples of 10 all finish with a zero. So I would use the hundreds chart when
reinforcing the multiplication facts