This is probably not the reply you wanted to get:I am a teacher candidate at the University of Melbourne and I am studying to be a primary (elementary) school teacher. We have been given a practice maths exam but have not been provided the answers (helpful, wouldn’t you agree?) The following are the 9 questions (out of 40) that I am either unsure about, or simply don’t know how to answer. I was hoping that if someone could provide the odd answer or two (showing their workings) to any of these questions (maybe just copy and paste the questions into a reply?) that I could actually have a chance of passing this thing. You will notice the questions are in metric – I hope this doesn’t freak you out too much!
Q1. Small garden gnomes are packed individually in cardboard boxes that are cubes of side length 1 decimeter. They are packed for export in crates that are cubes of edge length 1 meter.
a. How many gnomes can be packed in a crate?
b. What materials could be used in the primary school classroom to illustrate this problem?
c. How many crates could be stacked in a space measuring 15 metres by 5 metres and 3 metres high?
d. Explain why 1 cubic meter is equal to 1000 cubic decimeters
Q2. A teacher needs to order soil for a garden. The garden is a semicircle, with diameter 2.6m and she needs the soil to be 15cm deep.
- What will it cost if the soil is $45 per cubic metre?
- She wants to put a row of bricks around the outside of the whole semicircular garden. How many bricks will she need if the bricks are 24cm long?
Q3. Alice is renovating her spa bath, which is 120cm by 100cm and 60cm deep.
- The tiles she is using are 5cmx5cm tiles, which come in packets of 100. How many packets will she need to tile the sides and base of the spa?
- In the interests of water conservation Alice only wants to use 200 litres of water in the spa. How deep should she fill it?
a. Give two statements that could be used to explain the concept of angle to grade 4 children.
b. For each statement, describe a physical object that could be used to support the explanation
c. Name an appropriate informal unit of angle measure.
- Discuss how you might go about getting a year 5 class to determine the number of chairs that they could fit in the school yard
- Suppose you wanted to get a class to work out how much room would be taken up by all the milk cartons and containers bought in Melbourne in one day. What information would you need to know?
- Suppose you worked out the answer and it was 36000 m³. How could you make this answer meaningful?
- The study of mathematics in primary schools is sometimes characterized as arithmetic (i.e. the study of number). Briefly justify why studies in Measurement should also be included in primary mathematics courses.
- Repeat above, replacing Measurement by Space/Structure/Working Mathematically
- Discuss the reasons why representing three-dimensional objects in two dimensions is difficult.
You are preparing for a series of lessons on shape, with a focus on common 2-dimensional shapes. Describe an assessment activity you could use with a Grade 3/4 class that would help you find out more about children’s understanding of such shapes. Explain the method you would use to record student understanding.
I would have thought that it's the job of your teacher to be doing what you're asking.
So how about pointing out to your teacher that providing a practice exam without answers (as opposed to solutions) is poor teaching practice. Then request that answers be provided.
Be sure to offer these comments as constructive feedback, something a good teacher values.