1. Making Measurement Sense in levels 3 to 5 of the Curriculum
Sandra Cathcart

2. Look at what is important when we teach measurement
Today we will:
Look at what is important when we teach measurement
Consider some new ideas to try
Revisit some old ideas.
Big Picture

3. When we have completed a unit on measurement do our students
Measure accurately
Know what to measure with
Know how accurate to be
Know why they are measuring – have a reason
Can estimate
Can use the correct language
Be able to solve a problem using all of the above.
Have had some fun!

4. Add activities to this sheet as we look at them.
Activities and ideas

5. Attributes can be: a) spatial eg length, area, volume
b) physical eg weight (mass), temperature
c) No connection with physical objects eg time
Measurement units are used to quantify the attributes of objects.
To understand each attribute students need to move through stages of understanding.
From understanding the attribute concept
– what is length?
– to understanding what a unit of length looks like and how it is put together
- to connecting the idea that what you measure with is determined by what you are measuring.

6. Starters for a measurement lesson
1.The answer is 24. (cm, m, mm2)
What could the question be?
How might we extend this?
2 Raj said that he used 2 smaller shapes both the same to cover his large shape.
If his large shape looked like this what could the 2 smaller shapes be?
12cm x 8cm
3 The difference in the areas of 2 rectangles is 32cm2.
What might the widths and lengths of the rectangles be? Perimeters?
4 The answer to my question is 48 cubic metres. What might the question be?
5 Measurement Bingo
6 Write as a single number: /10 (write as a fr/dec/%)
3 ones and 4 tenths
24 Tenths and 24 tens
4 hundreds and 82 tenths
7 Estimation
Must be at least
Not greater than
Less than…..

7. Conversion Bingo 110cm 1.25m 12km 230cm 800m 0.7m 0.74 m 40cm 3m
Pick any 9 and fill in the grid.
110cm
12km
800m
0.74 m 3m
1.1m
2.9cm
600cm
9.6cm
1200m
1.25m
230cm
0.7m
40cm
28.5cm
1.8m
0.16m
115cm
280mm
3800m
1.25m cm
230cm 2.3m
0.7m 70cm
40cm 0.4m
28.5cm 285mm
1.8m 180cm
0.16m 16cm
115cm 1.15m
280mm 28cm
3800m 3.8km
110cm 1.1m
12km 1200m
800m 0.8km
0.74 m 74cm
3m 300cm
1.1m 110cm
2.9cm 29mm
600cm 6m
9.6cm 96mm
1200m 1.2km
Use in conjunction with conversion/area/volume loopies.

9. Estimation – this needs to be taught
In all measurement activities emphasize the use of approximate language (continuous/discrete)
Develop benchmarks -- make a square metre/cubic metre
Use “chunking” where appropriate
Use subdivisions
Iterate a unit mentally or physically eg using your stride to measure a driveway.
Accept a range
Sometimes have students give a range of measures
Include all attributes in estimation
Do estimation quickies and scavenger hunts
Use objects that will be reasonably close in attribute.
Move to using a measure and thinking about accuracy.
Estimation helps students focus on the attribute being measured.
If my unit was a playing card how would I need to cover this textbook?
Approximate language – the desk top is about……… ie emphasis on the fact that when measuring you are not getting an exact measurement
Eg measure a pencil– what if my ruler only measured in .cm – what would your answer be.
What if my ruler measured in mm etc…..
Chunking = to estimate the length of a room use eg 5 sets of windows that you know are about a 1m each.
Subdivisions eg to find length of a wall mentally divide in half and then half again until you get to a more manageable length.
Estimation quickies- a different attribute each day
Scavenger hunts find something in this room that
Has a length of 3.5cm
Holds about 200ml
An angle less than 45 degrees.

10. Must do:
At all levels students need to measure, measure, measure!
Show students how accuracy is important.

11. Team Puzzle

12. Making a square metre and cubic metre Then use these to estimate.
Each student makes a 10cm x 10cm square and labels the sides (10cm/100mm/0.1m)
Also label the Area mm2, etc
A very visual tool to have on the wall.

13. Activities to engage students

14. Purposeful Practice : August 5th, 2014 by Dan Meyer
Blog.mymeyer.com
Purposeful Practice : August 5th, 2014 by Dan Meyer
Practice may not always be fun, but it can be purposeful
Candy dandies – which uses least ribbon/least paper?

15. Changing Areas changing Perimeters
Students decide on the A and P of the shape. On their own squared paper draw as many shapes with same area or same perimeter etc record your data. Label the diagrams. This gets the students thinking about area and perimeter clearly.
Could use cubes.

16. How have they been arranged?

17. What do the rows and columns have in common?

18. As you go from left to right, the area of the shapes must increase
As you go from left to right, the area of the shapes must increase. As you go from top to bottom, the perimeter of the shapes must increase. All the shapes in the middle column must have the same area. All the shapes on the middle row must have the same perimeter.
Find the area and perimeter of each

19. Some questions for you
What do you notice about the shapes on the top row of the grid?
What do you notice about the shapes with the smallest perimeters
If two rectangles have the same area but different perimeters how can you decide which has the greatest perimeter.

20. For the smart ones
What do you have to decide first?

21. For extension

22. What is
the first question
that comes
to mind?

23. An nzmaths activity – body measurements
An investigation in 8 sections –
could take several classes to complete.
In this project, you will collect bone measurements in order to explore relationships that can be used to predict the height of a person.
Level 4/5
Can be used to link to Stats investigation.
Link to Vitruvian man

24. SS4 Evaluating statements about length and area

25. Some problems to solve Car boxes
Give out a toy car. Students are to
make a box to fit it in and then design a carton to take 100 snugly.
All documented. Extend to costs etc.
Fish tank My fish tank is old . I need a new one. My tank stand will only hold …..kg. if I buy a new one 20x40x10cm and fill it with water will the stand hold it?
Square pegs
Is there more space around a square peg in a round
hole or a round peg in a square hole?

27. Comparing Tubes Each student gets 2 pieces of A4 paper.
They need to make two cylinder tubes
A long fold one and a short fold one.
Stand them up.
Decide which cube holds the most.
Estimate first.
They need to prove it at least three different ways.
Try without formula first.

28. Arriving at School A Mathematical team Game
This covers Distance Speed and Time
Level 4
Best played at the end of the topic when students are more familiar with concepts
From a book by author Vivienne Lucas