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

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

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!

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

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.

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: 0.2 + 9/10 (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…..

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 125cm 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.

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.

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

Team Puzzle

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.

Activities to engage students

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 http://blog.mrmeyer.com/category/3acts/ Candy dandies – which uses least ribbon/least paper?

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.

How have they been arranged?

What do the rows and columns have in common?

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

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.

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

For extension

What is the first question that comes to mind?

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

SS4 Evaluating statements about length and area

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?

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.

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