Medieval Mesaure

Measuring an area has strong connections to tessellation in Geometry and multiplication in Number. For example, when using multilink cubes to find the area of a rectangle, students are creating a tessellation of squares

Students may use “one-by-one” counting to find the total number of cubes, but encourage them to use addition and multiplication as increasingly efficient strategies.
In this activity, it is important for students to describe the strategies they used by recording the number sentences. For the rectangle given above, the sentence might be:
5 + 5 + 5 = 15 or 3 x 5 = 15
3 + 3 + 3 + 3 + 3 = 15 or 5 x 3 = 15
This idea can be extended by using other arrays and masking parts of the arrays to encourage visualisation. For example:

How many apples are in the whole array?
When students use place value blocks as their unit of area, they should find that their answer is four times the answer they would get with multilink cubes. Their answers from the place value blocks could be written as cm², as in 15 cm² or 15 square centimetres.

This is a simple way of demonstrating enlargement in geometry. If the sides of a shape are enlarged by a factor of two (that is, the lengths are doubled), then its area will quadruple. For example:

Answers to Activity

1. 124 bricks
2. Answers will vary. Students may measure each defined area (for example, 2 x 2) or measure the front in two pieces and subtract the empty spaces.
3. Answers will vary.