Using units and partial units to measure area

1. Show students page 1 of the PowerPoint.
   Here are two mats from Thailand. Which mat has the biggest area?
   How can you work the answer out?
   Give students A3 (enlarged) copies of page 1 of the Copymaster to work with in pairs. Make square units of different sizes available. Let students work in pairs, possibly based on tuakana-teina, to explore the comparison problem. Roam as the students work. Look for the following:
   • Do they use the squares as unit?
   • Do they fit the squares with no gaps or overlaps?
   • Do they use additive or multiplicative ways to count the number of units?
      
2. After a suitable time gather the group to discuss their findings with a focus on the bullet point above. 
   Why is it sensible to use squares to measure area? (Fit together with no gaps or overlaps)
   Why is it important to use squares that are the same size?
   Are large squares better than small squares? (Larger units are quicker to use but smaller squares are more precise)
    
3. Use page 2 of the PowerPoint (animated) to measure the area of each mat in square units.
   Is there a straightforward way to count the number of squares on each mat?
   Use the calculators, if needed, to find the areas using 8 x 8 = 64 units (left-hand) and 6 x 11 = 66 units (right-hand) and make sure that students understand multiplication as equal addition.
    
4. Use page 3 (animated) to introduce a different pair of mats. The square units are too big to fit into each mat exactly.
   Can we still tell which mat has the biggest area? How?
   Students should suggest that the part squares are also counted. Half or quarter squares fits into the uncovered spaces exactly. The left-hand mat contains 8 full squares and 4 half squares. The right-hand mat contains 9 full squares and 3 half squares. The total areas as 10 squares and 10½ squares. Animating page 3 shows the half squares as well.
   You might introduce te reo Māori kupu for area (horahanga) during this learning.
    
5. Page 4 shows another two mats.
   Which mat looks to have the biggest area?
   Animate the page and the mats will have square units place on top of them.
   Invite the students to work in pairs to decide which mat has more area and justify their answer. Let students use a calculator.

• The top mat has 2 x 9 = 18 square units but some mat is uncovered.
• The bottom mat has 3 x 8 = 24 square units and covered completely.
• Students should use part squares to cover the rest of the top mat. Two half squares fit along the right side and 9 half units fit along the bottom. That leaves space for a one quarter square in the bottom right. Combining all the squares and part squares gives a total 23¾ squares. Therefore, the bottom mat has slightly more area.
   

6. Give students a copy of page 3 of the Copymaster to work through. In each example they must use the square units to decide which mat in each pair has greatest area. Roam as students work. Look for:
   • Do they use multiplication to find the number of squares in an array?
   • Do they create partial units to cover the missing space?
   • Do they use fraction knowledge to combine whole and part squares?

Next steps 

1. Give students a target number of squares to be the area, e.g., 16½ squares. Ask them to create a mat of that size.
2. Explore other fractions of units, such as thirds of a square, fifths, eighths, or tenths.
   Provide mats with areas that are not easily found using whole and half units.