Sushi Surgery

This activity builds multiplicative thinking by presenting students with a context in which “wholes” (rolls of sushi) are split and regrouped (boxes). It also uses the array model discussed in Face the Facts. The students are asked to record their ideas as equations to help them see the pattern (that 4 rolls of 8 pieces will become 8 boxes of 4 pieces). The grouping changes, but the total number of pieces of sushi remains the same.
For question 1, you could help students who are struggling by “making” sushi rolls out of multilink blocks, forming sticks that could be broken up and regrouped as needed. Alternatively, sushi rolls could be made of playdough and cut into rounds. While it may be useful to start off with physical models, remember to challenge the students to move towards using number patterns to solve subsequent problems. Continue the pattern by asking them how many pieces of sushi there are in 6, 8, 10 rolls and so on.
Questions 2 and 3 are designed to get the students to visualise the groupings, changing from rolls to pieces to boxes. In multiplicative thinking, students need to see numbers as comprising different groupings and to develop flexibility in changing them around. Use concrete materials, as suggested above, to aid students who become confused by this.
Question 4 uses the array structure but deliberately focuses students on the length and width of the rectangles. It prompts the students to use basic facts to solve the problems rather than counting the squares or skip-counting. Encourage this and look for students who can apply the strategy to solving part b of the question.
Question 5 also asks the students to formalise their thinking in equations. Look for students who write addition equations and those who write multiplications. Use a discussion of strategies, during which students explain their thinking, to help the students writing additions.
Encourage the writing of multiplication problems for question 6 by providing materials to model problems, such as boxes to put pieces in and blocks to use as sushi pieces. Ask the students to make up some “sushi boxes” and then write a problem that matches what they have made. This is quite challenging. Pairing students will allow them to discuss their ideas. (See the notes for question 3 of Party to the Max for ways to help students when they are making up their own problems.)
 

Answers to Activities

1. a. 16. (2 x 8)
b. 32. (4 x 8)
2. a. 8 boxes. (1 roll fills 2 boxes. 2 x 4 = 8.
Or: 4 rolls is 4 x 8 = 32 pieces.
32 ÷ 4 pieces per box = 8 boxes)
b. 16 boxes. (4 rolls in a makes 8 boxes. 8 rolls is double 4 rolls, so
2 x 8 boxes = 16 boxes.)
c. 12 boxes. 1 roll fills 2 boxes. 2 x 6 = 12. Or: 6 rolls is 6 x 8 = 48 pieces; 48 ÷ 4 = 12 boxes.
3. Answers will vary. For example, to work out the pieces: 8 + 8 + 8 + 8 = 32 pieces or 4 x 8 = 32 pieces. To work out the boxes: 32 ÷ 4 = 8 boxes,
or 32 – 4 – 4 – 4 – 4 – 4 – 4 – 4 – 4 = 0, or 4 x = 32.
4. a. i. 4 x 5 = 20 or 5 x 4 = 20
ii. 3 x 5 = 15 or 5 x 3 = 15
iii. 7 x 6 = 42 or 6 x 7 = 42
b. i. 12
ii. 8
iii. 30
Strategies may vary, for example:
i. 3 x 4 or 4 x 3; or 20 – 8
ii. 2 x 4 or 4 x 2; or 15 – 7
iii. 6 x 5 or 5 x 6; or 42 – 12
5. a. i. 32 pieces. 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32; 8 x 4 = 32
ii. 36 pieces. 6 + 6 + 6 + 6 + 6 + 6 = 36; 6 x 6 = 36
iii. 30 pieces. 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30; 10 x 3 = 30
iv. 32 pieces. 8 + 8 + 8 + 8 = 32; 4 x 8 = 32
b. Salmon sushi (based on the number of pieces sold) or vegetarian sushi (based on the number of boxes sold)
6. Problems will vary.