# 25 frame (initiation to multiplicative structures)

#### Learning objective

Players (6-8 years old) visually recognise numbers (0-25) structured in a rectangular form. Through using a holistic structured analysis of pictures, players can potentially develop elementary calculation strategies (counting, adding up, compensation, and grouping). The game offers a possibility to work the multiplicative decomposition of numbers up to 25 (4=4×1=2×2).

#### Preparation

Print, laminate, and cut out playing cards. There are 30 cards in total. You can select the level of difficulty (green, yellow, or red) or just select the pairs of cards (numbers and images) you want to play with. Each card presents a written number or a frame of 25 spots (5×5) containing a colored rectangle (no colored squares for 0). Do not hesitate to discuss with students various calculation strategies to determine the number represented in the frame!

If there are only two of you playing (the teacher and the student, for example), try to win not more than one third of all games (teacher-student ratio should be 1:2).

#### Game

To begin with, choose cards representing numbers from 0 to 10 (22 cards).

Spread the cards facing down on the table. First player flip over 2 cards. If the two cards represent the same number, the player names the number and takes them for himself/herself and flips over 2 other cards. If the two numbers are not equal in value, the player flips them back facing down. Next player will play now. The goal of the game is to collect as many cards as you can.

#### Discussion

Flip all cards to see frames with colored rectangles. Organise a discussion using following questions:

• What numbers do you see? How are they represented? (as rectangles)
• What number is represented two times? Why? (4=1×4=2×4)
• What number is not represented? Why? (7, we cannot make a rectangle with 7 squares inside the 5×5 frame)
• What rules are used to represent numbers? (make a rectangle inside the frame 5×5)
• What other numbers can you represent using these rules? How? (Provide students with manipulative materials to facilitate the task. 12=4×3, 15=5×3, 16=4×4, 25=5×5)

Add cards to the game and continue to play.