What do we mean by

Extending Mathematical Thinking?  

It is important to ensure that the students learn math concepts deeply. The visual models in the puzzles are a great resource for extending student thinking and helping them make critical connections within mathematics itself.

ST Math provides different resources that illuminate the mathematics in the puzzles and allow for deeper exploration and sense-making of visual models. These resources include:

• Math Mats

• Game Mats

• Creature Cards

Mathematical Resources for Extending Thinking

Math Mats

Resources

Math Mats are common math tools that can be useful for making sense of a concept. 

Also available in Spanish

Math Mats are printable visual aids that assist students in visualizing and comprehending mathematics.

Game Mats

Resources

Game mats can be used to help students work through the mathematics of a puzzle!

Game Analysis

Resources

Level 1

Play the four different Levels of the game Fruit Monster

As you explore each level, think about how they are the same and how they are different. 

Level 4

Level 3

Level 2

Game Analysis

Resources

In Level One, we were given the number of fruit in a group and the number of groups - how many total fruits did we need to find?

Game Recap 

Game Analysis

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In Level Two, we were given the number of fruit in a group and the total number of fruit - how many groups do we need?

Game Recap

Resources

In Level Three, it was mixed up. Sometimes we were trying to find the total number of fruit and other times we were trying to discover how many groups there were.

Game Analysis

Game Recap 

Resources

In Level Four, we still had it mixed up but instead of having the ten blank plants or 20 blank pieces of fruit to choose from, we were presented with a visual that required us to think of them in a more symbolic way.

Game Analysis

Game Recap 

Game Mats

Resources

There are a couple of things happening here.

• First, students are exploring multiplication and division.

Reflect on how you see multiplication and division in this game.

Level 3

Game Mats

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Second, the game offers students a chance to shift from additive to multiplicative thinking, helping them transition from counting individual items to thinking in terms of groups.

Activity

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After engaging in the puzzle students can further explore the mathematics, make connections, and examine strategies by engaging in activities that extend their thinking.

Example Activity: How Much Fruit?

How Many in Each Group (Number of Plants)

=

Students match a card to the number of plants that was rolled.

Student 1 rolls a 2 - (Meaning there are 2 plants)

Student 1 then puts down a 10 card

Student 1 then needs to identify the number in each group (number of fruit) = 5

Example:

And write or say the number sentence, 2 x 5 =10

Creature Cards

Resources

These cards are to be used with games to enhance the learning experience for students by providing visuals to make sense of the Math in the game.

Creature Cards Activity Example

Resources

There are 20 shoes to fit on 6 creatures. Show two different combinations of 6 creatures that would need 20 shoes. Write an equation to represent each of your combinations.

5 + 5 + 3 + 3 + 2 + 2 = 20

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Creature Cards Activity Example

Resources

As students deepen their understanding with the model, they'll also explore relationships. For example, they may notice that two ostriches equal one dog, or that two robots are the same as one ant.

Those connections help students create multiple solutions to the problem. Discussions should focus on exploring those relationships.

Modules to Support Student Discourse

The End 

Some things to Remember:

• Extending Mathematical Thinking is about the mathematics in the puzzle and how it connects. 
• ST Math has student tools like Game Mats and Math Mats that aid in Extending Mathematical Thinking.