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Packing Bags - Proportional Reasoning

Teacher Notes

Given pictures of two, three, or four bags, one of which is filled with circles, squares or triangles, students use their tiles to fill the other bags to look the same. They then identify the total number of tiles of each shape. Patterns for cutting tiles from heavy stock paper are supplied at the end of this activity. If you have shape tiles, students may use those.

For each Packing Bags, problem, always begin by asking students to identify the contents of the “filled” bag, describing or naming the shapes, and counting to determine the number of each.

For your convenience, each packing bags problem is reduced in size and shown along with questions and directions for you to follow to engage students in the activity. The pictures only are available for you to duplicate to give to each student.

Packing Bags 1

Teacher Questions

Look at the picture.

What do you see?

(2 bags. One bag has 2 circles and one triangle. The other bag is empty.)

Point to the bag with the triangle.

How many triangles are in the bag? (1)

Point to the circles.

How many circles are in the bag? (2)

This is Ann’s bag.

Use your shape tiles.

Put one triangle into the empty bag.

Put 2 circles into the empty bag.

Count the shapes.

How many circles in all? (2)

How many triangles in all? (4)

Packing Bags 2

Teacher Questions

Look at the picture.

What do you see?

(2 bags. One bag has 2 triangles, 1 circle and one square. The other bag is empty.)

Point to the bag with the triangles.

How many triangles are in the bag? (2)

Point to the circles.

How many circles are in the bag? (1)

Point to the square.

How many squares are in the bag? (1)

This is Ted’s bag.

Use your shape tiles.

Put 2 triangles into the empty bag.

Put 1 circle into the empty bag.

Put 1 square into the empty bag.

Count the shapes.

How many triangles in all? (4)

How many circles in all? (2)

How many squares in all? (2)

Packing Bags 3

Teacher Notes

Look at the picture.

What do you see?

(3 bags. One bag has 1 circle and 2 squares.. The other two bags are empty.)

Point to the bag with the shapes.

How many squares are in the bag? (2)

How many circles are in the bag? (1)

This is Bob’s bag.

Use your shape tiles.

Put 2 squares into each empty bag.

Put 1 circle into each empty bag.

Count the shapes.

How many squares in all? (6)

How many circles in all? (3)

Packing Bags 4

Teacher Notes

Look at the picture.

What do you see?

(3 bags. One bag has 2 square, 2 triangles, and 1 circle. The other two bags are empty.)

Point to the bag with the shapes.

How many squares are in the bag? (2)

How many triangles are in the bag? (2)

How many circles are in the bag? (1)

This is Sue’s bag.

Use your shape tiles.

Put 2 squares into each empty bag.

Put 2 triangles into each empty bag.

Put 1 circle into each empty bag.

Count the shapes.

How many squares in all? (6)

How many triangles in all? (6)

How many circles in all? (3)

Packing Bags 5

Teacher Notes

Look at the picture.

What do you see?

(3 bags. One bag has 4 circles, 1 triangle and 1 square. The other two bags are empty.)

Point to the bag with the shapes.

How many circles are in the bag? (3)

How many triangles are in the bag? (1)

How many squares are in the bag? (1)

This is Sue’s bag.

Use your shape tiles.

Put 3 circles into each empty bag.

Put 1 triangle into each empty bag.

Put 1 square into each empty bag.

Count the shapes.

How many circles in all? (9)

How many triangles in all? (3)

How many circles in all? (3)

Packing Bags 6

Teacher Notes

Look at the picture.

What do you see?

(4 bags. One bag has 2 triangles, 1 circle and 2 squares. The other three bags are empty.)

Point to the bag with the shapes.

How many triangles are in the bag? (2)

How many circles are in the bag? (1)

How many squares are in the bag? (2)

This is Debbie’s bag.

Use your shape tiles.

Put 2 triangles into each empty bag.

Put 1 circle into each empty bag.

Put 2 squares into each empty bag.

Count the shapes.

How many triangles in all? (8)

How many circles in all? (4)

How many squares in all? (2)

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