Use pattern-block puzzles to teach shape and area.

Most of us have them stashed in our classrooms - buckets full of pattern blocks. Here are two problem-solving ideas to add to your repertoire of hands-on pattern-block activities.

INTERMEDIATE Activity

PREDICTING SIMILAR SHAPES

PURPOSE

To provide first-hand experience with similar shapes

MATERIALS

pattern blocks, overhead pattern blocks (optional)

TIME NEEDED

1 hour

1 I place an orange square on the overhead projector and ask students to imagine how they might use additional orange squares to build a larger square. I ask, "How many orange squares would you need to build a larger square?" I have volunteers demonstrate with blocks.

2 On the chalkboard, I sketch three larger squares and write underneath each the number of blocks used - 4, 9, and 16.

3 I tell students to build three enlargements of each of the other pattern block shapes (triangle, rhombus, and so on) and trace the blocks to show how they built each. I remind them that the new, larger shapes must have exactly the same shape as the original block. I tell them, "When shapes are different sizes but are exactly the same shape, they're similar."

4 I demonstrate with orange squares how to check that enlargements really are similar to the original shape. I show how I hold an orange block up and eyeball whether it covers the larger square exactly. If I can't make the orange block cover the larger shape exactly, then they're not similar.

5 As we discuss their findings, students discover that it's possible to build enlargements of all the shapes except for the hexagon. For those that are possible, the numbers of blocks needed for the enlargements are the same - 4, 9, and 16. I ask students to predict the numbers of blocks needed to build even larger shapes.

PRIMARY Activity

MULTIPLE WAYS TO MEASURE AREA

PURPOSE

To introduce area and give experience with a problem that has multiple solutions.

MATERIALS

pattern blocks, overhead pattern blocks (optional)

TIME NEEDED

1 hour

MULTIPLE WAYS TO MEASURE AREA

1 I gather the whole class on the rug, put one green triangle on the overhead, and write the number 1 underneath. (If you don't have overhead blocks, use doublesided tape to stick regular blocks to an easel.) Then I place a blue rhombus next to the block and write the number 2 underneath it. I add a red trapezoid and a yellow hexagon, and write the numbers 3 and 6 below them.

2 I ask, "Why do you think I wrote these numbers?" Often children guess that they're the number of sides or corners, but I point out a block that doesn't fit and ask them to think again. If a child does not guess it, I explain that the numbers tell how many green triangles it would take to cover each shape. I demonstrate with blocks, explaining, "When we figure out how many blocks it takes to cover a shape, we're measuring its area."

3 I make a shape with one red trapezoid and two green triangles and tell students that if the triangle is worth 1, the area for this shape is 5. Underneath I write 3+1+1 = 5. Then I ask, "Who can think of how to make a shape with different blocks that also has an area of 5?" The class sees that there are many possible solutions. I ask: "Can you make a shape with an area of 5 using two blocks? What is the greatest number of blocks you could use to make an area of 5?"

4 I distribute unlined paper and pattern blocks and say, "Find as many shapes as you can that have an area of 10. When you find a shape, trace around the blocks to record it. Then write a number sentence underneath to show that the area of the blocks add up to 10."

5 I have students show their work and I copy their number sentences on chart paper. We notice that number sentences can contain the same numbers in different orders, and that the same number sentence can describe shapes that look different.

STEPHANIE SHEFFIELD, a first-grade teacher in Houston, Texas, and RUSTY BRESSER, a fifth/sixth-grade teacher in San Diego, California, are the authors of Math and Literature books, published by Math Solutions Publications, available from Cuisenaire. MARILYN BURNS is the creator of Math SoLutions inservice workshops.