We’ve previously explored great manipulatives for teaching fractions and in that blog post, I touched on pattern blocks. Pattern blocks are so versatile, but are underutilized in the realm of fraction instruction. Today, let’s dig further into the world of pattern blocks and unravel why they are so great for teaching fractions!

## Why Pattern Blocks?

Pattern blocks are a set of geometric shapes in different colors: yellow hexagon, red trapezoid, blue rhombus, green triangle, orange square, and tan rhombus. Each of these shapes are related sizes with 1-inch sides, with the exception of the trapezoid, which has a 2-inch side. Their consistent sizes and angles allow them to fit together well to explore geometric and fraction concepts.

When teaching fractions, we primarily use the hexagon, trapezoid, blue rhombus, and triangle. These manipulatives are often familiar to students starting in kindergarten, where they are commonly used to explore shapes, compose figures, and create patterns. This familiarity makes it easy to incorporate pattern blocks seamlessly into fractions lessons.

Additionally, when students initially begin grappling with fractions, they often attempt to model them by drawing circles and attempting to divide them into equal-sized pieces. Unfortunately, it can be really tricky to divide circles equally when drawing and students often have a difficult time with the task. As a result, their models do not truly represent the fractions that are intended to model. These errors can lead to misunderstandings that we want to avoid. Pattern blocks can help us sidestep these issues because their straight sides make them much easier to draw. They can even be traced!

## Parts of a Whole with Pattern Blocks

Pattern blocks shine when teaching foundational fractions concepts, especially the idea that fractions represent parts of a whole. Ask students questions like the ones below to get them thinking about how fractions relate to a whole:

- If the hexagon is 1, what shape is 1/3? (Blue rhombus)
- If the trapezoid is 1/2, what shape is 1? (Hexagon)
- How many triangles does it take to make 1? How can we represent that as a fraction? (6 triangle, 6/6)

These questions address the concepts of unit fractions, fractions equivalent to 1, and encourage students to think flexibly about how we describe the shapes. Eventually, when students become quite comfortable with this work, we can make another shape 1 whole. For example, if the trapezoid is 1, then the triangle is 1/3 and the hexagon is 2. This flexibility allows the introduction of fractions greater than 1.

## Fraction Mega Pack

## Fractions Greater than 1 with Pattern Blocks

Using the triangle, blue rhombus, or trapezoid to represent 1, we can begin to introduce fractions greater than 1 with both mixed numbers and improper fractions. Questions such as the ones below can lead students to explore fractions greater than 1.

- If the trapezoid is 1, what fraction does the triangle represent? (1/3)
- If the trapezoid is 1, what fraction does the hexagon represent? (2)
- If the trapezoid is 1, build 2 1/3. (Two trapezoids and a triangle or a hexagon and a triangle)
- If the trapezoid is 1, build 4/3. (Two blue rhombuses, four triangles, or a trapezoid and a triangle)
- Now that you have 4/3, build 1 1/3. (A trapezoid and a triangle)

Those final two questions allow for discussion about the equivalence of 4/3 and 1 1/3. These questions are not the only ones that can be asked, of course. Try using another pattern block as 1 and continue the investigation!

## Equivalent Fractions with Pattern Blocks

Pattern blocks are also excellent tools for investigating equivalent fractions. Using the hexagon provides the most options for this work because it allows exploration with equivalent fractions of halves, thirds, and sixths without going into fractions greater than one whole. Of course, when students are ready, use any other piece as one whole to investigate equivalent fractions less than *and* greater than 1.

So how do pattern blocks help teach equivalent fractions? One half is often very intuitive for students and is a great place to start. Ask students to show half of the hexagon by only using one shape (i.e. all trapezoids, all triangles, etc.). Students will be able to do this by using one trapezoid or three triangles which then be represented using equations:

- 1/6 + 1/6 + 1/6 = 1/2
- 3/6 = 1/2

This process can be repeated with other pattern blocks to determine fractions equivalent to thirds and one whole.

If we open up the options for students and allow them to use any shapes, they will find that they can also make ½ using a rhombus and a triangle or 1/3 + 1/6 = 1/2. This discovery leads us to the next way to use pattern blocks when teaching fractions: addition and subtraction!

## Adding and Subtracting Fractions with Pattern Blocks

Pattern blocks seamlessly support the addition of fractions with like denominators. For example, if adding 2/3 + 4/3, students would build 2/3 using two blue rhombuses and then add on four more. They could then answer 6/3 or if they use other pattern blocks to determine equivalence, they could answer 2.

When beginning to add fractions with unlike denominators, such as in the problem 1/3 + 2/6, students could model this using one blue rhombus and two triangles. However, determining the sum is not as simple as in the previous problem. Instead, this time, students will need to find equivalent shapes by either trading the blue rhombus for two triangles to get all sixths or the two triangles for one blue rhombus to get thirds. Once they have done this, they will be able to determine the sum to be 4/6. This is a great way to introduce the importance and meaning of a common denominator!

Subtracting fractions with like denominators mirrors the process of adding fractions with like denominators. Students simply build the first fraction and remove the subtrahend.

Pattern blocks can help with subtracting fractions with unlike denominators too! This time though, it isn’t as easy to “remove” the subtrahend. Often students will place the block or blocks that represent the subtrahend on top and look for the block or blocks that make up the difference. Similar to addition, this can lead to a conversation about common denominators and using benchmark numbers.

## But Wait, There’s More!

While I certainly haven’t covered every way to use pattern blocks for teaching fractions, I hope these ideas have inspired you. Once students are comfortable with pattern blocks and fractions, one of my favorite projects is to have students create a design using pattern blocks and then determine the fraction of their design that is green, blue, red, and yellow. Depending on student understanding, students can simplify their fractions, express them as mixed numbers or improper fractions, or even write addition equations to represent the entire design.

Even when not instructing students to use the pattern blocks in specific ways to demonstrate concepts, students can use them to solve equations. Add them to your math shelf and allow students to get them anytime they need them. I’m always impressed to see how students can transfer the work we’ve done together to their independent work to effectively demonstrate their learning!

Are there limitations to using pattern blocks to teach fractions? Sure, as there can be limitations to all manipulatives. That’s why I don’t think you should *only* use pattern blocks. However, pattern blocks can really challenge students to think flexibly, a crucial skill in math. Finally, pattern blocks provide a great bridge between concrete and abstract representations of fractions.

Curious to try using pattern blocks but don’t have access to physical pattern blocks? Don’t worry; I’ve got you covered! Here are free printable manipulatives that include pattern blocks. Enjoy!

Terri

Great suggestions! Thank you!