*do*math in order to

*understand*math. Manipulatives provide a way for students to do math in a concrete way before moving to the abstract. Many middle school students are still in the developmental stage where they are moving into being able to think abstractly, but they aren't there yet. Struggling high school students benefit from manipulatives because it gives them an anchor for them to remember the lesson and reduces the stress of thinking abstractly.

While there are awesome manipulatives that you can purchase, but I wanted to focus on easy things you may have around your house. Teaching math with manipulatives doesn't have to be expensive! One of my favorite things to use as a manipulative for high school students is paper. I also wanted to focus on things that actually

*teach*the lesson versus just being a fun part of an interactive lesson.

## Pre-Algebra Manipulative Ideas

**Integers -**This review lesson uses two-sided counters, but could easily be modified to use heads and tails on a few pennies. If you prefer, you can buy two-sided counters here.

**Classifying Triangles -**If you want a fun way for students to actually make triangles, then this is it!

**Naming Polygons -**This is a cool idea using Anglegs to have students make their own shapes. You can give them parameters to see what they can make. Read about it here.

**Adding and Subtracting Integers -**This manipulative is such a great way for students to

*understand*what is happening on a number line when they are adding and subtracting. Each student can easily make their own with paper and a brad fastener.

**Fraction, Decimal, Percent -**This activity uses M&Ms and includes a free download.

**Area of a Circle -**I believe students need to

*understand*formulas instead of merely memorizing them. If you have a sheet of paper, you can show students this demo so they will understand how the formula works.

**Area and Perimeter -**This awesome idea uses foam blocks, but you could easily substitute Legos. Students use the same number of blocks to create as many perimeters as they can. If you prefer foam blocks, you can find a set here.

**Decimal Place Value -**If your students struggle with place value, this activity (and free download) is perfect. It uses base ten blocks, but you can print paper versions if you would like. If you want to buy real base ten blocks, you can here.

## Algebra Manipulative Ideas

**Solving Equations -**This cool activity uses paper algebra tiles to help students solve equations. If you want a real set of algebra tiles, this magnetic set would be great to use on a markerboard.

**Multiplying Polynomials -**This is the best tutorial I've seen about how to use algebra tiles to multiply polynomials. Students would love this.

**Factoring Polynomials -**If your students need a hands-on way to learn factoring, this activity uses paper algebra tiles to teach factoring.

## Geometry Manipulative Ideas

**Intersecting Planes -**My students always have such a hard time "seeing" planes and lines intersecting at the beginning of the year. This easy demo with index cards and an extra pencil really helps!

**Congruent Triangles -**Students often have a hard time visualizing congruent triangles that overlap. This quick paper activity helps students figure it out.

**Parallel Lines and Transversals -**If your students struggle with spatial awareness, this activity using masking tape is for you!

**Midsegments of Triangles -**This paper folding activity helps students understand the Triangle Midsegment Theorem.

**Right Triangle Trigonometry -**When you are teaching trig ratios, get out a measuring tape and go outside on a sunny day! Students can measure their height and then the length of their shadow. They can use tangent to find the angle of elevation of the sun.

**Altitudes and Angle Bisectors of Triangles -**Students can figure out the properties of these special segments by paper folding. Read more about it here.

**Triangle Inequality Theorem -**This lesson idea uses markers to teach the Triangle Inequality Theorem. Bonus? The markers don't even need ink!

**Similar Right Triangles -**It's so easy for students to learn the theorems about similar right triangles when they do this paper cutting activity.

**Pythagorean Theorem -**This proof without words is the perfect way to teach students the Pythagorean Theorem. Since all you need is paper, I have my students make their own and include it in their interactive notebooks.

**Mapping a Shape Onto Itself (Rotations) -**Using patty paper, students can discover how to map shapes onto themselves. Read about it.

**Isometric and Orthographic Drawings -**This is a fun activity for students to build different views out of blocks. A free download is also included.

**Area of Rectangles, Parallelograms, and Trapezoids -**Students have an easier time remembering and using formulas when they do this paper cutting activity.

**Pyramids -**I love having students make a 3D pyramid out of an envelope. It helps them see the different parts so much better.

**Volume of 3D Shapes -**Water pouring when teaching volume of solids is SO helpful for students to understand the formulas. This geometric solids set is so awesome that it's one of the few manipulatives I purchased with my own money. You can also write on them with wet-erase markers to help students remember different segments in the figure.

## Algebra 2 and Pre-Cal Manipulative Ideas

**The Unit Circle -**I wish I had learned the unit circle using this paper plate lesson. It's my favorite way I've seen the paper plate done.

**Graph Transformations -**When I first teach graph transformations, I like to have students make a "V" or a "U" out of a pipe cleaner. Then I have them physically move the pipe cleaner on the graph as we look at different equations together. They can glue it in their interactive notebook as a reminder of the activity as well. You can find pipe cleaners at the dollar store, but you can also find them here.

What is your favorite way to use easy manipulatives?