Math Manipulatives for Middle and High School Students that You Can Print!
Manipulatives have the power to make math come to life! They make math concepts tangible and accessible to students. Whenever we have the chance to make math lessons hands-on, they instantly become more engaging and meaningful.
In middle and high school, manipulatives are less common than elementary school. However, they are appropriate for all grade levels and all abilities. A common misconception is that manipulatives are only needed in early grades or for students who struggle. Let’s bust that myth! Manipulatives encourage deeper thinking and sense-making. Instead of following procedures without thinking, we can use manipulatives to help students reason and make sense of the math.
I’m sharing some helpful math manipulatives you can use with middle and high school students, and the best part is that they are printable!
Unit Tiles
Unit tiles are simply squares (all the same size). They are one of the simplest manipulatives but they give students something tangible for many math topics. Here are some ideas for how to incorporate them into your math lessons:
Multiplication: Create arrays to find products of two factors.
Factors & Division: When given a total, create a rectangle to find its factors.
Area: Estimate areas of different 2D figures by laying unit tiles on top.
Adding & Subtracting Integers: Print the tiles on 2 different colors to represent positive and negative integers.
Protractor & Lengths
A protractor is a must when students are learning about angles. If students do not have their own, you can print protractors if needed. I also like to provide students with a set of “lengths” (which are just thin strips of paper to represent segments). The teacher can guide different experiments if every student has the same “lengths.” Here are some ideas:
Angle Measures: Use the 2 longest lengths to practice measuring angles with a protractor and creating angles given a measure.
Triangles: Create equilateral, isosceles, and scalene triangles using the lengths. Use the protractor to make observations about the angles. Notice which combinations of lengths can (and cannot) be used to create triangles.
Angle Relationships: Create vertical angles, supplementary angles, and parallel lines cut by a transversal using the lengths. Use the protractor to observe relationships.
Fraction Strips & Fraction Number Lines
Manipulatives are critical in helping students make sense of fractions. Many elementary classrooms make use of fraction tiles, fraction strips, and fractions number lines. Since fractions are so critical for students success (and since fractions are often misunderstood), I still like to use these manipulatives in middle school. Here are some ideas for using fraction manipulatives with your students:
Comparing Fractions: Use the visuals to find equivalent fractions and compare fractions.
Adding and Subtracting Fractions: Support algorithms with fraction visuals to make sense of the solutions.
Dividing Fractions: Explore how many of one fraction fit into another fraction.
Converting Fractions to Decimals: Cut out fraction strips and align with the number line showing tenths.
Cubes & 3D Figures
Three-dimensional figures can be an exciting and challenging topics for students in middle school. By making the lessons hands-on, we can help students visualize the relationships and formulas they need to learn. Starting with the net of a cube and creating a 3D cube, we can incorporate printable nets and 3D figures into our lessons.
Nets: Explore how different nets create cubes and different 3D figures.
Volume: Create several unit cubes and use them to fill boxes and 3D figures. Fill 3D figures with beans (or something small) to compare values.
Volume of Composite Figures: Use several cubes to create composite figures.
Surface Area: Examine what makes up the surface area of one cube. Then create a figure made of several cubes and examine the surface area. Examine the faces that create the surface area of other 3D figures. Use a ruler to measure and calculate the total surface area.
Triangles
Triangles cut from paper are a great way to allow students to explore different properties. While seeing a drawing of triangle is helpful, sometimes being able to hold and cut a paper triangle helps students make observations and discoveries on their own.
Area: Using two of the same triangle to create a parallelogram. Relate the formulas for area of triangles and parallelograms.
Angle Sums: Cut the three vertices of a triangle and arrange to create 180°.
Transformations & Congruent Figures: Discuss how transformations create congruent triangles but cutting out the triangles and physically transforming them.
Algebra Tiles
Algebra tiles help students make sense of working with equations and polynomials. They give a visual representation of an unknown value, allowing students to manipulate that unknown value based on properties they have learned in previous grade levels. If you have never used algebra tiles, be sure to check out my videos to help you get started!
Equations: Use the x bars and unit squares as a visual when balancing equations.
Multiplying Binomials: Create an area model using algebra tiles to represent multiplying with the area as the product.
Factoring Trinomials: Arrange given algebra tiles into a rectangle and find the length and width, which are the factors.
Completing the Square: Arrange given algebra tiles into a square and see what is missing to complete the square.
For a free set of all the printable math manipulatives mentioned here, fill out the form below!
