Printable Manipulatives, Mats & Rulers - First Grade Mathematics

Mathematicians understand that learning math is an active, hands-on experience! When you can physically touch counters, slide rods across a place-value mat, or line up paperclips along an object, abstract ideas become clear and tangible. While plastic manipulatives are wonderful, you can create your very own durable math toolkit right at home or in class using printable templates, cardstock, scissors, and paper. In this chapter, you will find printable templates, mats, and rulers that you can copy, cut out, and use for all your mathematical investigations.

The Printable Five-Frame and Ten-Frame Mats

Use these grid frames to practice number combinations, Friends of 10, and addition strategies.

PRINTABLE FIVE-FRAME:
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
+-----+-----+-----+-----+-----+

PRINTABLE TEN-FRAME:
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
+-----+-----+-----+-----+-----+
|     |     |     |     |     |
+-----+-----+-----+-----+-----+

DOUBLE TEN-FRAME MAT:
+-----+-----+-----+-----+-----+   +-----+-----+-----+-----+-----+
|     |     |     |     |     |   |     |     |     |     |     |
+-----+-----+-----+-----+-----+   +-----+-----+-----+-----+-----+
|     |     |     |     |     |   |     |     |     |     |     |
+-----+-----+-----+-----+-----+   +-----+-----+-----+-----+-----+

How to Use the Ten-Frame Mats

Draw dots or place small physical counters (like dry beans, pennies, or buttons) into each box. Always fill the top row from left to right first before moving to the bottom row!

The Printable Place-Value Mat

A place-value mat keeps your bundles of ten separated cleanly from your loose single units.

PRINTABLE PLACE-VALUE WORK MAT:
+-----------------------------+-----------------------------+
|            TENS             |            ONES             |
|                             |                             |
|                             |                             |
|  (Place your Rods here)     |  (Place your Units here)    |
|                             |                             |
|                             |                             |
+-----------------------------+-----------------------------+

Using Base-Ten Cutouts

You can cut out strips of graph paper that are 10 squares long to act as rods of ten, and single 1-square squares to act as units of one. Place them in their respective columns when building numbers like 43 or when practicing regrouping!

The Printable Paper Ruler (Scale of Inches)

Here is a 6-inch paper ruler you can trace and cut out along its border:

PRINTABLE 6-INCH PAPER RULER:
+-----------------------------------------------------------+
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0       1       2       3       4       5       6           |
|<- 1 Inch ->|                                              |
+-----------------------------------------------------------+

Ruler Care Tips:

Glue your paper ruler to a piece of thin cardboard or cereal box to keep it stiff and straight. Always remember: when measuring, line up the zero mark (0) with the left edge of your object!

Practice Exercises

Exercise 1: Describe how you would create a homemade set of base-ten rods and units using paper and scissors.

Exercise 2: How does using a physical place-value mat help prevent errors when adding two-digit numbers?

Exercise 3: When using your printable paper ruler, what part of the ruler must be placed against the very start of the object you are measuring?

Exercise 4: Explain why gluing paper manipulatives to cardstock or an old cereal box makes them easier to use.

Solutions and Explanations

Solution to Exercise 1: You can take a sheet of grid or graph paper, color a strip of 10 connected squares blue and cut it out to make a rod of ten, and cut out individual 1-by-1 squares to make single units of one.

Solution to Exercise 2: A place-value mat physically separates the tens from the ones into labeled columns, preventing you from accidentally mixing up rods and units or adding a tens digit to a ones digit.

Solution to Exercise 3: The zero mark (0 line) on the ruler must be aligned with the starting edge of the object.

Solution to Exercise 4: Cardboard or cardstock gives paper cutouts stiffness and weight, preventing them from curling, blowing away, or tearing easily when handled during math activities.