Working with Five-Frames & Ten-Frames - First Grade Mathematics

Our entire number system is built around the number ten. Because we have ten fingers on our hands, grouping quantities into tens is the most natural and powerful way to understand math. To help us visualize these groupings, mathematicians use two special organizers called the five-frame and the ten-frame. A frame provides structured "parking spaces" for counters, allowing you to see numbers as parts of a whole. In this chapter, you will master how to fill, read, and use five-frames and ten-frames to explore numbers up to 10.

Understanding the Five-Frame

A five-frame is a single row of five equal rectangular boxes connected side by side.

Empty Five-Frame:
+---+---+---+---+---+
|   |   |   |   |   |
+---+---+---+---+---+

Five-Frame Showing 3:
+---+---+---+---+---+
| * | * | * |   |   |
+---+---+---+---+---+
3 filled boxes + 2 empty boxes = 5 total boxes!

The Reading Rule: Left to Right

Just like you read words on a page from left to right, you always fill a five-frame starting from the leftmost box and moving toward the right without skipping any spaces.

Seeing Combinations that Make Five

When you look at a five-frame with counters, you see two things at once: how many boxes are filled, and how many boxes are empty. If 4 boxes are filled, 1 box is empty. This shows that 4 and 1 make 5. If 2 boxes are filled, 3 boxes are empty, showing that 2 and 3 make 5.

Understanding the Ten-Frame

A ten-frame is made by placing two five-frames together, creating a rectangle with two rows of five boxes each.

Structure of a Ten-Frame:
+---+---+---+---+---+
| 1 | 2 | 3 | 4 | 5 |  -> Top Row (5 boxes)
+---+---+---+---+---+
| 6 | 7 | 8 | 9 | 10|  -> Bottom Row (5 boxes)
+---+---+---+---+---+

Filling Rules for the Ten-Frame

To keep your ten-frame clear and easy to read, always follow two essential rules: Rule 1: Fill the top row completely from left to right first. Rule 2: Once the top row has all 5 boxes filled, place remaining counters in the bottom row, also starting from the left and moving right.

Ten-Frame Showing 8:
+---+---+---+---+---+
| * | * | * | * | * |  -> 5 on top
+---+---+---+---+---+
| * | * | * |   |   |  -> 3 on bottom
+---+---+---+---+---+
Total: 5 + 3 = 8 (with 2 empty boxes left!)

Seeing Benchmark Numbers (5 and 10)

A ten-frame highlights two critical benchmark numbers: 5 and 10. When the top row is full, you instantly know you have 5. When the entire frame is full, you instantly know you have 10. You can quickly see how close any number is to 5 and how close it is to 10.

Using Two-Color Counters in a Ten-Frame

Placing two-color counters (red on one side, yellow on the other) inside a ten-frame makes addition and number partners come alive.

Partners of 10 on a Ten-Frame:
+---+---+---+---+---+
| R | R | R | R | R |  -> 5 Red
+---+---+---+---+---+
| R | R | Y | Y | Y |  -> 2 Red + 3 Yellow
+---+---+---+---+---+
Red Counters: 7  |  Yellow Counters: 3  |  Total: 7 + 3 = 10

Seeing Partners of Ten

Notice how easy it is to find what number pairs with 7 to make 10. Look at the 7 red counters; there are 3 empty spots. If you place 3 yellow counters in those empty spots, the entire ten-frame is full. Therefore, 7 and 3 are partners that make 10!

Practice Exercises

Exercise 1: Describe the two rules you must follow when placing counters into a ten-frame.

Exercise 2: A ten-frame has 6 counters in it. How many counters are in the top row, how many are in the bottom row, and how many empty boxes remain?

Exercise 3: If you want to show the number 10 on a ten-frame, how many boxes will be empty? What addition sentence can you write using the number of filled boxes and empty boxes?

Exercise 4: You place 4 counters in a ten-frame. How many more counters do you need to add to completely fill the frame to make 10?

Solutions and Explanations

Solution to Exercise 1: The first rule is to fill the top row from left to right first. The second rule is that once the top row is full with 5 counters, place additional counters in the bottom row, also starting from the left and moving to the right.

Solution to Exercise 2: To show 6 on a ten-frame, the top row has 5 counters (completely full), and the bottom row has 1 counter on the left. Since a ten-frame has 10 boxes in total, there are 4 empty boxes remaining.

Solution to Exercise 3: When showing 10 on a ten-frame, every single box is filled, so there are 0 empty boxes. The addition sentence showing this is 10 + 0 = 10.

Solution to Exercise 4: You need 6 more counters to fill the frame. Since 4 boxes are filled, there are 6 empty boxes remaining in the ten-frame (4 + 6 = 10).