Understand Tens and Ones

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SWBAT use models and write to represent equivalent forms of ten and ones.

Big Idea

Math Counts! In this lesson students will use models to represent tens and ones.

Activating Strategy

10 minutes

In this lesson, children use concrete and pictorial models to represent tens and ones. Children see that 1 ten can be shown by filling a ten frame with 10 connecting cubes. Any extra cubes outside the ten frame are ones. Representing two-digit numbers in this way supports children’s understanding of the base-ten number system.  When children make connections between models for teen numbers and an expression that gives the value in each place, these multiple representations will extend children’s understanding of place value and help establish a foundation for two-digit addition strategies.

To get students thinking about groups of 10, have two children stand in front of the class and hold up their hands with fingers spread.  Ask the class:

  • How many fingers does each child have? (10)
  • How can you find out how many fingers both children have in all? (Count all the fingers; count by tens.)
  • How many fingers are there altogether? (20)

Repeat the activity with groups of 3 to 9 children. Ask classmates to count by tens to find the total number of spread fingers.

Teaching Strategies

15 minutes

I start by displaying the first slide of the PowerPoint, then I read the following problem aloud and have children model the problem with connecting cubes:

Tim has 10 pennies. He gets 2 more pennies. How many pennies does Tim have now?

  • How can you use the ten frame and connecting cubes to show how many pennies Tim has to start?  (I can put 10 cubes in the top ten frame to show the 10 pennies Tim has to start.)
  • How can you show the 2 more pennies Tim gets?  (There is no room in the top ten frame, so I can put 2 cubes in the bottom ten frame.)

Guide children to place the appropriate number of cubes inside the ten frames and then draw the cubes to represent their model.

  • How many cubes are inside the top ten frame?  (There are 10 cubes inside the top ten frame.)
  • How many cubes are inside the bottom ten frame? (There are 2 cubes inside the bottom ten frame.)
  • How can you find the total without counting each cube?  (When a ten frame is full, it is 10. I can start at 10 and count on the 2 cubes in the other ten frame to get a total of 12.)
  • How many pennies does Tim have now?  (Tim has 12 pennies.)

Work through the model on the next PowerPoint slide with the children. Explain that the filled ten frame shows 10 ones, which is the same as 1 ten.

  • What do the two digits in 13 mean? (The digit on the left means 1 ten. The digit on the right means 3 ones.)
  • How do the cubes show 13?  (The cubes show 1 ten and 3 ones. There are 10 cubes in the ten frame and 3 cubes outside the frame.)
  • How does addition show the number? (10 + 3 is another way to show 1 ten and 3 ones, or 13.)
  • What are 4 different ways the number is shown? (a ten frame filled with cubes and 3 extras, 1 ten and 3 ones, 10 + 3, the number 13)

Independent Practice

30 minutes

I then hand out the worksheet to the students, and review the model at the top of the page.  Encourage children to model each problem as they complete the exercises.

  • What does a filled ten frame show? (1 ten)
  • What is outside the ten frame? (ones)

Once students have grasped the concept, of ten and ones, I release them to complete the Worksheet on their own. 


5 minutes

To close out the lesson, I have students show the number 12 using words, pictures, and tens and ones.