Counting on to add

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Objective

SWBAT use counting on as an addition strategy to find sums within 20.

Big Idea

Movin’ on up! Counting on is a strategy that can help foster mental math skills.

Activating Strategy

10 minutes

I start this lesson by introducing the term “counting on” to the students.  I demonstrate how to solve an addition sentence by adding 2 or 3, such as 5 + 2 = ___.  To demonstrate, I say, “I’m going to put 5 in my head, and then I hold up 2 fingers, and I keep counting on my fingers.”  I point to my head and say “5”, then count on my fingers saying, “6, 7”.  “So I know that 5 + 2 = 7”.  I repeat using different facts with sums within 10.  I encourage children to count along with me.

To continue keeping them thinking about counting on, I give each student 10 counters.  Have them turn 4 counters to the “red” side, have the students turn 2 counters to the yellow side.  Demonstrate how to count on using 4+2=6.  Have shoulder partners model adding using the counting on strategy for a few minutes.  Allow partners to share their addition facts and models with the class.

Having the students turn the counters over to different colors will help them to model the strategy.  This is directly aligned with MP4.

Teaching Strategies

15 minutes

I start by reading the following problem on the board/chart paper: (word problems are included in the PPT: counting on to add)

Sam has 9 books in a box.  He gets one more.  How many books does Sam have?

I explain to children that counting on is a special way to show adding that can be used when we are adding 1, 2, or 3 to a number.  I have children use the picture of the box and the book on the PowerPoint presentation to solve 9 + 1 = ___.  If needed, I allow children to use the counters to show the number counted.  I use these questions to guide the process:

  • Why might 9 be shown first in the addition sentence? (9 is shown first because you start counting on from the greatest number.)
  • Why do you start with the greatest number? (It is faster to count on 1 from 9 than to count on 9 from 1.)
  • How can you find the sum of 9 + 1 by counting on?  (I start with 9, then I count on 1 from 9 to get 10.  The sum is 10.)

I then read the next two word problems aloud to students: 

Sam had 9 books.  He gets 2 more.  How many books does he have now? 

Sam had 9 books.  He gets 3 more books.  How many books does he have now? 

I use the following questions to guide the discussion:

  • Look at the three addition facts.  How are they the same? How are they different? (They all have 9 as the first addend.  The other addend is 1, 2, or 3.)

I demonstrate how we start with the greatest number when we are counting on.  In the sentence 3 + 5, discuss with the students how we will start with the greatest number, and we will circle it to show that we will start with that number.

I have shoulder partners complete some more addition sentences by circling the greatest number and counting on to add.  While partners are doing this, I walk around the room to make observations.

Independent Practice

30 minutes

I have students complete a worksheet to practice their counting on strategy.  I provide them with counters to help with counting on.

In this video, you will see a student demonstrating the strategy of counting on.  

To extend their thinking, have the children use the counting on strategy to write and solve addition sentences with teen numbers.  For example, children may write 15 + 2 = 17.  Then challenge children to write and solve addition sentences with greater numbers.  Point out that even though these sentences use greater numbers, they still have one addend that is 1, 2, or 3 so they can be solved by using the strategy of counting on.

For struggling students, I give them 5 counters or connecting cubes and I write a number on a small white board.  I demonstrate counting on using an addend plus 1 to start.  For example:

  • I write 4 + 1 = __ - I place 1 counter on the table and say, “You can count on 1 to add.  Start with 4.  What is 4 and 1 more? (5)
  • I continue counting on 1 from numbers 5-9 using counters.
  • I then repeat the activity counting on 2 and then three for numbers 4 – 9.

Closing/Summarizing

5 minutes

To close out the lesson, I have students use pictures or words to show how they can use counting on to solve 9 + 3 by counting on.