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TouchMath Extend

Lesson 23: Subtraction within 20

Lesson Objectives

  • Use the Concrete-Representational-Abstract (CRA) sequence 
  • Count backward on TouchPoints 
  • Relate subtraction to counting backward 
  • Use relationships of operations to solve for unknowns 
  • Find one-digit differences 
  • Subtract within 20 efficiently 
  • Use number lines, number sentences, and part/whole relationships to explain subtraction 


  • Extend Workbook (Page 23) 
  • Counters or manipulatives 
  • TouchMath’s Foam Numerals and TouchPoints with or without pictures 
  • Number lines 0-20 
  • Linking cubes 
  • White boards and dry erase markers 

Step 1: Warm Up (5 min)

Explain to students that when we say and write subtraction sentences, we use minus to mean take away. Repeat the number sentence: 10 minus 3 = 7. The answer, 7, is the difference. Take out linking cubes to illustrate subtraction. Take out 10 cubes linked and show students. Show the students as you take away 3 cubes. Ask how many cubes you have left (Yes, 7 cubes.). The number sentence is 10 minus 3 = 7. 

Step 2: Vocab Review (5 min)

Review prior vocabulary: subtraction, difference, minus, part, subtract, take away, whole, solving for unknown minuends. Explain to students that they will subtract a part from the whole by taking away one part. Remind them that when they added, they put the parts together. When they joined the parts, they found the sum, or the whole. Now, when they subtract, they will start with the whole and take away one part. When you take away one part, you have one part left. It is called the difference. Show basic examples: hold up three fingers, take one away, and now you have 2 fingers left. So, 3 fingers minus 1 finger equals 2 fingers left, or 3 take away 1 equals 3. Show various examples with counters and manipulatives. 

Step 3: Model (5 min)

Take out counters and TouchMath’s Foam Numerals and TouchPoints. Write a subtraction problem on the board (12-4) and show 12 counters and then ask students how many should be taken away (4). Take away 4 and ask how many are left? (8). Ask students to repeat the subtraction number sentence: 124=8. Give real examples of this (e.g. I had 12 stickers gave away 4 stickers. Eight stickers were left). Show the Write a number 12 on the white board and take out the number 4 Foam Numeral. Place four TouchPoints on the Numeral. Tell students to say the first number, and then cross it off, and then count backwards on the TouchPoints of the 4 (11, 10, 9, 8). Tell students to physically remove the TouchPoints on the 4, since you are “taking away” 4. Then repeat the math fact (12-4=8). Show a few examples using both the counters and Foam Numerals and TouchPoints.

Step 4: Guided Practice (5 min)

Have students work together with their TouchMath Foam Numerals and TouchPoints to solve subtraction problems within 10, following the correct steps: 1) say the larger/first number, 2) cross it off on the white board, 3) count backward on the TouchPoints of the other number (using Foam Numerals whenever possible), 4) repeat the math subtraction fact (e.g. “10-2=8”). Then work with subtraction problems within 15 following the same steps. Following this, students can practice with number lines up to 20 to work with subtraction problems within 20. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (23). Read the directions at the top of the page. Tell students they will be solving subtraction problems within 20. In the first problem, tell students to 1) say the larger/first number (14), 2) cross it off on their paper, 3) count backward on the TouchPoints of the other number, 3, (13, 12, 11), 4) repeat the math subtraction fact (e.g. “14-3=11”). Then, write the difference on the line provided to the right of the equation sign. For the second problem, follow the same steps, but count backward from 20, placing a dot in the box as you count down until you get to 12 (“19, 18, 17, 16, 15, 14, 13, 12”). There should be 8 dots in the box. Tell students to write a number 8 in the box and that they found the missing minuend. Support students to find the missing minuends for the rest of the problems on the page, as needed. Remind students to take out their counters, use the number line and scoop backwards or forward to find the missing minuend, or use the TouchPoints to count backwards. 

Step 6: Wrap Up (5 min)

To wrap up the lesson, review the learning objectives and core vocabulary words again and ask your students about their experience. Circle back to those real-life connections and experiences.