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TouchMath Extend

Lesson 27: Mixed Addition and Subtraction

Lesson Objectives

  • Represent and use number bonds within 20 
  • Apply TouchPoints on lesser numerals 
  • Identify pairs of numbers whose sum or difference is within 20  
  • Use TouchPoints as a strategy in computation  
  • Join or take away groups of objects to add or subtract 
  • Add or subtract using Pictorial TouchPoints 
  • Count on or backwards using TouchPoints 
  • Skip count using patterns 
  • Use arrays as a strategy for skip counting 


  • Extend Workbook (Page 27) 
  • Counters or manipulatives 
  • TouchMath’s Foam Numerals with TouchMath’s TouchPoints with or without pictures 
  • Number bond template 
  • Highlighters, markers, or crayons 
  • TouchMath’s number line 

Step 1: Warm Up (5 min)

Use a number line 0-20. Teach skip counting by 2’s as repeated addition. Start on the 2 and skip every other number (2,4,6,8) until you get to 20. Have them look at the sequence and point out that when skip counting on 2’s, that the first two 2’s make 4, and in other words means 2+2. The third 2 means 2+2+2, which is 6. The fourth 2 means 2+2+2+2, which is 8. Explain that skip counting is adding multiple addends – the same addend over and over. It is easier to skip count than to add all of the addends when we get to larger numbers. Explain that this also means we are adding groups of the same number of items together. 

Step 2: Vocab Review (5 min)

Introduce repeated addition and skip counting, and review number bonds. Skip counting is a tool that will help us find pairs of equal addends. It is also the foundation of multiplication. Tell students that they will be learning a process that will make it very easy for them to learn how to multiply. Remind them that they can count forward and backward, but that they can also skip numbers in sequence. When we skip count, we start on a number and skip every other number in sequence. 

Step 3: Model (5 min)

For this repeated addition and skip counting concept, take counters and divide 6 into three sections. Ask students to tell you how many counters are in each group (3) and then ask how many groups are there total (2). Tell students that this is the same thing as 2+2+2, which equals 6 total counters. Show several examples of repeated addition using counters or manipulatives. Then, review number bonds. Now show number bonds (e.g. numnber bonds of 10), and color the sum (top circle) one color (e.g. blue) and the bottom circles another color (e.g. yellow). Then, re-write all the number bonds (e.g. for 10 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5). Following this, write all the addition sentences below it (e.g. for 10: 1+9=10, 2+8=10, and so forth). The addends should be yellow and the sums blue. Review that the yellow numbers are parts and the blue numbers are whole, helping to expand on whole-part relationships. 

Step 4: Guided Practice (5 min)

When practicing repeated addition, remind students to have equal number of objects in each group (3 counters in 4 groups, 2 counters in 3 groups, and so forth). Then, have students try to come up with the repeated addition statements (3+3+3+3, 2+2+2 from the above example), as well as the sums of each. When having students first practice number bonds on their own or with guided support, use manipulatives to represent the numbers, whether the TouchPoints, counters, or other actual items (e.g. food, candies, toys, blocks, etc). Arrange the objects into parts and wholes to get the students to answer number bond questions relating to the objects (e.g. 5 candies in the top circle, and 2 and 3 candies in the bottom circles; 5-3=2; or 2+3=5). Give students different addition or subtraction problems and let them represent those problems using the selected objects of your choosing in the number bond templates. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (27). Read the directions at the top of the page. Tell students they will answer a variety of addition and subtraction problems (repeated addition, with TouchPoints, or with number bonds. Looking at the first problem, ask students how many groups of rackets do they see (3) and have them circle each group. Then, ask how many rackets are in each group (3). Students will then fill in the repeated addition statement (3+3+3=9). Have students complete the addition and subtraction problems below, using the correct steps and using the TouchPoints. Have them fill in the statements to the left (e.g. 5 more than 3 is 8). Last, have students complete the number bond, using the TouchPoints in the addition problem. Remind them to put their answer on the line provided but also in the circle within the number bond. 

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.