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TouchMath Extend

Lesson 33: Expanding Addition and Multiplication

Lesson Objectives

  • Use objects, pictures, drawings, and number lines to understand multiplication  
  • See multiplication as repeated addition 
  • Use addition to find the total number of objects and dots in arrays 
  • Write equations of repeated addition and multiplication 
  • Apply skip counting and the TouchMath approach for finding products 
  • Apply vocabulary (factors and products) in explaining multiplication 
  • Apply the commutative property to multiplication 
  • Use arrays as a strategy for skip counting 


  • Extend Workbook (Page 33) 
  • Counters or manipulatives 
  • Highlighters, markers, or crayons 
  • TouchMath’s Foam Numerals and TouchPoints (for more concrete) 
  • Skip counting multiplication songs (multiples 2-6) (as needed) 

Step 1: Warm Up (5 min)

Review prior vocabulary showing a few multiplication problems with visuals (e.g. arrays) and going through each part (factor x factor = product), look at the groups of dots and circle/ring, count the number of items in each group to determine the factors (3 groups of 4 = 12 total items). Review that multiplication is repeated addition (3+3+3+3, but also if factors are reversed, the result is same product (4+4+4). Optional: review skip counting songs for multiples of 2-6.  

Step 2: Vocab Review (5 min)

Review prior vocabulary: arrays (an arrangement of a set of numbers or objects in rows and columns) products of multiplication problems, factors (a number that you multiply with another number to get a product). Introduce new vocabulary: Commutative Property of Multiplication (changing the order of factors does not change the product, e.g. 4×3 = 3×4). 

Step 3: Model (5 min)

Expanding on the warm-up, show several examples of commutative property of multiplication with visuals underneath both examples (3×4 and 4×3) and illustrating the separate repeated addition problems, with the same products. Use counters and the whiteboard to physically break down this concept in the concrete and then representational. Show a few multiplication problems with multiples of 5-6 and teach skip counting by one number while touching the TouchPoints on the other number (e.g. if skip counting by 5’s, skip count on the 7 by 5’s in 5×7: 5, 10, 15, 20, 25, 30, 35). Using TouchMath’s Foam Numerals, show how to skip count on one number (place visual examples with counters underneath, as well).  

Step 4: Guided Practice (5 min)

Pull out 100s Chart and multiples of 2-6 resource pagess made in prior lessons, or make a resource page prior to this lesson. In groups, ask students to draw arrays with dots/circles/dots with multiples of 5’s and 6’s (5x4, 6x2, 5x8, 6x6, etc.). Have students circle each group. Ask them, “how many groups of dots/stars did you circle? How many dots/stars are in each group?” Then have them write down their multiplication sentences/problems next to their arrays (e.g. “We circled 6 groups of dots and there are 7 dots in each group. Therefore, my multiplication sentence is 6x7=42. There are 42 total dots altogether. This means the product of 6x7 is 42.”). Ask what the repeated addition statements would look like (e.g. 6+6+6+6+6+6+6 OR 7+7+7+7+7+7). Have students practice skip counting by one number while touching the TouchPoints on the other number using TouchMath’s Foam Numerals. 

Step 5: Student Practice (5 min)

Go to Student Workbook Page (33). Read the directions at the top of the page. Tell students they will be practicing filling in two multiplication sentences, based on the commutative property of multiplication. They will also ring (or circle) the groups of dots and determine the missing or unknown factors. In the first problem, they will ring/circle 4 groups of 3 dots, indicating 12 dots in all. They will fill in the repeated addition statement (3+3+3+3), and the two multiplication problems (4×3=12 and 3×4=12). Students will complete the same steps in the next two problems. 

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.