Distributive Property Lesson 1.10:

Application Problem  A guitar has 6 strings. How many strings are there on 3 guitars?  Write a multiplication sentence to solve.  Solution

Guided Instruction Concept Development :  Draw an array to represent the total number of guitar strings. Let the number of strings on 1 guitar be one row.  Make a dotted line below the first row to show just 1 guitar.  Write and solve a multiplication to describe each part of your array.  1 x 6 = 6 and 2 x 6 = 12  = 3 sixes Why is this true?  (1 x 6) + (2 x 6) = 3 sixes. How do you know the 2 number sentences on the board are equal?

Guided Instruction Concept Development :  1 × 6 is the same as 6, and 2 × 6 is the same as 12. You just rewrote 6 and 12 as multiplication facts.  (1x 6) + (2 x 6) = 6 +____ With your partner discuss what number completes the equation.  (1x 6) + (2 x 6) =  Notice the symbols around my multiplication expressions. They are called parentheses. Let’s say that word together

 (1x 6) + (2 x 6) = _____  (1 + 2) x 6 = ____  My parentheses show how I make groups. How did I rearrange the groups?  We added the number of rows. Then we multiplied by 6.  Look back at the array you drew. Do the 1 and 2 represent the number of groups or the size of groups?  The 1 and 2 represent the number of groups.  What does the 6 represent?  The size of groups Guided Instruction Concept Development :

 Use that language—the number of groups and the size of groups—to tell your partner about my second equation.  We added the number of groups first. That’s Then she multiplied the number of groups times the size of the groups, which is 6.  equals?  3 × 6 = _____ under the second equation. Look back at the work you did on today’s application problem. How does this equation compare with what you did?  It’s the number of groups times the size of groups, just like we did. Guided Instruction Concept Development :

 Rewrite each equation on your board and solve them. What is the answer to all 3 equations?  18 what?  18 strings  (1 × 6) + (2 × 6) = 3 × 6 True or false? Guided Instruction Concept Development :

 In your own words, tell your partner how we got 3 × 6 and why it’s equal to (1 × 6) + (2 × 6). Use the 3 equations you just solved to help you explain. Guided Instruction Concept Development :

Guided Practice Problem 1, page 50  7 x 3 = (5 x 3) + (2 x 3) = _____  (5 x 3) + (2 x 3) =  ____ + ____ = _____ x 3 = _____ 2 x 3 = _____

Guided Practice Problem 2, page 50  8 x 3 = (4 x 3) + (4 x 3) = m  (4 x 3) + (4 x 3) = m  _____ + _____ = ____ x 3 = _____

Guided Practice Problem 3a, page 50  Ruby is making a photo album. She puts 3 pictures in each row.  Use the multiplication sentences on the left to show the photos on the upper and lower parts of Ruby’s album page = --- ___x 3 = 6 ___x 3 = 9

Guided Practice Problem 3b, page 50  Ruby calculates the total number of pictures as show below. Use the array you drew from the previous slide to help explain her calculation. 5 x 3 = = 15