Module 2 Lesson 4 Objective: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

Fluency Practice – Estimate Products 409 x 21 = ____ x ____ = ____ (Round each factor to arrive at a reasonable estimate of the product) 287 x 64 = ____ x ____ = ____ (Round each factor to arrive at a reasonable estimate of the product) 3,975 x 92 = ____ x ____ = ____ (Round each factor to arrive at a reasonable estimate of the product) 400 x 20 = 8,000 or 410 x 20 = 8,200 290 x 60 = 17,400 or 300 x 60 = 18,000 4,000 x 90 = 360,000 or 3900 x 90 = 351,000

Fluency Practice – Decompose Multiplication Sentences 12 x 3 = ____ (Write the multiplication sentence. Distributive Property) (10 x 3) + (__ x 3) = ____ (12 is the same as 10 and what number?) 2 (Finish writing the statement.) (10 x 3) + (2 x 3) = 30+ 6 = 36 (8 x 3) + (___ x 3) = ____ (12 is the same as 8 and what number?) 4 (8 x 3) + (4 x 3) = 24 + 12 = 36 Now complete the following problems: 14 x 4 13 x 3 15 x 6 (10 x 4) + (4 x 4) = 40 + 16 = 56 (10 x 3) + (3 x 3) = 30 + 9 = 39 (10 x 6) + (5 x 6) = 60 + 30 = 90

Fluency Practice – Write the Value of the Expression 11 x (15 + 5) = ____ (Write the expression as a single multiplication sentence without parenthesis and find the product.) 11 x 20 = 220 (41-11) x 12 (75 + 25) x 38 (20 x 2) + (6 x 2) 30 x 12 = 360 100 x 38 = 3800 40 + 12 = 52

Application Problem Jaxon earned $39 raking leaves. His brother, Dayawn, earned 7 times as much waiting on tables. Write a numerical expression to show Dayawn’s earnings. How much money did Dayawn earn? $39 Jaxon Dayawn 1 unit = $39 7 units = $39 x 7 = $273 Dayawn earned $273 waiting tables.

Concept Development – Problems 1 & 2 8 x 31 What does this expression mean when I designate 31 as the unit (another way to look at the problem)? Add 31 ones 8 times or 8 times as much as 30 ones. What does it mean when I designate 8 as the unit? Add 8 ones 31 times or 31 times as much as 8 ones. Does our choice of unit change the product of the two factors? No Why not? What property allows for this? The commutative property (any-order property) says that the order of the factors doesn’t matter. The product will be the same.

Concept Development – Problems 1 & 2 8 x 31 Let’s designate 8 as the unit. I’ve drawn diagrams of 8 x 31 and 8 x 30. Use the diagrams to consider how 8 x 30 helps us to solve 8 x 31 when we designate eight as the unit, (point to the diagram) and the other factor as the number of units 31 and 30. (Run your finger down the length of each bar.) Turn and talk. ….. 8 8 8 8 30 eights 30 eights ….. 8 8 8 8 8 31eights

Concept Development – Problems 1 & 2 8 x 31 31 eights is the same as 30 eights plus 1 eight. 30 eights = 240 and one more 8 makes 248. How many more eights are in the second bar than in the first bar? 1 more Record our thinking. (Write 31 eights = 30 eights + 1 eight. (31 x 8) = (30 x 8 ) + (1 x 8) 240 + 8 = 248 31 times 8 is? 248 Show 8 x 29 (in your notebook or whiteboard) What does this expression mean when we designate eight as the unit? Add 29 eight times. ---- Add 8 over and over 29 times.

Concept Development – Problems 1 & 2 8 x 29 How does 8 x 30 help us solve 8 x 29? (discuss) 30 eights minus 1 eight is equal to 29 eights, this is one group less. How could you write the problem? (30 x 8) – (1 x 8) = 8 x 29 What is the value of 30 eights minus 1 eight? 240- 8 – 232 Could we have decomposed 29 eights in another way to help us evaluate the expression mentally? Discuss as a group or small groups? 29 eights = (20 x8)+ (9 x 8) or (25 x 8) + (4 x 8)

Concept Development - Problems 3 & 4 49 x 20 How can we look at this problem mentally? (50 x 20) – (1 x 20) (40 x 20) + (9 x 20) (45 x 20) + (4 x 20) How could you look at this visually using a diagram? What is the answer for 49 x 20? 980 49 twenties 20 20 20 20 …… 20 50 twenties

Concept Development - Problems 3 & 4 20 x 51 How can we look at this problem mentally? (20 x 50) + (20 x 1) (20 x 30) + (20 x 20) + (20 x 1) (20 x 20) + (20 x 31) What is the answer for 20 x 51? 1000 + 20 = 1020

Concept Development - Problems 5 & 6 101 x 12 and 12 x 98 (complete independently or in small groups) What ways did you look at it? (100 x 12)+ (1 x 12) (100 x 12) – (2 x 12) What is the answer for 101 x 12 and 12 x 98? 1200 + 12 = 1212 1200 – 24 = 1176

Debrief Review Commutative Property Distributive Property How to decompose numbers into unit form to do adding, subtracting, and multiplying of like units.

Exit Ticket – Lesson 4