Estimate Products

Lesson 3: I can write and interpret numerical expressions and compare expressions using a visual model 5th Grade Module 2 – Lesson 3

Estimate Products 421 x 18 ≈ ___ x ___ = ____ 400 20 8,000 Round 421 to the nearest hundred Round 18 to the nearest ten What is 400 x 20? 5th Grade Module 2 – Lesson 3

Estimate Products 323 x 21 ≈ ___ x ___ = ____ 300 20 6,000 On your boards, write the multiplication sentence rounding each factor to arrive at a reasonable estimate of the product. 5th Grade Module 2 – Lesson 3

Estimate Products 2,480 x 27 ≈ ____ x ___ = ____ 2000 30 60,000 On your boards, write the multiplication sentence rounding each factor to arrive at a reasonable estimate of the product. 5th Grade Module 2 – Lesson 3

Decompose a Factor: The Distributive Property Write the multiplication sentence. 9 x 3 = 27 (5 x 3) + (__ x 3) 4 15 + 12 = 27 5th Grade Module 2 – Lesson 3

Application Problem Robin is 11 years old. Her mother, Gwen, is 2 years more than 3 times Robin’s age. How old is Gwen? 5th Grade Module 2 – Lesson 3

Concept Development From word form to numerical expressions and diagrams. What expression describes the total value of these 3 equal units? How about 3 times an unknown amount called A? Show a tape diagram and expression. 5 A 3 x 5 3 x A 5th Grade Module 2 – Lesson 3

Concept Development From word form to numerical expressions and diagrams. How about 3 times the sum of 26 and 4? OR… 3 x (26 + 4) (26 + 4) x 3 26 + 4 5th Grade Module 2 – Lesson 3

3 x (26 + 4) Why are parentheses necessary around 26 + 4? Talk to your partner. We want 3 times as much as the total of 26 + 4. If we don’t put the parentheses it doesn’t show that we are counting 3 of 26 + 4. 3 x 26 + 4 This means 3 times 26 then add 4. Not the same! 5th Grade Module 2 – Lesson 3

Evaluate the expression. 3 x (26 + 4) 3 x (30) 90 5th Grade Module 2 – Lesson 3

Let’s try it again! Write 6 times the difference between 60 and 51 6 x (60-51) OR… 60-51 (60-51) x 6 5th Grade Module 2 – Lesson 3

Are these expression equivalent? 6 x (60-51) (60-51) x 6 What is the name of the this property? Commutative Property! What is the commutative property in your own words? 5th Grade Module 2 – Lesson 3

Let’s try it again! Write the sum of 2 twelves and 4 threes. 12 12 3 3 3 3 (2 x 12) + (4 x 3) 5th Grade Module 2 – Lesson 3

8 x (43 – 13) 8 x 43 – 13 It sounds likes you are saying that we should multiply 8 and 43 and then subtract 13. Is that what you meant? Read this expression in words… Let me write down what I heard you say… Are these two expressions equivalent? 5th Grade Module 2 – Lesson 3

We need to use words that tell that we should subtract first and then multiply! 8 x (43 – 13) So we can say and write, “8 times the difference of 43 and 13” What other ways can we say this? Let’s name the two factors we are multiplying. Turn and talk. What could we say to make sure we are talking about the answer to the subtraction problem? Turn and talk. And what is happening to the difference of 43 and 13? Why can’t we read every expression left to right? We are multiplying 8 and the answer to 43-13 The difference of 43 and 13! It is being multiplied by 8! 5th Grade Module 2 – Lesson 3

(16 + 9) x 4 The sum of 16 and 9 times 4 We cannot just say 16 plus 9 times 4! How can we say and write this expression correctly? 5th Grade Module 2 – Lesson 3

(20 x 3) + (5 x 3) We cannot just read this left to right! How can we say and write this expression correctly? The product of 20 and 3 plus the product of 5 and 3 OR… The sum of 20 threes and 5 threes 5th Grade Module 2 – Lesson 3

We don’t even need to evaluate these expressions to compare them! Let’s use < , > , or = to compare each expression 9 x 13 8 thirteens > 13 13 Let’s use a tape diagram for each expression and compare them! 5th Grade Module 2 – Lesson 3

Let’s compare these expressions without evaluating them! = The sum of 10 and 9, doubled (2 x 10) + (2 x 9) 10 9 10 9 10 10 9 9 5th Grade Module 2 – Lesson 3

Let’s compare these expressions without evaluating them! = 30 fifteens minus 1 fifteen 29 x 15 15 15 5th Grade Module 2 – Lesson 3

Get Ready to Complete theProblem Set on Your Own! When completing your problem set, remember to use what you know about whole numbers to help you divide the decimals. Complete Pages 2.B.10 - 2.B.12 You will have 10 minutes to work. Try your Best! 5th Grade Module 2 – Lesson 3

Debrief • Return to the Application Problem. Create a numerical expression to represent Gwen’s age. • In Problem 1(b) some of you wrote 12 x (14 + 26) and others wrote (14 + 26) x 12. Are both acceptable? • When evaluating the expression in Problem 2(a), some of you got 85. Can you identify the error? • Look at Problem 3(b). Talk to your partner about how you know they are not equal. How can you change the second expression to make them equal? 5th Grade Module 2 – Lesson 3

Debrief • In 4(a), what mistake is being made that would • produce 5.6 ÷ 7 = 8? • Correct all the dividends in Problem 4 so that the quotients are correct. Is there a pattern to the changes that you must make? • 4.221 ÷ 7 ____= • Explain how you would decompose 4.221 so that you only need knowledge of basic facts to find the quotient. 5th Grade Module 2 – Lesson 3

Exit Ticket Time! 5th Grade Module 2 – Lesson 3

Estimate Products