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August 21, 2013: Sierra Vista Learning Center: Grades 3 and 4: Room 6

Multiplying Multi-Digit Numbers

Common Core State Standards for Mathematics

Introduction

Big Picture

Sign In Clearly: External evaluation team will be contacting you via email to complete online

questionnaires.

Dates of the 7 Wednesday workshops and the proposed topics:

August 21Multiplying Multi-Digit Numbers

September 18Division

October 16Fractions

November 20Add and Subtract within 1000

December 25to be determined

January 15Perimeter and Area

February 19 MeasurementMarch 19to be determined

Today

Problem based instruction

Models for multiplication

Contextual word problems for multiplication

The distributive property of multiplication

Double-digit multiplication

Exit Ticket at the end of each session

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Problem Based Learning-One component of Mathematics Instruction

Students learn through solving problems

Problem Based Lesson Planhas three parts:

1) Introduce the Problem:The introduction should help students understand the contextof the problem and what

isexpectedin their solutions (pictures/diagrams, numbers, and words). If students have a lot of

questions when they are working on the problem, it might be because it was not introduced

well and they do not fully understand it. The introduction should notbe modelinghow to solve

a similar problem.

2) Support students as they work in small groups:

Whole class instruction should not be a part of this time. The instructor walks around

and looks at students work, listens actively, provides hints for students who are stuck, and

provides extension for students who solve the problem quickly.

3) Debrief:

Conduct a classroom discussion based on students sharing their work. Promote

acommunity of learners that includes all students. Listen actively without evaluating.

5 strategies for classroom talk.

Revoicing (So you are saying that what you did in number 1 was like dealing a deck ofcards, one to each and repeat.)

Asking a student to restate someone elses reasoning. (Can you repeat what______ justsaid in your own words?)

Asking students to apply their own reasoning to someone elses reasoning. (Do youagree or disagree with what _____ said and why?

Prompting students for further participation. (Would someone like to add on to that?)

Using wait time. (Take your time, we will wait.) Give students time to formulate answersin their minds. Also give them time to think about (process) important ideas.

* Comments:

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Multiplication Grade 3

3.OA.1. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of

objects in 5 groups of 7 objects each. For example, describe a context in which a total number of

objects can be expressed as 5 7.

3.OA.3. Use multiplication and division within 100 to solve word problems in situations

involving equal groups, arrays, and measurement quantities, e.g., by using drawings and

equations with a symbol for the unknown number to represent the problem. (See Table 2.)

Students use a variety of representations for creating and solving one-step word

problems, i.e., numbers, words, pictures, physical objects, or equations. They use

multiplication and division of whole numbers up to 10 x10. Students explain their

thinking, show their work by using at least one representation, and verify that their

answer is reasonable.

** Show 3 X 4 Four different ways

Array, Equal Groups, Repeated Addition, Number line (measurement)

*** Write word problems for 3 X 4 for which the following representation align: Array, Equal

Groups, and Measurement.

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Distributive Property

Students are introduced to the distributive property of multiplication over addition as a

strategy for using products they know to solve products they dont know.For example, if

students are asked to find the product of 7 x 8, they might decompose 7 into 5 and 2 and then

multiply 5 x 8 and 2 x 8 to arrive at 40 + 16 or 56. Students should learn that they can

decompose either of the factors. It is important to note that the students may record theirthinking in different ways.

****Draw a diagram that shows 5 X 6 is the same as 2 X 6 + 3 X 6

3.MD.7. Relate area to the operations of multiplication and addition.c. Use tiling to show in a concrete case that the area of a rectangle with whole-number sidelengths a andb + c is the sum of a b and a c. Use area models to represent the distributiveproperty in mathematical reasoning.

*****Joe and John made a poster that was 4 by 3. Mary and Amir made a poster that was4 by 2. They placed their posters on the wall side-by-side so that that there was no spacebetween them. How much area will the two posters cover?Use pictures, words, and numbers to explain your understanding of the distributive property in

this context.

Using the above to help students learn their multiplication facts. Handout.

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******Represent 16 x 14 and possible representations.

1) Array, 2) Equal Groups,3) Repeated Addition,4) Number line (measurement)

******* Which model seems most doable?

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Model for 16 times 14.

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AZ.4.OA.3.1 Solve a variety of problems based on the multiplication principle of counting.a. Represent a variety of counting problems using arrays, charts, and systematic lists, e.g., tree diagram.b. Analyze relationships among representations and make connections to the multiplication principle of

counting. Tree Diagrams, Chart (Array)

******** List all the different two-topping pizzas that a customer can order from a pizza shop that onlyoffers four toppings: pepperoni, sausage, mushrooms, and onion.

Produce a Systematic List

A Chart

A Tree Diagram

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35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicativecomparisons as multiplication equations.

A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to getanother quantity (e.g., a is n times as much as b). Students should be able to identify and verbalizewhich quantity is being multiplied and which number tells how many times.

A blue hat costs $6. A red hat costs 3 times as much as the blue hat.

How much does the red hat cost?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue

hat?

4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answersusing the four operations, including problems in which remainders must be interpreted. Represent theseproblems using equations with a letter standing for the unknown quantity. Assess the reasonableness ofanswers using mental computation and estimation strategies including rounding.

Chris bought clothes for school. She bought 3 shirts for $12 each and a skirt for $15. How much moneydid Chris spend on her new school clothes?

Kim is making candy bags. There will be 5 pieces of candy in each bag. She had 53 pieces of candy. Sheate 14 pieces of candy. How many candy bags can Kim make now? (7 bags with 4 leftover)

Kim has 28 cookies. She wants to share them equally between herself and 3 friends. How many cookieswill each person get? (7 cookies each) 28 4 = aThere are 29 students in one class and 28 students in another class going on a field trip. Each car can hold 5 students.

How many cars are needed to get all the students to the field trip? (12 cars, one possible explanation is 11 cars

holding 5 students and the 12th holding the remaining 2 students) 29 + 28 = 11 x 5 + 2

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AZ.4.OA.3.1 Solve a variety of problems based on the multiplication principle of counting.a. Represent a variety of counting problems using arrays, charts, and systematic lists, e.g., tree diagram.b. Analyze relationships among representations and make connections to the multiplication principle ofcounting. Tree Diagrams, Chart (Array)

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How were the processes different?

Determine the number of objects in each share (partitive division, size of groups unknown)

A bag has 92 hair clips and Laura and her three friends want to share them equally. How many

hair clips will each person get?

Explain the diagram below.

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Draw a similar diagram using lines for tens and dots for ones to solve this problem.

Snicklefritz has 72 cricket cards. He wants to store them in three empty shoeboxes. If he puts

an equal amount in each, how many cards will be in each of the boxes?

Determine the number of shares (measurement division, number of groups unknown)

Max the monkey loves bananas. Molly, his trainer, has 24 bananas. If she gives Max four

bananas each day, how many days will the bananas last?

Explain the diagram below

Equations in the form of a x b = c and c = a x b should be used interchangeably, with the

unknown in different positions.

Examples: Solve the equations below:24 = ?x 6 Rachel has 3 bags. There are 4 marbles in each bag. How many

marbles does Rachel have altogether? 3 x 4 = m

Students may use interactive whiteboards to create digital models to explain and justify

their thinking.

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3.OA.4. Determine the unknown whole number in a multiplication or division equation relating

three whole numbers. For example, determine the unknown number that makes the equation

true in each of the equations 8 ? = 48, 5 = 3, 6 6 = ?.

Students apply their understanding of the meaning of the equal sign as the same as to

interpret an equation with an unknown. When given 4 x ? = 40, they might think:

4 groups of some number is the same as 40, 4 times some number is the same as 40. I

know that 4 groups of 10 is 40 so the unknown number is 10 The missing factor is 10

because 4 times 10 equals 40.

Equations in the form of a x b = c and c = a x b should be used interchangeably, with the

unknown in different positions.Examples: Solve the equations below:

24 = ?x 6 Rachel has 3 bags. There are 4 marbles in each bag. How many

marbles does Rachel have altogether? 3 x 4 = m

Students may use interactive whiteboards to create digital models to explain and justify

their thinking.