**98 + 54**

Multiplication and Division Problem Structures

Total unknown

Sarah has 6 five dollar bills. How much money does Sarah have? 6 x 5 = ?

Group size unknown

Sarah has $30 worth of $5 bills. How many five dollar bills does she have? 30 / 5 = ? or 5 x ? = 30

Number of groups unknown

Sarah has 6 bills of the same amount totaling $30. What piece of money does Sarah have? 6 x ? = 30 or 30 / 6 = ?

Student-centered vs. Standard Algorithms

"The

standard

algorithms are clever strategies for computing that have been

developed over time

. Each is

based on

performing the operation on one

place value

at a time with transitions to an adjacent position. Unfortunately, standard algorithms

tend to make students think in terms of digits

rather than the composite number that the digits make up, so

students lose the essence of the actual place value of a digit

." Van de Walle, Karp, & Bay-Williams (2013), p. 236

Student-focused

Multiplication Strategies

**Week 8: Whole Number Multiplication and Division**

**Do Now:**

Estimate the sum of the problem below.

Today's agenda(3/7):

Mid-term Assessment

Basic Fact Mastery

Multiplication/Division Problem Structures

Student-centered strategies for multi-digit multiplication and division

Multiplication Fact Mastery

Complete your 12x12 chart as efficiently as you can

On the back, summarize your overall strategy

Turn to your partner and discuss your strategy

Whole class discussion

Now watch this (the sound doesn't work, but it is a good strategy):

Repeated addition

34 + 34 + 34 + 34...23 times

Partial products methods:

Box method

Cluster problems

Standard Algorithm

Division

Repeated subtraction

128/8 would be 128 - 8 - 8 - 8 - 8.....

Partial quotients methods:

Subtracting/Adding up multiples

Explicit trades

Standard Algorithm

Efficient

Intuitive

Efficient

Intuitive

Try it out...

Write a word problem using each problem structure:

Total unknown

Group size unknown

Total of groups unknown

Solve your problems. Trade with a partner and solve.

You try...

Solve your problem below using 3 different methods.

You try...

Solve the problem below using at least 3 methods.

186 / 12

Reminders...

Math/Literature Integration due tonight by 11:59pm

Differentiated activity due in class on 3/28

Read VDW Ch. 15, Lamon chapter, Brennan article

Based on the part you do not know

Announcements

Stop reading until we get to

fractions

Task Analysis clarification

Math & Literature due 3/20, 11:59pm

Tiered Activity due 3/27, 11:59pm

3/21 Announcements/Agenda

Midterm feedback- 93.79 average

Math/Lit Integration due tonight

Tiered Activity due next Monday

in class

- bring handout (see eCampus) and materials for 12 ppl

plus a handout for me

Try out WIPS

Multiplication progression analysis

Back to problem types with your problems from 3/7 (PPW plate)

Division strategies