Warm up Problem: Without doing any calculation, explain why 35 base 7 > 35 base 6.

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Presentation transcript:

Warm up Problem: Without doing any calculation, explain why 35 base 7 > 35 base 6.

Musical Chairs! Change your table groups. One person may remain at each table. The remaining students move to another table—each going to a different new table. All tables should have groups that have no more than one person from a previous group.

Meanings for Multiplication Repeated addition: 3 4 = = = = 12 Area: 4 2 = 4 feet 2 feet

Meanings for Multiplication Measured Units: 5 times x units long Cartesian Product: combinations e.g., 3 shirts, 5 pair pants Shirt 1Shirt 2 Shirt 3 J B R K C J B R K C J B R K C

Meanings for Multiplication Arrays: 3 5

Meanings for Multiplication Rate: 8 miles per hour for 5 hours: 8 5 = 40 miles

Exploration 3.13 First, read through the Egyptian Duplation example. Focus on the Hindu-Arabic numerals. With a partner, can you explain what is going on here? If so, can you explain why it works? With your partner, see if you can do 14 41; 65 17; Do not use a calculator!!

Exploration 3.13 Use Egyptian Duplation for

Exploration : Now: = ( ) 41 = = 574

Exploration 3.13 Use Egyptian Duplation for

Exploration 3.13 Do this one with your partner: = 65 (1 + 16) = = 1105

Exploration 3.13 Lattice Multiplication--this is used today in certain schools. Kids love this!

Exploration 3.13 With a partner, can you explain what is going on in Lattice Multiplication? If so, can you explain why it works?

Exploration 3.13 You try Lattice Multiplication for

Exploration 3.13 Cross Product. Read this with your partner three times. Now, do it together. 5 6 x = 4 tens 8 ones 8 50 = 40 tens = 4 hundreds 40 6 = 24 tens = 2 hundreds 4 tens = 20 hundreds = 2 thousands

Exploration 3.13 Think of as (50 + 6)(40 + 8), and reread the directions. Can you follow it better? In algebra, we learned to multiply binomials: (x + a)(y + b) = xy + xb + ay + ab. (FOIL). Do you see it now???

Homework for Monday Read Textbook section 3.3 Do Textbook problems pp : 1, 12 Exploration 3.13 Do #1 and #2

Warm Up Can you explain what is going on here? =

Class Notes--Vidoes In general, watch the videos, and try to notice: a) what is the child doing? b) mathematically, what is going on? c) mathematically, why is it correct or incorrect.