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One Note on the Standard Algorithm

Interpreting Our Answers 400 students are going on a field trip. If each bus can fit 83 students, how many busses are necessary? 400÷83=4R68 4 means: 68 means: Answer is:

On your calculator: Calculate: 3 • 4 – 8 ÷ 2 =

On MY calculator 3 • 4 – 8 ÷ 2 =

Now try: (3 • 4) – (8 ÷ 2) = 3 • (4 – 8) ÷ 2 = 3 • (4 – (8 ÷ 2)) =

Order of Operations Parenthesis Exponents Multiplication/Division Addition/Subtraction Note: We use parenthesis to “override” the order of operations

Can you… Give examples of related facts? Show 4 different ways to find: 37 • 41? Show 4 different ways to find: 2795 ÷ 23? Explain why each solution method applies to multiplication or division? Vocabulary: factor, product, partial product, dividend, divisor, quotient, remainder Write word problems for: repeated addition, repeated measure, area, Cartesian product, repeated subtraction, and partitive division?

What have I learned? Can you give an example of each model? Repeated addition Repeated subtraction Repeated measures Partition (Partitive) Cartesian Product Rectangular Area Arrays

What have I learned? Commutative, associative, distributive properties. Write examples, and when are they used? Identity and inverse properties Write examples and when are they used? Related facts. If 6 • 3 = 18, then…

What have I learned? Show 35 • 24 using 4 different methods. At least 1 from videos; at least 1 from explorations Show 2977 ÷ 14 using 4 different methods.

Can I explain… Why each different solution method is an example of multiplication or division? Vocabulary: factor, product, partial product, dividend, divisor, quotient, remainder

Explain what is wrong: “50 ÷ 7 is the same as 50 ÷ 10, (which is 5) then because I adding 3 to the divisor I now need to subtract 3: 5 - 3 = 2.”

Estimate 35 • 49. Show 3 different ways to find: 35 • 49. Estimate 27984 ÷ 82. Show 27984 ÷ 82 using the scaffolding method.

35 • 49 is about 35 • 50. Think: 30 • 50 = 1500, and 5 • 50 = 250, so 1750. Methods: rectangular area, lattice multiplication, Egyptian Duplation, any of the methods used by the kids. 27984 ÷ 82: 82 • 1 = 82; 82 • 10 = 820; 82 • 100 = 8,200; 82 • 1000 = 82,000. So, the quotient is between 100 and 1000, and is closer to 100. Now: 8 • 3 = 24, so guess 300.

27984 ÷ 82 82 ) 27984 24600 3384 1640 1744 1640 104 82 22 1 20 20 300 82 • 1 = 82; 82 • 10 = 820; 82 • 100 = 8,200

I’m thinking of a number. It is less than 50 I’m thinking of a number. It is less than 50. When I divide it by 8, I get a remainder of 5. But when I divide it by 7, I get a remainder of 2. Use the manipulatives to find my number.

Do I Understand??? Given: 4 7 X 3 9 4 2 3 1 4 1__ 1 8 3 3 Question: Without doing any work, what is 30 • 47? How do you know?

Do I Understand? Given: 208 R 7 18 ) 3751 36 151 144 Question: Without doing any work, what is 200 • 18? How do you know?

Make this true for order of operations 12 ÷ 4 - 2 • 5 = 30 What other values can we get using 12 ÷ 4 - 2 • 5? 20