Week 5 I am thinking of 3 numbers whose sum is greater than 70. Look at each statement below. Mark it as true or false. Be ready to explain why. All three numbers are greater than 20. If two of the number are less than 20, the other must be greater than 20. *sign in! (are you here?)

Announda Exam 1 is on Friday! See assignments page for some practice questions. Office Hour Today! MATH 303 at 11am! Don’t forget to get the class notes from the bookstore. Homework Comment Subtraction Algorithms Continued Exam Review

Which Model of Subtraction? Your story problems made me hungry. In fact, they made me want to eat 1049 candy bars. I ate 233 instead. How many fewer candy bars did I eat than I wanted to eat?

Key Word Strategy… Sometimes emphasizing key words such as how many “more” or “fewer” or “difference” help students remember what type of problem they are being asked to compute. Unfortunately, this strategy doesn’t always work (though in some situations this can be extremely helpful) – but it can sometimes emphasize memorization over understanding.

Simpler Problem Strategy… Your story problems made me hungry. In fact, they made me want to eat 1049 candy bars. I ate 233 instead. How many fewer candy bars did I eat than I wanted to eat? This problem may be hard to visualize. Choose smaller numbers: I wanted to eat 7 and ate 2 instead. I’m findnig a difference so now I know this is a subtraction problem and can solve using the original numbers!

Subtraction the way you learned it… Why did you cross out the 6? Why did you put a little “1” next to the 7? Can you show this with pictures?

Here are three other ways to think about subtraction Explain why this works--use pictures or manipulatives

Why does this work? This way worked because is the same as adding 10 to both numbers: = = = =

Use drawings or manipulatives to explain… Here is another one. ProblemFirst stepSecond step

Use drawings or manipulatives to explain… Here is yet another one = 32

A quick review of subtraction Try this: Explain what the student is doing >

A quick review of subtraction Find a, b, c, and d that will make this subtraction problem work. (a, b, c, d all different numbers.) 6 a b - c 8 b 1 d a Is there more than one answer???

Use manipulatives or diagrams to show or use words to explain why…

Exam Comments Scientific calculators are allowed – if you do not have one, a four function calculator will be available.

Exam Comments Remember – Exam questions will not be exactly like… Familiar questions may require additional steps before reducing to problems that you have seen before. The type of response required (strategy, justification, explanation, etc.) will be indicated in the directions of each problem.

Some Key Topics Problem solving – techniques, justification, representation, extending patterns, and identifying strategies. Numeration and number systems – Know Babylonian, Mayan, Alphabitian, Egyptian (up to Lotus Flower), Roman, Hindu-Arabic, Base-?? numbers, systems (base-?, additive, subtractive, properties (zero?)), and how to translate between them. Place Value, addition, subtraction – How are they related, different, algorithms, models and representations.