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Be able to identify and construct growing patterns and repeating patterns.
- Repeating patterns-core repeats. 123123123
- Growing patterns - expand something you start with. 123'45'56
- see index card for picture examples
Be able to show alternative methods of multiplication
- see index card for examples
- a. Partial Products Method
- b. Trachtenberg model
- c. Lattice Method
What is the difference between a recursive expression and an explicit expression?
- Recursive- requires you to know the previous step to get to the next step.
- Explicit/Direct- formula that allows you to plug numbers to solve.
What is meant by a function?
Every number input has a specific output.
Describe the three phase process that teachers can do to assist children in learning basic facts.
- Start where they are
- build understanding
- give hints on how to remember facts
List and describe the three meanings of fractions.
- Part-to-whole- take whole and partition it
- Quotion-(3/5) means 3 divided by 5
- Ratio - (3/5, 3:5, 3 to 5) single comparison in fraction form.
What are some strategies that children can use to remember basic addition facts?
- Communitative property
- adding 1's and 0's
- adding doubles and near doubles
- counting on
- combinations of 10
- adding to 10 and beyond
Know how to show addition and multiplication of fractions pictorially
- Addition - one box for EACH fraction
- Multiplication - one box total
- See index card for examples
Know the general sequence of activities for helping children to develop meaning of the four basic operations
Be able to list and describe the four basic models of the part-whole meaning
- See index card for examples
What are benchmark fractions and what is their importance in teaching fraction concepts to elementary school students?
Easy convienant fractions to work (1/2, 1/3, 1/4, 1/8)
If students can gain understanding of benchmark fractions they can get more complex fractions.
What are the three criteria necessary before students start practicing fact retrieval?
- Can state or write related facts (fact families) when given one basic fact.
- Can explain how they got an answer in more than one way.
- Can solve facts in more than one way.
What is the primary purpose of drill?
Make students proficient in recalling facts.
Know how to differentiate between separation problems, comparison problems, and part-whole problems when doing addition and subtraction.
Separtation (take away) one quantity given and remove certain amount. ex. tom has 13 pencils, he gave 3 to Sue. How many does he have?
Comparison (finding the difference) start with two quantities. You want to know the difference between the two. Tom has 11 pencils, Sue has 8 pencils. How many more does Tom have?
Part-Whole (how many in set) you are given how many are in entire set and how many in one part of a set, you have to find out how many in remaining set. Tom has 11 toy cars, 3 are toyotas, how many are hondas?
Know three different ways to show the ratio of 5 to 1
Know what a proportion is and how to calculate the correct proportion in a missing number problem.
- Equivilant fraction
- see index card for calculations
Know when a calculator should be used as a computational tool.
- if it can:
- facilitate problem solving
- ease burden of tedious computation
- help focus meaning on lesson
- remove anxiety
- provide motivation and confidance
Be aware of and be able to determine the three different uses of variables
- Place holder (3+A=7) Specific value for A
- Generalization (A-A=0)All value of A make the sentence true
- Function (B=2xA) each value of A produces and holds place of B
What are the prerequisite skills for students in order for them to be able to learn percents?
- know decimals
- know multiplication
- know & understand fractions
- understand equations w/variables
- understand missing numbers
Know the meaning of percent, and how to work various percent problem.
- means of 100
- see index card for problem example
Know how to show addition and subtraction using Base Ten Blocks.
- Addition - combine blocks
- Subtraction - take away blocks
Know how to demonstrate the use of repeated subtraction in division.
- Partial difference subtraction
- see index card
Know different forms of estimation.
Front end estimation - ex. 7865 + 9999= estimate to 7000+9000.
Front end with adjustance - ex. would change to 8000+10000=18000.