You should be able to:
(1) Write word problems that use (a) comparison subtraction, (b) take-away model of subtraction, and (c) missing addend.
(2) Analyze students' methods for adding, subtracting, multiplying, or dividing. (Analyze means be able to explain the child's procedure or solution method, whether their procedure is reasonable, and if they got the answer correct or not. )
(3) Make a sketch that models the multiplication of two numbers (repeated addition, array, area, Fundamental Counting Principle), whether using whole numbers or fractions.
(4) Write division word problems that use equal share or repeated subtraction models.
(5) Estimate and explain your thinking when dividing very large numbers to determine an approximate percent.
(6) Use scientific notation to solve problems with really big numbers or really small numbers and be able to convert those numbers into other units that provide a better understanding of what those numbers represent.
Wednesday, January 20, 2010
Friday, January 15, 2010
3.4 Lecture Notes
Multiplication can be modeled in different ways and have different cognitive learning levels:
Level 1 - Repeated Addition: If I eat 2 cookies each day for three days, how many cookies have I eaten? 3x2 would be modeled as 2+2+2
Level 2 - Array(a discrete model): The room has three rows and each row has 4 chairs, how many chairs are in the room? This can be modeled with dots representing the chairs showing 4 dots in three rows. In this model we start with chairs in each row and find total chairs in the room.
Level 3 - Fundamental Counting Principle: You have two shirts and three pairs of pants, how many different outfits do you have? we use a tree diagram to solve this type of problem.
Level 4 - Area(a continuous model): If a room is 10 feet by 8 feet, what is its area? In this model the units change, we start with feet for width and length but end with square feet (difficult concept for students).
Level 5 - Fractional Part: I bought 6 pizzas for the party and ordered half of them as pepperoni, a third as plain, and the rest veggie. How many are pepperoni? This is a hard concept for students because it is solved by (1/2) x 6. Students have difficulty with this concept because they think about multiplication as repeated addition, which means the answer should be larger than what you start with if you use multiplication to solve.
Level 1 - Repeated Addition: If I eat 2 cookies each day for three days, how many cookies have I eaten? 3x2 would be modeled as 2+2+2
Level 2 - Array(a discrete model): The room has three rows and each row has 4 chairs, how many chairs are in the room? This can be modeled with dots representing the chairs showing 4 dots in three rows. In this model we start with chairs in each row and find total chairs in the room.
Level 3 - Fundamental Counting Principle: You have two shirts and three pairs of pants, how many different outfits do you have? we use a tree diagram to solve this type of problem.
Level 4 - Area(a continuous model): If a room is 10 feet by 8 feet, what is its area? In this model the units change, we start with feet for width and length but end with square feet (difficult concept for students).
Level 5 - Fractional Part: I bought 6 pizzas for the party and ordered half of them as pepperoni, a third as plain, and the rest veggie. How many are pepperoni? This is a hard concept for students because it is solved by (1/2) x 6. Students have difficulty with this concept because they think about multiplication as repeated addition, which means the answer should be larger than what you start with if you use multiplication to solve.
Thursday, January 7, 2010
CH1&2 Test Review
1. Carry out a quantitative analysis: make sure to explain your reasoning and draw a picture to help you relate the quantities.
2. Find many different ways to think about a number: i.e. 123.7 can be thought of as 120 ones and 37 tenths or 12 tens and 37 tenths.
3. Bases Other Than Ten: be able to change a base ten number into another base; or change a number in another base to base ten.
4. Operations in Different Bases: be able to solve addition and subtraction problems in other bases, show your work with drawings that represent manipulatives and/or base tables.
2. Find many different ways to think about a number: i.e. 123.7 can be thought of as 120 ones and 37 tenths or 12 tens and 37 tenths.
3. Bases Other Than Ten: be able to change a base ten number into another base; or change a number in another base to base ten.
4. Operations in Different Bases: be able to solve addition and subtraction problems in other bases, show your work with drawings that represent manipulatives and/or base tables.
Tuesday, January 5, 2010
Welcome to Math for Elementary School Teachers
Please add 1.4 #4 to your homework assignment due Weds. 1/6/10
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