Math Practicum Midterm

Front 1

List and describe 3 rationales for changing the way math is currently being taught:

Back 1

1. Test scores are falling behind
2. Technology and economy changing demanding more from our students
3. National security

Front 2

List and describe the math plan that works:

Back 2

Problem solve daily
Practice mental math skills
Review previously covered concepts/skills
State the objective of the lesson
Introduce the new vocabulary and concept
Guide student practice
Assign 10 problems
Journal about math

Front 3

The four types of math problems:

Back 3

Word: routine story problems that involve calculations
Puzzle: non-routine problems that involve logical reasoning or thinking strategies.
Process: non-routine problems that involve strategies necessary to solve the problem. Use the Polya plan
Real world: non-routine problems that involve real world applications of mathematics. The numbers are not usually given.

Front 4

Four reasons why students have a difficult time solving problems:

Back 4

Method of problem presentation
Misconceptions or misunderstandings of information
Lack of experience in problem solving
Student affective factors

Front 5

Polya Plan:

Back 5

ICAN
Identify the problem
Choose a strategy
Answer the question
Now it makes sense

Front 6

2 math concepts for using a calculator:

Back 6

calculator
practice facts
fractions
dividing with remainders

Front 7

10 Problem solving strategies

Back 7

guess and check
use or look for a pattern
work backwards
make it simple
brainstorm
act out or use objectives
make a picture or diagram
use or make a table
make an organized list
use logical reasoning

Front 8

3 pieces of advice for instructors teaching problem solving:

Back 8

1. make each daily problem-solving experience successful for the students
2. model a positive attitude that can rub off students
3. model problem-solving strategies daily as an anticipatory set or math class opener
4. use collaborative problem solving
5. allow students to use calculators
6. connect with real-life examples for true understanding
7. have students communicate daily in oral and written form
8. accept a student’s ideas even if the student is not on the right path

Front 9

How to teach addition, subtraction, multiplication and division with money boards

Back 9

Addition: Roll a random number generator and place that many pennies on the money board. Once there are 10 pennies, you can REGROUP the pennies into a dime.
Subtraction: When subtracting two digit numbers, you have to RENAME the dime into 10 pennies. Then you can subtract from all the pennies.
Multiplication: (Repeated Addition) multiply using pennies lined up. Example: 6x2=12. Represented on the money board by placing six pennies with another six pennies. REGROUPING 10 pennies into a dime.
Division: (Fair Sharing) 12/3=4 Money Board: you can’t split a dime three ways so it must be RENAMED into 10 pennies.

Front 10

6 Strategies for learning addition facts:

Back 10

1. Identity Element: Adding 0 to any number equals that number
2. Adding One: Adding 1 to any number equals the next number
3. Counting: Start with the largest digit and count on; works when adding 1, 2, or 3.
4. Doubles: the number plus itself
5. Near Doubles: doubles + 1
6. Bridging 10: Use when one addend is close to ten; example 9+4=13 would become 10+3=13

Front 11

Estimation Strategies:

Back 11

• Nice Numbers: find the numbers that add up to exactly 10 or exactly 100
• Compatible numbers: the numbers that fit together easier to get started/estimate. The numbers are close to 100 or 74/23 would have the compatible of 75/25
• Front-End: line the numbers up and draw a vertical line between the first number and the rest. Add the numbers up and then look to see if the remaining numbers are compatible. If they are, then add one to the estimation. If they are not, don’t add one more.
• Clustering: find the number that the numbers “cluster” around and multiply them by how many numbers there are.
• Rounding: round the number to the nearest 10 or 100

Front 12

Two ways to practice computation:

Back 12

1. Card Games: Tweeners (trio; cards A-9; divide cards between trio; each person shows their top two cards and multiply; the one who’s product is in the middle gets the cards), Snap (partners; each partner shows one card, the first to say the math sentence correctly gets the cards), Krypto (add on to the cards to try and get to 100 exactly. With a partner)
2. Dominoes: Like Bingo. 3x3 array of dominoes. Teacher calls out an answer, 8, and the students flip over all dominoes that add up to 8. First one with blackout wins.