Math Methods Test 2

Front 1

What is the primary purpose of drill of basic facts?

Back 1

• Students have to have this base knowledge in order to be able to do math at later levels. Students have to be quick with the basic facts to have success.

Front 2

Identify basic fact strategies for addition (adding to 10, doubles, counting on, commutativity)

Back 2

• Adding to 10: 8+5= (8+2)+3= 10+3=13
• Doubles: Knowing that 4+4=8 6+6=12 7+8 = 7+7+1 = 15
• Counting on: 2+6= 6…7…8
• Commutativity: Children should understand that it does not matter which number comes first in an addition problem. 3+4 provides the same answer as 4+3

Front 3

Identify basic fact strategies for subtraction (double, using 0 and 1, counting on, counting back)

Back 3

• Doubles: 16-8= 8+ = 16 8+8=16 so 16-8=8
• Using 0 and 1: Once students know how to add 0 and 1, it is easy for them to subtract 0 and 1.
• Counting on: 8-6= 6…7…8
• Counting back: 9-2= 9…8…7

Front 4

Identify basic fact strategies for multiplication (commutativity, repeated addition, skip counting, splitting the product into known parts)

Back 4

• Commutativity: Students should understand that it does not matter which numbers comes first in a multiplication problem. 3 x 4 provides the same answer as 4 x 3
• Repeated addition: 4 x 5 = 5+5+5+5=20
• Skip counting: 4 x 5 = 5, 10, 15, 20
• Splitting the product into known parts: 9 x 8 = 8 x 8 = 64 + 8 = 72

Front 5

How is the calculator a valuable computational tool?

Back 5

• It facilitates problem solving
• It relieves tedious computation
• It focuses attention on meaning
• It removes anxiety about computational failure
• It provides motivation and confidence
• It facilitates a search for patterns
• It supports concept development
• It promotes number sense
• It encourages creativity and exploration

Front 6

Spending time on mental computation is important because…

Back 6

• It’s useful. ¾ of all calculations done by adults are done mentally.
• It provides a direct and efficient way of doing many calculations.
• It is an excellent way to develop critical thinking and number sense and to reward creative problem solving.
• It contributes to increased skill in estimation.

Front 7

Strategies in teaching mental computation

Back 7

• Encourage students to do computations mentally
• Check to learn what computations students prefer to do mentally
• Check to learn if students are applying written algorithms mentally
• Include mental computation systematically and regularly as an integral part of instruction
• Keep practice sessions shorts—perhaps 10 minutes at a time

Develop children's confidence.
Encourage inventiveness.
Make sure children know difference between mental computation and estimation.

Front 8

Four phases for the classroom assessment process (in sequential order)

Back 8

1. Plan assessment
2. Gather evidence
3. Interpret evidence
4. Use results

Front 9

Know the difference between mental computation and estimation

Back 9

• With mental computation, we want kids to be able to get the right answer in their head
• With estimation, we want kids to get in the ballpark

Front 10

The most difficult computational algorithm is…

Back 10

Division

Front 11

Appropriate math assessment to utilize (self-assessment, performance task assessment, interview assessment, etc)

Back 11

• Interview: Use interview when you want to find out what a student knows or what a student is thinking about a certain math concept. It is one-on-one between the teacher and student.
• Performance task assessment: Use this when you want to see what a child can do. Certain math concepts require performance to see if the student has really mastered the material. Using a ruler to measure is a good example of a performance task.
• Self-assessment: Use self-assessment to develop some independence for the student. Teach them to ask what they are doing and why they are doing it.

Front 12

The most common type of assessment is…

Back 12

Observation

Front 13

Differences and similarities between problem, exercise, routine problem, nonroutine problem

Back 13

• Problem: involves a situation in which the solution route is not immediately obvious
• Exercise: a situation in which the solution route is obvious
• Routine problem: the application of a mathematical procedure in the same way it was learned
• Nonroutine problem: the choice of mathematical procedures is not obvious

Front 14

Strategies in teaching problem solving effectively

Back 14

• Allow mathematics to be problematic for students
o Give students problems that challenge them, that allow them to struggle, and that help them examine and make sense of different approaches
• Focus on the methods used to solve problems
o Encourage student to talk with each other about their methods, to compare the methods, and to think about their advantages and disadvantages
• Tell the right things at the right time
o Speaking up too soon can eliminate the challenge and much of the learning, but it is also important not to leave student floundering when you can see they aren’t making progress

 Instruction should build on what children already know
 Engaging children in problem solving should not be postponed until after they have “mastered” computational skills
 Children should be taught a variety of problem-solving strategies to draw from
 Children’s problem-solving achievements are related to their developmental level. Thus, they need problems at appropriate levels of difficulty

Front 15

Problem strategy not explained in book (What is an example of change your point of view?)

Back 15

• The 9 dots, 4 lines problem.

Front 16

Prerequisites for numerical operations

Back 16

• Counting expertise: forward, backward, 2’s, 3’s, etc.
• Experience with concrete situations
• Familiarity with problem-solving situations: “I don’t know the answer, but I can work it out!”
• Experience in using language to communicate math ideas

Front 17

Name and demonstrate two common algorithms for subtraction with regrouping

Back 17

• Decomposition algorithm. This is the one we use in the United States.
• Equal-additions algorithm: this is used in Europe and South America.

Front 18

Common myths about using calculators in the classroom (dispel myths)

Back 18

• Calculator use does not require thinking
• Use of calculators will harm students’ math achievement
• Computations with calculators are always faster
• Calculators are useful only for computation

Front 19

Why is division so hard for kids?

Back 19

• It combines several math algorithms. Kids must be able to do multiplication, subtraction, and division.
• Computation begins at the left instead of at the right.
• Interactions move from one spot to the other. There is a lot of jumping around.
• Trial quotients may not be successful the first or second tries.

Front 20

Why should the concept of remainders be introduced to students early?

Back 20

• Students should understand that real-life problems do not always come out even and things cannot always be divided evenly.

Front 21

Major Shifts in Assessment Practices (look for chart in book)

Back 21

• Shifts in assessing to make instructional decisions
o Toward integrating assessment with instruction
o Toward using evidence from a variety of assessment formats and contexts
o Toward using evidence of every student’s progress toward long-range planning goals
• Shifts in assessing to monitor students’ progress
o Toward assessing progress toward mathematical power
o Toward communicating with students about performance in a continuous, comprehensive manner
o Toward using multiple and complex assessment tools
o Toward students learning to assess their own progress
• Shifts in assessing to evaluate students’ achievement
o Toward comparing students’ performance w/performance criteria
o Toward assessing progress toward mathematical power
o Toward certification based on balanced, multiple sources of information
o Toward profiles of achievement based on public criteria

Front 22

George Polya model for problem-solving

Back 22

• Understand the problem
• Devise a plan for solving it
• Carry out your plan
• Look back to examine your solution

Front 23

How are CCS in Math different than the original ILS?

Back 23

• Define specific grade levels for certain tasks
• Define specific tasks the kids should be able to do
• Includes math processes

Front 24

Compatible numbers in estimating

Back 24

• With compatible numbers, you look for sets of numbers that are easily computed.

Front 25

Front-end estimation

Back 25

• In front-end estimation, you only use the number with the highest place value and make all the number behind it a 0. Then you add them up. For example, 38+27+62+75. 30+20+60+70=180

Front 26

Why are Race to a Flat and Give a Flat Away important math games to play?

Back 26

• These are really important games to play because they help develop a child’s sense of place value. They give the student a lot of practice with regrouping or trading in. It helps prepare them for using base-10 blocks for addition, subtraction, etc.

Front 27

To what three audiences will assessment be communicated?

Back 27

To student
To parents/guardians
To administrators

Front 28

How many addition facts are there?
Subtraction?
Multiplication?
Division?

How many addition do kids have to work hard at to memorize?
Multiplication?

Back 28

100
100
100
90

10
15