Midterm

Question 0

What is conceptual thinking?

Answer 0

Being able to conceptualizer activities.

Different kinda if understanding, could be performed in different ways.

Question 1

What is procedural thinking?

Answer 1

Step-by-step process/algorithm.

Following “procedures” which are usually memorized.

Question 2

What are two reasons a teacher might use Quick Draws in class?

Answer 2

1) help build spatial sense- emphasize on what they see.

2) builds geometric vocab- building properties of geometric shapes.

Question 3

Describe what is meant by a sharing task.

Answer 3

(Equal sharing activities-fair shares)

Usually posed in a story problem: Four friends are sharing two pizzas. How much pizza will each friend get?

Question 4

Describe the goal of a sharing task and when you would use them.

Answer 4

• goal: develop initial fraction concept, equivalence, and ordering of fractions
• use them: in the early grades

Question 5

Example of a sharing task.

Answer 5

Ten brownies shared with four children

Question 6

What are the two meanings of division problems?

Answer 6

• partitive

- measurement

Question 7

Describe and model the two meanings of division-6/2

Answer 7

1) partitive: share and rate problems
• 6/2 (if there are two groups, how many are in each group?) if 6 are in half a group, how many in a while group? 12
2) measurement: repeated subtraction/ equal groups.
• 6/2 (how math groups of 2 are in 6?) how many halves are in 6? 12

Question 8

List and use: Region/area model

Answer 8

• circular pieces
• rectangular regions
• pattern blocks
• paper folding
• grids/ dot paper

Question 9

List and use: length/ measurement models

Answer 9

• fraction strips—cuisine ire rods
• number line
• paper strips

Question 10

List and use: set models

Answer 10

• counters

- objects: 1” tiles, cars, marbles

Question 11

What are some common benchmarks?

Answer 11

• 0.1.1/2

- powerful tool for gauging the size of fractions, making quick estimates and judging computed results.

Question 12

Purpose for fraction benchmarks

Answer 12

Enables students to estimate and gives them a took for judging the reasonableness of the answer

Question 13

What is a unit fraction and why are they useful?

Answer 13

A rational number written as a fraction where the numerator is one and the denominator is a positive number.

1/2, 1/3, 1/4…

Question 14

Why should the term “reduce” not be used?

Answer 14

You’re not reducing anything. You should say “simplify” because you’re putting it into simplest form.

Question 15

Communicate the meaning of the too and bottom number in a fraction.

Answer 15

Students tend to think that the numerator and denominator are separate values.

Help them by:
• finding fraction values on a # line
• don’t say 3 out of 4 for three fourths

Question 16

What are the five fraction constructs?

Answer 16

1. Part-whole
2. Measurement
3. Division
4. Ratio
5. Operator

Question 17

What is part-whole?

Answer 17

Part of a group/ length (2 parts out of 3 equal parts= 2/3)

Question 18

What is measurement?

Answer 18

Use length as a measurement piece to determine length of an object (2 1/3 units)

Question 19

What is division?

Answer 19

Splitting a number into parts/ groups (2 divided by 3)

Question 20

What is ratio?

Answer 20

How much of one thing there is compared to another (2 to 3)

Question 21

What is operator?

Answer 21

Represents a fraction of a whole number (2/3 of something)

Question 22

What are some problems when beginning with rules for computation fractions?

Answer 22

• they memorize procedures and rules

- they don’t understand what the too and bottom number represent

Question 23

What are some tools used to help develop a conceptual understanding of fractions?

Answer 23

• models (area, length, set)
• games (fraction face off)
• # line, shapes
• sharing tasks

Question 24

What is the common denominator algorithm?

Answer 24

1) change to an improper fraction

2) find a common denominator and multiply top and bottom

Question 25

Common misconceptions: drawing/ recognizing fractions

Answer 25

Dividing a nontraditional shape into parts (triangle)

Question 26

Common misconceptions: fraction comparison

Answer 26

Ranking fractions- think 1/5 is bigger than 1/4 because 5 is larger than 4

Question 27

Common misconceptions: fraction computation

Answer 27

Not seeing a fraction as a whole unit

Question 28

Name 3 activities to help make connections between familiar fractions and decimal equivalent in conceptual manner:

Answer 28

1) 10 x 10 grid
2) hundredths disk
3) bar diagram

Question 29

Describe burners models of representations with examples

Answer 29

1) enactive (action based)
- manipulatives
2) iconic (image based)
- draw shapes, diagrams, graphs
3) symbolic (language based)
- variables (+,-,x,/, X or Y)

Question 30

What does “scaffold” mean?

Answer 30

• a task that is out of a students ZPD can be accessible if it’s carefully structured.
• provides support for those students who may not have a robust collection of “blue dots”

Question 31

What are the 4 guidelines develop instructional strategies to develop fraction computation?

Answer 31

1) use contexts
2) use a variety of models (drawings)
3) include estimation and informational methods
4) address misconceptions