Deck 2: Defining a Comprehensive Mathematics Program

Question 1

Describe how communication might be enhanced through activities and situations found in the elementary mathematics class. What is the value of communication?

Answer 1

Answers will vary.

Question 2

According to the Mathematical Practice "Look for and Express Regularity in Repeated Reasoning," mathematically proficient students should be able to do all of the following except: ​

A)recognize patterns in familiar algorithms and in invented methods for computations.
B)view "shortcuts" as viable methods for solving problems.
C)attend to reasonableness of partial and final answers.
D)understand what is being asked and plan a general solution strategy.

Answer 2

understand what is being asked and plan a general solution strategy.

Question 3

Which of the following problems is the most open and would require students to do the most creative problem solving? ​

A)Mary has 4 apples and John has 3 apples. How many apples do they have together?
B)Shyam has $64. He spends $13 on a CD and $35 on a backpack. How much money does he have left?
C)Tanika has 12 friends and she wants to make each of them 5 pictures. How many pictures will she have to make in all?
D)Rosa has pennies, nickels, dimes, and quarters in her purse. How many different ways can she pay for a book that costs $1.37?

Answer 3

Rosa has pennies, nickels, dimes, and quarters in her purse. How many different ways can she pay for a book that costs $1.37?

Question 4

Patterns and functions are associated most closely with the following Common Core State Standards domains except for : ​

A)numbers and number operations.
B)operations and algebraic thinking.
C)geometry.
D)statistics and probability.

Question 5

Geometry and spatial sense are central mathematical ideas in our world. Give two examples that show how elementary children could be introduced to these ideas.

Question 6

Explain why problem-solving is the overriding theme for teaching all mathematics, according to the NCTM.

Question 7

According to the Mathematical Practice "Construct Viable Arguments and Critique the Reasoning of Others," mathematically proficient students should be able to do all of the following except: ​

A)understand that every conjecture can be explained in an organized manner.
B)critique the reasoning of others by focusing on the argument and not on the presenter.
C)use specific and precise mathematics terms to express reasoning.
D)provide support for a conjecture that is logical and contains supporting evidence or proof.

Question 8

Marcus sketches a graph of a function on the chalkboard. His friend creates a table of values for the function, and another friend creates a set of ordered pairs for the function. Determine which Mathematical Practices are being utilized and explain their significance in this situation.

Question 9

Kindergarteners determine their favorite ice cream flavor and use sticky notes to create a bar graph of their favorite flavors. Determine which of the content standards is being utilized and explain why it is important for children to learn this content.

Question 10

Use the mathematical number idea of ¼. Describe four ways that children might represent ¼. You may include concrete, pictorial, and symbolic forms. Explain which mathematical practice this pertains to.

Question 11

According to the National Assessment of Educational Progress (NAEP), a test that is given to elementary, middle, and high school students in the United States, measurement is one of the significant weaknesses of many students. Give several suggestions for why this is one of the weakest areas in mathematics and explain what you would do as a future teacher to improve on this state of affairs.

Question 12

Sara adds 45 + 32 by adding 45 + 2 to obtain 47, then by adding 30 to get 77. Determine which content standard her strategy relates to and explain why her strategy should be encouraged.

Question 13

Number and number operations should emphasize: ​

A)memorizing basic facts.
B)procedural learning.
C)number sense and computational fluency.
D)learning isolated mathematical information.

Question 14

According to the Mathematical Practice "Make Sense of Problems and Persevere in Solving Them," mathematically proficient students should be able to do all of the following except:

A)understand what is being asked and plan a general solution strategy.
B)realize that a problem in any context can be represented with numerical expressions.
C)develop a specific strategy but show flexibility when solving the problem.
D)show persistence in solving the problem.

Question 15

Describe a real-life situation in which mathematics is used in everyday life. Which Mathematical Content and Practices are represented in the situation you described?

Question 16

Explaining why the area of a triangle is half that of a related rectangle involves several process standards. Choose two process standards and explain how they relate to this problem.