# Math Test 1

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1. Common Core creates potential for collaborative groups in states and districts to get more economic mileage for ____, ____, and ____.
• curriculum development
• assessment
• professional development
2. Intent of the Common Core: ____, ____, ____, and ____.
• the same goals for all students
• coherence
• focus
• clarity and specificity
3. ____ and ____ are emphasized equally in the Common Core.
• Conceptual understanding
• procedural skills
4. NCTM states that coherence also means that ____, ____, and ____ are aligned.
• instruction
• assessment
• curriculum
5. Key ideas, understandings, and skills are identified in the Common Core.  ____ of concepts is stressed, which means that time is spent on a topic and on learning the topic well.
Deep learning
6. ____ and ____ are clearly defined in Common Core.
• Skills
• concepts
7. Common Core sets the expectation that students are able to apply ____ and ____ to new situations.
• concepts
• skills
8. CCSSM stands for ____.
Common Core State Standards for Mathematics
9. The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students.  These practices are similar to NCTM’s ____ ____ from the Principles and Standards for School Mathematics.
Mathematical Processes
10. CCSSM Mathematical Practices:
1) Make sense of problems and ____ in solving them.
persevere
11. CCSSM Mathematical Practices:
2) Reason ____ and ____.
• abstractly
• quantitatively
12. CCSSM Mathematical Practices:
3) Construct viable ____ and critique the ____ of others.
• arguments
• reasoning
13. CCSSM Mathematical Practices:
4) ____ with Mathematics.
Model
14. CCSSM Mathematical Practices:
5) Use appropriate ____ strategically.
tools
15. CCSSM Mathematical Practices:
6) Attend to ____.
precision
16. CCSSM Mathematical Practices:
7) Look for and make use of ____.
structure
17. CCSSM Mathematical Practices:
8) Look for and express regularity in ____ ____.
repeated reasoning
18. Common Core Format: ____ are larger groups of related standards.  Standards from different --- may sometimes be closely related.  Overarching big ideas that connect topics across grades.
Domains
19. Common Core Format: ____ are groups of related standards.  Standards from different --- may sometimes be closely related, because mathematics is a connected subject.
Clusters
20. Common Core Format: ____ define
what students should be able to understand and be able to do.
Standards
21. The format of the Common Core for Grades K-8 is 1)____, 2)____, and 3)____.
• Domain
• Cluster
• Standards
22. ____ are content statements.
Standards
23. For grades preK-8, a model of implementation can be found in NCTM’s ____ ____ ____.
Curriculum Focal Points
24. Build new knowledge from ____ ____.
prior knowledge
25. Provide opportunities to talk about ____.
mathematics
26. Build on opportunities for ____ ____.
reflective thought
27. Encourage ____ ____.
multiple approaches
28. Treat errors as ____ ____ ____.
opportunities for learning
29. ____ new content.
Scaffold
30. Honor ____.
diversity
31. You must have a ____ and a ____ to have mathematics proficiency.
• conceptual understanding
• procedural understanding
32. ____ ____ is knowledge about the relationship or foundational ideas of a topic.
Conceptual understanding
33. ____ ____ is knowledge of the rules and procedures in carrying out mathematical processes and also the symbolism used to represent mathematics.
Procedural understanding
34. What are the five strands of mathematical proficiency?
• 1) conceptual understanding
• 2) procedural fluency
• 3) strategic competence
• 5) productive disposition
35. Comprehension of mathematical concepts, operations, and relations
conceptual understanding
36. Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
procedural fluency
37. Ability to formulate, represent, and solve mathematical problems
strategic competence
38. Capacity for logical thought, reflection, explanation, and justification
39. Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
productive disposition
40. The most critical period for the development of whole number place value is grades ____ ____ ____.
pre-k to 3
41. Children are exposed to
patterns in grades ____ and ____.
• K
• 1
42. Children formally learn that groups of ten are connected to our place-value system in grade ____.
2
43. Understanding of patterns and place value are extended and decimals are introduced in grades ____ and ____.
• 3
• 4
44. In grades ____ and ____, ideas with whole numbers are extended to decimals.
• 4
• 5
45. ____ ____ requires an integration of new and difficult-to-construct concepts of groupings by tens with procedural knowledge of how groups are recorded in our place-value scheme, how numbers are written, and how they are spoken.
Place-value understanding
46. What are three different way sin which children begin counting?
• 1) counting by ones
• 2) counting by groups and singles
• 3) counting by tens and ones
47. This is the only way children can be convinced that quantities are equal before base-ten ideas develop.  (one-to-one correspondence)
counting by ones
48. This counting must be coordinated with a count by ones before it can be a means of telling “how many”.
counting by groups and singles
49. An idea or abstraction that represents a quantity
number
50. A symbol representing numbers
numeral
51. Used to describe how many elements are in a finite set
cardinal number
52. Numbers used to denote order, i.e., “second in line”
ordinal number
53. What five principles must students understand before they can engage in real counting?
• 1) Any collection of real or imagines objects can be counted
• 2) Counting numbers are arranged in a sequence that does not change
• 3) One-to-one correspondence
• 4) Order-irrelevance
• 5) Cardinality principle
54. One and only one number is used for each item counted, and each item is counted only once
one-to-one correspondence
55. The order in which items are counted is irrelevant
order-irrelevance
56. There is a special significance to the last number counted. It is not only associated with
the last item but also represents the total number of items in the set
cardinality principle
57. For the most basic strategies, children use physical objects (counters) or fingers to ____ ____ the action or relationships described in each problem.
directly model
58. Over time, children’s strategies become more abstract and efficient. ____ ____ strategies are replaced by more abstract
Student-Invented Strategies/Counting Strategies, which in turn are replaced with ____ ____.
• Direct Modeling
• Number Facts
59. This strategy is distinguished by a child’s explicit physical representation of each quantity in the problem and the action or relationship involving those quantities before counting the resulting set.
direct modeling
60. A child essentially recognizes that it is not necessary to actually construct and count sets. The answer can be figured out by focusing on the counting sequence itself.
counting
61. Physical objects are used to represent objects in a problem.
direct modeling
62. Physical objects are used to keep track of counts.
counting
63. Children learn ____ before other number combinations.
doubles
64. Children learn sums of ____ relatively early.
ten
65. ____ ____ solutions are based on understanding relations between numbers.
Derived Fact
66. Even without specific instruction, most children use ____ ____ before they have mastered all their number facts at a recall level.
Derived Facts
67. When children have the opportunity to discuss
alternative strategies, the use of ____ ____ becomes even more prevalent.
Derived Facts
68. Children appear to “____ ____” Direct Modeling, Counting, and Derived Fact strategies when number choices/kinds of quantities are consistent across problems.
move through
69. ____ ____ strategies are not easily used with some problem types.
Direct Modeling
70. ____ ____ are extensions of modeling strategies.
Mental strategies
71. Children learn ____ ____ and apply this knowledge to solve problems.
number facts
72. Children learn certain ____ ____ before others.
number combinations
73. Children often use a small set of memorized facts to derive solutions for problems involving other ____ ____.
number combinations
74. What are the three primary strategies used by children to solve math problems?
• 1) modeling strategy
• 2) split strategy
• 3) increment/jump strategy
75. Involves drawing pictures of tens and ones and
counting, first by tens and then by ones
modeling strategy
76. Involves splitting the numbers in the strategy into smaller numbers that are easier to work with and then adding the totals together to get the answer
split strategy
77. Primarily through the use of an empty number line
increment/jump strategy
78. Mental strategies involve decomposing numbers by tens and ones
modeling strategy
79. Representational strategies involve modeling and carrying out operations using tens sticks and units and documenting using drawings of tens sticks and ones with ‘actions.’
modeling strategy
80. Notational strategies involve recording work with numbers as tens and ones
split strategy
81. Mental strategies involve holding one number in memory and then decomposing the second number, mentally joining or separating
increment/jump strategy
82. Representational strategies involve modeling and carrying out operation using an empty number line (which also provides written documentation)
increment/jump strategy
83. Classroom instruction is generally organized and orchestrated around ____ ____
84. The ____ with which students engage determine what they learn about mathematics and how they learn it
85. The inability to enact ____ ____ well is what distinguished teaching in the U. S. from teaching in other countries that had better student performance on TIMSS
86. “Not all tasks are____ ____, and different tasks will provoke different levels and kinds of student thinking.”
created equal
87. Task-Focused Activities: ____ between high and low cognitive demand mathematics tasks
Distinguishing
88. Task-Focused Activities: ____ the cognitive demands of high-level tasks during instruction
Maintaining
89. A ____ ____ ____ task begins where the students are (zone of proximal development; scaffolding)
high cognitive demand
90. The problematic or engaging aspect of a ____ ____ ____ task is due to mathematics that students are to learn.
high cognitive demand
91. A ____ ____ ____ task requires justifications and explanations for answers and methods.
high cognitive demand
92. ____ ____ ____ tasks or activities are the vehicle through which the curriculum can be developed. Maintaining the cognitive demands of ____-____ tasks during instruction affects the learning that occurs.
• high cognitive demand
• high-level
93. First step of the Mathematical Tasks Framework:
TASKS as they appear in curricular/instructional materials or are designed by teachers
94. Second step of the Mathematical Tasks Framework:
TASKS as they are set up by the teacher
95. Third step of the Mathematical Tasks Framework:
TASKS as they are implemented by students
96. Fourth step of the Mathematical Tasks Framework:
TASKS as they are summarized by teacher and students
97. Fifth step of the Mathematical Tasks Framework:
Student learning
98. SUBITIZING CARDS:
Recognizing a number instantly in a pattern
perceptual
99. SUBITIZING CARDS:
Uses colors to show separate patterns together so that you can recognize two different patterns make a whole
conceptual
100. Subitizing cards are both ____ and ____.
• perceptual
• conceptual
101. What are the five process standards of NCTM?
• 1) problem solving
• 2) reasoning and proof
• 3) representation
• 4) communication
• 5) connections
102. What are the five proficiency strands of NCSM?
• 1) conceptual understanding
• 2) procedural fluency
• 3) strategic competence
• 5) productive reasoning
103. What two things are combined to make up the eight standards in the Common Core?
• 1) The five process standards of NCTM
• 2) The five proficiency strands of NCSM
104. What are the eight standards for mathematical practice under the Common Core?
• 1) Make sense of problems and persevere in solving them
• 2) Reason abstractly and quantitatively
• 3) Construct viable arguments and critique the reasoning of others
• 4) Model with mathematics
• 5) Use appropriate tools strategically
• 6) Attend to precision
• 7) Look for and make use of structure
• 8) Look for and express regularity in repeated reasoning
105. Strategies become more ____ over time.
abstract
106. An ____ has an equals sign.
equation
107. An ____ does not have an equals sign.
expression
108. What are the three primary strategies for solving problems that are invented by students?
• 1) increment/jump strategy
• 2) split strategy
• 3) modeling strategy
109. What are the three phases that are typical to mastering basic number combinations?
• 1) counting strategies
• 2) reasoning strategies
• 3) mastery
110. What are some of the reasoning strategies used for addition facts?
• 1) one more
• 2) two more
• 3) using five as an anchor
• 4) make 10
• 5) doubles
• 6) near doubles
111. What are some of the reasoning strategies used for subtraction facts?
• 1) subtraction as think addition
• 2) down over ten
• 3) take from ten
112. What are the four basic types of addition and subtraction problems?
• 1) joining
• 2) separating
• 3) part-part-whole comparisons
• 4) comparison situations
113. Using object counting or verbal counting to get an answer (counting on, direct modeling, etc.)
counting strategies
114. Using known information to logically figure out an answer
reasoning strategies
115. Developing meanings for operations
operations sense
116. Gaining a sense for the relationships among operations
operations sense
117. Determining which operation to use in a given situation
operations sense
118. Recognizing that the same operation can be applied in problem situations that seem quite different
operations sense
119. Developing a sense for the operations’ effects on numbers
operations sense
120. Realizing that operation effects depend upon the types of numbers involved
operations sense
121. There were significant positive correlations between ____ ____ of how their children solved addition and subtraction problems and their ____ ____ to solve the problem.
• teachers' knowledge
• children's ability
122. Teachers who believed that children bring ____ to instruction and instruction should be built on that ____, had higher levels of ____ than did teachers who did not agree as strongly with that perspective.
• knowledge
• knowledge
• achievement
123. Classes with the highest levels of achievement were those of teachers who believed most strongly that the teacher was not the ____ ____ ____ ____ and that instruction should be designed to help children ____ ____ ____ ____ for themselves.
• ultimate source of knowledge
• construct solutions to problems
124. What does CGI stand for?
Cognitively Guided Instruction
125. What are the basic ideas of CGI?
• 1) Children bring to school informal or intuitive knowledge of mathematics.
• 2) Children intuitively solve word problems by modeling the action and relations described in them.
• 3) One of the most useful ways of classifying problems focuses on the types of action or relation described in the problem. Providing a framework to identify the relative difficulty of problems.
126. A basic idea of CGI is that children bring informal or intuitive ____ of mathematics to school.
knowledge
127. A basic idea of CGI is that children intuitively solve word problems by ____ the action and relations described in them.
modeling
128. A basic idea of CGI is that one of the most useful ways of classifying problems focuses on the types of ____ or ____ described in the problem, providing a framework to identify the relative difficulty of problems.
• action
• relation
129. The teacher's role in CGI is to learn how students initially use ____ ____, ____, and how they evolve.
• concrete materials
• modeling
130. The teacher's role in CGI is to focus is on what children ____ do rather than on what they ____ do.
• CAN
• cannot
131. The teacher's role in CGI is to work back from ____ to find out what valid conceptions students do have.
errors
132. The teacher's role in CGI is to ____ problems their students can solve.
identify
133. The teacher's role in CGI is to shift the emphasis from personally finding ways of ____ ____ ____ to the students ____ ____ ____ representations.
• representing mathematical knowledge
• constructing their own
134. Lucy has 8 fish.  She wants to buy 5 more fish.  How many fish would Lucy have then?
8 + 5 = ?
join result unknown
135. Janelle has 7 trolls in her collection.  How many more does she have to buy to have 11 trolls?
7 + ? = 11
join change unknown
136. Sandra has some pennies.  George gave her 4 more.  Now Sandra has 12 pennies.  How many pennies did Sandra have to begin with?
? + 4 = 12
join initial unknown
137. TJ had 13 chocolate chip cookies.  At lunch she ate 5 of them.  How many cookies did TJ have left?
13 - 5 = ?
separate result unknown
138. 11 children were in the sandbox.  Some children went home.  There were 3 children still playing in the sandbox.  How many children went home?
11 - ? = 3
separate change unknown
139. Max had some money.  He spent \$9.00 on a video game.  Now he has \$7.00 left.  How much money did Max have to start with?
? - \$9 = \$7
separate initial unknown
140. Susan has 8 red apples and 5 green apples. How many apples does she have?
8 red + 5 green = ? apples
part-part-whole ~ whole unknown
141. Brandy has 16 Gummy Bears. 8 are red and the rest are green. How many green Gummy Bears does she have?
16 gummy bears = 8 red + ? green
part-part-whole ~ part unknown
142. Willy has 12 crayons.  Lucy has 7 crayons.  How many more crayons does Willy have than Lucy?
12 - 7 = ?
compare difference unknown
143. George has 4 more pennies than Sandra.  Sandra has 8 pennies.  How many pennies does George have?
8 + 4 = ?
compare larger unknown
144. Lydia had 4 fewer pencils than Henry.  Henry has 10 pencils.  How many pencils does Lydia have?
10 - 4 = ?
compare smaller unknown
145. What is another term for the borrowing method?
decomposition method
146. This method is based upon the idea that adding the same amount to two different numbers will not change the different between the two numbers.