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Chapter 9: Helping Students Master the Basic Facts
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
1) What statement most accurately describes a person who has mastered basic facts?
A) He or she can use a model or a picture to figure out the answer to a basic fact problem.
B) He or she has a conceptual understanding of the basic facts and can access her background
knowledge to, with some time, figure out the answer to a basic fact problem.
C) He or she has obtained a set of essential understandings and progressed through a set of stages
so that she just “knows” the answers to certain basic fact problems.
D) He or she can use a set of manipulatives and reasoning to figure out the answer to a basic fact
problem.
2) Three developmental phases for learning the basic facts are identified below. Which one is the
initial phase?
A) Drawing strategies.
B) Counting strategies.
C) Mastery.
D) Reasoning strategies.
3) Despite the fact that many learners in the past learned basic facts from memorization, there is
strong evidence that this may not be the most effective strategy for all of the following reasons
EXCEPT:
A) Many facts to memorize, and it’s an inefficient process.
B) When facts are memorized, students are less likely to check their work.
C) Counting by ones is inefficient, students delay developing efficient reasoning strategies.
D) Students are motivated when they are assessed with timed tests.
4) Research shows that guiding students to use effective reasoning strategies can help them
achieve mastery. Identify the explicit teaching strategy below.
A) Memorization of facts.
B) Guided invention.
C) Use of known facts and relationships.
D) Object or verbal counting.
5) Story problems can provide a valuable context to help students apply reasoning strategies for
computation for all of the reasons EXCEPT:
A) Provides relevance to student’s life.
B) Become better problem solvers.
C) Practice basic facts in the story.
D) Become proficient with algorithms.
6) Which of the problems below would provide an opportunity for students to apply the use of
the Anchor Number reasoning strategy?
A) In three weeks we will be going to the zoo. How many days until we go?
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B) Juan has 9 trading cards in his backpack and 6 more cards in his pocket. How many cards
does he have altogether?
C) 4 × 7 =
D) 13 – 5 =
7) The reasoning strategies below are used when a student knows a fact and uses that fact to
derive the unknown fact EXCEPT:
A) Double.
B) Near Doubles.
C) Think addition.
D) Making 10.
8) The ________ property is valuable because it cuts the number of multiplication/addition facts
to be learned in half.
A) Commutative.
B) Associative.
C) Zero.
D) Distributive.
9) Using a clock to learn basic facts is appropriate for what strategy?
A) Nifty nines.
B) Foundational facts.
C) Down under 10.
D) Think addition.
10) The reasoning strategies listed below are effective to help students learn the difficult facts
EXCEPT:
A) Doubling.
B) Close Facts.
C) Arrays.
D) Double and one more set.
11) Complete this statement, “Games can support basic fact fluency because…”
A) They can be more engaging for high performing students than other forms of practice.
B) They provide competition like timed tests.
C) They are more appealing to ELL and students with disabilities.
D) They infuse reasoning strategies and encourage students to self-monitor.
12) Three of the reasons below support why using timed tests is not effective for student mastery
of basic facts. Identify the one that supports the use of reasoning strategies.
A) More student-to-student interaction.
B) Does not assess four elements of fluency.
C) More meaningful time spent on other learning.
D) Does not affect student number sense.
13) Supporting older students who still struggle with basic facts can be done through the
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following steps EXCEPT:
A) Provide hope and build in success.
B) Inventory known and unknown facts.
C) Drill to strengthen memory and retrieval capabilities.
D) Provide engaging activities.
14) All of the following are recommendations that can support students’ ability to quickly recall
basic facts EXCEPT:
A) Drilling activities during mathematics instruction.
B) Involving families.
C) Using technology.
D) Encouraging students to self-monitor.
15) When assessing basic fact fluency identify an interview probe you could use to identify a
student’s efficiency.
A) Is this a good strategy?
B) Which pile of cards shows the facts you just know and which one shows the ones you used a
strategy?
C) How do you know this is correct?
D) Can you show me another strategy you could use?
16) Identify the reasoning strategy that would work for multiplication and division facts.
A) Double and doubles plus one.
B) Arrays.
C) Down under ten.
D) Combinations of 10.
17) The statements below would assist students in thinking about how to solve 42 ÷ 7 EXCEPT:
A) Seven times what is forty-two?
B) 7 × ________ = 42
C) What are the factors of 42?
D) 7 + 7 + 7 + 7 + 7 + 7 + 7
18) The following statements below are effective for teaching the basic facts EXCEPT:
A) Ask students to self-monitor.
B) Work on facts over time.
C) Practice in longer time frames.
D) Use technology.
19) Bowl a fact uses dice and numbered circles in bowling pin formation. If a student rolled a 5,
3 and 6, what equation would knock out the least number of bowling pins?
A) 5 + 3 – 6 =
B) 6 × 5 × 3 =
C) 6 + 5 + 3 =
D) 5 × 3 + 6 =
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20) This reasoning strategy is commonly used in high performing countries and takes advantage
of student’s knowledge of combinations. Identify the equation that represents this strategy.
A) 15 – 8, think 10 + 5 – 8, take from the 10: 10 – 8, add back on the 5 to get the answer.
B) 14 – 8, take away 4 to get to 10, then take away 4 more to get the answer.
C) 12 – 5, it takes 5 to get to 10 and 2 more to 12 and 5 + 2 = to get to the answer.
D) 7 + 6, 5 + 2 is seven and 6 is 5 + 1, add 5 + 5 and add the 2 and 1 to get the answer.
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
21) Discuss two or more reasons to approach multiplication facts through the foundational facts
2,5,0,1.
22) Identify and discuss three teaching recommendations that support students’ development to
mastery of basic facts.
