MATH3033 Test 2 Study Guide
Lynne used the partitioning strategy to multiply 27 x 4. Which problem below shows this strategy?
27 x 4, 20 x 4 plus 7 x 4 =
Use inductive reasoning to predict the next three numbers in the pattern. 12, 15, 18, 21, 24,...
27, 30, 33
Which of the following open number sentences represents partition division?
3 x __= 18
When presenting addition problems, which of the following would you use last?
356 + 127 =
Fill in the blank to make a true statement and identify the property of whole-number addition that is illustrated. 7+ (4+9)= (7+___) + 9 Identify the property.
4; associative property
The integration of whole-number place-value involves using precise language. What statement below would confuse students about the groupings of tens and ones?
53 is the digits five and three
Fill in the blank to make a true statement and identify the property of whole-number addition that is illustrated. 6+ (8+2)= (8+2)+___ *Identify the Property*
6; Commutative Property of Addition
Write a related addition sentence. 15-y= 7
7+y=15
Use 10 is a different strategy than Making 10. It does not require decomposition or recomposing a number. Identify the equation below that shows Use 10.
9 + 6 = student thinks 10 + 6 is 16 and 9 is one less so the answer is 15
Which of the following is an example of a student demonstrating the skill of subitizing?
A student rolls a "5" on a die and is able to say it is a five without actually counting the dots.
What type of problem structure does this phrase describe "the first factor represents the number of rows and the second factor represents the equal number found in each row"?
Array
State the name of the property illustrated. 7+[8+(5)]= (7+8)+ (5)
Associate Property of Addition
Which of the following properties would this phrase describe "allows that when you multiply three numbers in an expression you multiply the first pair and then multiply that answer by the third"?
Associative
Three statements below support students in their development of fluency with basic facts. Identify the statement that does not support basic fact fluency.
Calculators can interfere with learning the basic facts and they should not be used until after the facts have been mastered.
Identify the activity below that should not be counted as the mathematics lesson for the day?
Calendar activities
Which of the following strategies is a foundational strategy that must precede the learning of the others?
Combinations of 10
State the name of the property illustrated. 3+ (4+8)= (8+4)+3
Commutative Property of Addition
Which problem structure is related to the subtraction situation "how many more?"
Comparison
Identify the statement below that would represent the child that has the level of understanding to work with the units of 10.
Counts tiles and makes 3 piles of tens and 1 pile of fives and says 10, 20, 30, and 5 more is 35
Marek was asked to multiply 34 × 5. He said, "30 × 5 = 150 and 4 × 5 = 20, so I can add them to get 170." Which property did Marek use to solve this multiplication problem?
Distributive property of multiplication over addition
Which of the following is not a strategy for supporting students' learning of basic facts?
Drill
Three of these statements are examples of effective formative assessment of basic facts. Identify the one that is often given as the reason given to use timed tests of basic facts.
Easier to implement
To find 9+6, a student says she thinks of 9+6 as 9+(1+5)=(9+1)+5=10+5=15. What property or properties is she using?
First she separated 6 into 1+5. Then she used the associative property to get the 9 and 1 together. Next, she added the 9 and 1. Finally she added 10 and 5.
Language plays and important role in thinking conceptually about division. Identify the statement below that would not support students thinking about the problem 4 ÷ 583.
Four goes into 5 how many times?
Base-ten riddles are a method for showing equivalent representations. Identify the base-ten riddle what would not equal 42.
I have 20 ones and 2 ten. Who am I?
Which of the following student explanations uses the Making 10 strategy to solve 8 + 9?
I took 9 + 1 and added on 7 to get 17.
Verbal counting has two separate skills. Using the string of counting words in the correct order and connect the sequence of counting words with the objects or set being counted. Identify the activity below that would support both skills.
Line up five chairs and five children and ask a child to count as each child sits down.
Think addition to solve a subtraction story would be effective for three of these problems. Which of the following would not be efficient?
Lynn had a collection of 52 pencil and she gave 6 of them to her best friend. How many pencils does she have now? (Because it is subtracting only a single digit number)
Which of the following statements would not be evidence of about teaching the basic facts effectively?
Memorizing facts is important to mastering the facts.
When asked to solve the division problem 143 ÷ 8, a student thinks, "What number times 8 will be close to 143 with less than 8 remaining?" Which strategy is the student using?
Missing factor
Identify the strategy that relies on the student knowing specific facts to use this to "plus one or minus one."
Near doubles
What are compatible pairs in addition?
Numbers that easily combine to equal benchmark numbers
Which of the following assessments can be used to determine students' understanding of base-ten development?
Observe students counting out a large collection of objects and see if they are grouping the objects into groups of ten.
To support knowledge about the commutative property teachers should do what to help the students' focus on the relationship?
Pair problems with same addends but in different orders
What method below would students be able to infuse reasoning strategies, select appropriate strategies and become more efficient in finding the answer?
Playing games
For problems that involve joining (adding) or separating (subtracting) quantities, which of the following terms would not describe one of the quantities in the problem?
Product
Effective basic fact remediation requires three phases of intervention. Identify the statement below that would not be a part of an intervention.
Providing more fact drill and worksheets
What is the main reason for teaching addition and subtraction at the same time?
Reinforce their inverse relationship
When students use the break apart of decomposition strategy with division, what must they remember?
Remember that you cannot break apart the divisor
What division approach is good for students with learning disabilities that allows them to select facts the already know?
Repeated subtraction
Problems that involve take away or take from involve a part of a quantity that is being removed from the start. Identify the name of the change problem structure that the start amount can be is the whole or the largest amount.
Separate
Algorithms should have the following characteristics. Which of the follow does not belong?
Series of steps (memorized)
Identify the reasoning strategy that is used in high performing countries that takes advantage of students' knowledge of combinations that make ten.
Take from 10
Which of the following statements about standard algorithms is true?
Teachers should spend a significant amount of time with invented strategies before introducing a standard algorithm.
Why are teaching students about the structure of word problems important?
The structures help students focus on sense making and the development of the meaning of the operations.
What is the correct way to say 32 using base-ten language?
Three tens and two ones
The zero and identity properties can often be challenging for students. Which of the following would help students understand the reason behind the products?
Use a number line and have students make 5 jumps of 0
Strategies for building a good lesson around a context problem include all of the following for student with the exception of which one?
Use only paper and pencil to solve
What is the best way to help students see the equal sign as a relational symbol?
Use the language "is the same as" when you read an equal sign.
Which of the following instructional activities would be an important component of a lesson on addition with regrouping?
Using base-ten materials to model the problem
Which of the following statements about names for numbers is true?
When a student writes "three hundred fifty-eight" as "300508," the student may be at an early stage in moving accurately between oral three-digit numbers and written three-digit numbers.
A child with number sense is best defined as having:
a flexibility with thinking about numbers and their relationships.
Each of the following equations is an example of one of the properties of whole-number addition. Fill in the blank to make a true statement, and identify the property. a. 3+4=——+3 b. 8+(6+7)=(6+7)+—— c. 8+——=8 d. 4+ (8+9)=(4+__)+9
a. 4; commutative property b. 8; commutative property c. 0; identity property d. 8; associative property
One fact in a fact family is 2+8=10. Complete part (a) below. a. What are the other three members of this fact family?
a. 8+2=10; 10-2=8; 10-8=2
Multiples of 10, 100, 1000, and occasionally other numbers, such as multiples of 25, are referred to as _____________ numbers.
benchmark
A pre-place-value understanding of number relies on children:
counting by ones.
One way to effectively model multiplication with large numbers is to:
create an area model using base-ten materials.
Here are some general principles for guiding student's development of computational estimation except:
focus on answers not on methods.
When asking children to make estimates, it is often helpful to:
give three possible ranges of estimates and ask them to pick the one that is reasonable.
Young children tend to have more difficulty learning the relationship of:
less than.
The following statements are true about the benefits of invented strategies except:
more teaching is required.
When adding 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to:
move down one row directly below the number.
When subtracting 10 on a hundreds chart, the most efficient strategy that demonstrates place value understanding is to:
move up one row directly above the number.
An effective way in which to support young children's learning of numbers between 10 and 20 and to begin the development of place value is to have the children think of the teen numbers as:
numbers that are ten and some more.
The three components of relational understanding of place value integrate:
oral names for numbers, written names for numbers, and base-ten concepts.
Proficiency with division requires understanding:
place value, multiplication, and the properties of the operations.
According to the learning trajectory for counting by Clements and Sarama (2009), a child who can count verbally in an accurate order, but not consistently, is called a:
reciter
Invented strategies are:
the basis for mental computation and estimation.
Children who know that the last count word indicates the amount of the set understand:
the concept of the cardinality principle.
Which reasoning strategy below would require students to know their addition facts to effectively use it for subtraction facts?
"Think-addition" and "missing addend."
Which of the following equations illustrates the associative property for addition?
(2+5) + 4 = 2 + (5+4)
Which of the following equations illustrates the distributive property of multiplication over addition?
2 (5+3)=2×5 + 2×3
Although all of these children would benefit, which of the following children would benefit the most from using a ten-frame?
Pedro, who does not know that 8 is 2 away from 10
