Math Methods
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"
Assessing place value with the Digit Correspondence Task helps the teacher recognize the student's level of understanding. According to Ross, which of the following statements represents a full understanding of place value when using the task with 36 blocks?
"3 is correlated with 3 groups of ten blocks and 6 with 6 single blocks."
The benchmark numbers that are most important for very young learners are:
"5 and 10."
Simplify: 6×2+3÷3
13
A teacher wants to demonstrate the process that could have been used to solve the equation 8 + 5 = ? Which is not an appropriate representation of a correct process?
13=8+8+8+8+8
How is the number 12 represented in Base 6?
20 Base 6 has six digits, with the number six become 10. Counting in Base 6 would look like this: 0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, .... Starting with 1, count up twelve units. The number in Base 6 that represents 12 is 20.
Which of the following is a composite number?
21
What is the number 8 written in Base 3?
22 Base 3 has three digits, with the number three becoming 10. Counting in Base 3 would look like this: 0, 1, 2, 10, 11, 12, 20, 21, 22, 30, 31, .... Starting with 1, count up eight units. The number in Base 3 that represents 8 is 22.
Which of the following open number sentences represents partition division?
3 x ___ = 18
Which of the following numbers is correctly represented by prime factorization?
30 = 2 × 3 × 5
Steve is told that milk must remain at 50 degrees so it will not spoil and that a turkey must be cooked at 375 degrees for 2 hours. What is the difference in temperature of the milk and the turkey (while it is cooking)?
325 dregrees
How are 3 tens and 4 ones represented in a Base 10 system?
34 3 tens = 30; 4 ones =4. Put these values together to get 34.
When presenting addition problems, which of the following would you use last?
356 + 127 = ____
Simplify to a single term in scientific notation: (2 x 10)^3 x (6 x10^4)
4.8 x 10^8
A second grade student created the following model using Base 10 Blocks. 4-100's - 5- 10's - 6- 1's What number is represend by this model?
456
What is another way to write 4×4×4?
4^3
Which of these sets of numbers represents a true statement?
5 < 7
Which of the following is equivalent to 17(64 + 8^2)-4^3?
64 x 33
An example of a prime number is
67 Response Feedback: A prime number is a number whose only factors are one and itself. Even numbers greater than 2 can always be factored by 2, eliminating "682." "9" can be factored as 3 times 3 and "49" can be factored as 7 times 7. Therefore, "67" must be the right answer as it only has factors of 1 and 67.
Which groping is in order from least to greatest?
6^1, 2^3, 3^2, 4^2
Guadalupe Peak in Texas is 8,751 feet high. What is 8,751 rounded to the nearest hundred?
8,800
Wright and his colleagues (2006) identified a three-level progression of children's understanding of 10. Which of the following is not one of these levels?
A mastery concept of 10
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.
Which of the following statements is false?
After learning three-digit number names, students are easily able to generalize to larger numbers.
A fourth grade teacher is working with a group of students to find a measurement in ounces that is equal to 2.5 pounds. One student answers with 25 ounces, another student answers with 40 ounces, and the third student answers with 16 ounces. What step should the teacher take next?
Ask each student to explain their method of solving the problem.
Identify the mathematical properties involved in the following problem: (6 + 2) + 5 = 6 + (2 + 5).
Associative property of addition
Which of the following cultures is correctly paired with its mathematical contribution?
B & C B. Indian - Base 10 numbering C. Mayan - Calendars
A teacher is planning a lesson to introduce second graders to solving subtraction problems that require regrouping from the tens place to the ones place. Which of the math manipulatives listed below would be best for the teacher to use when presenting a lesson on subtraction with regrouping at the concrete level?
Base ten blocks
Which of the following should not be counted as the mathematics lesson for the day?
Calendar activities
In teaching through problem solving, students are engaged in doing all of the following except which?
Checking their answers with others or the textbook to confirm that it is correct
Which of the following statements about multiplication strategies is true?
Cluster problems use multiplication facts and combinations that students already know in order to figure out more complex computations.
Which problem structure is related to the subtraction situation "How many more?"
Comparison
Which of the following is a good strategy for teaching computational estimation?
Compatible numbers
A pre-place value understandinf of number relies on children:
Count by ones.
Which of the following statements is not true?
Developing procedural knowledge requires practice and drill.
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
A third grade teacher shows this math problem to her students: "Julianna, Margaret, Shonette, and Lisa are in a footrace. Julianna is 10 meters ahead of Margaret. Shonette is 5 meters behind Julianna, Margaret is 12 meters behind Lisa. In what order are the runners from first to last?" Which problem solving strategy is the most effective for solving this?
Draw a picture
Ms. Quinones is teaching her second graders to use calculators. To successfully use calculators, however, her students must be skilled in which of the following:
Estimation
Delia was asked to estimate 489 + 37 + 651 + 208. She said, "400 + 600 + 200 = 1200, so it's about 1200, but I need to add about 150 more for 80 + 30 + 50 + 0. So, the sum is about 1350." Which computational estimation strategy did Delia use?
Front-end
The National Research Council identified all but one of the following as a foundational area in mathematics content for young children. Which area of mathematics content is not one of the NRC's foundational areas?
Geometric Shape Core
Mrs. Wright asks her third graders the following question: "Does changing the order in which you subtract numbers change the answer?" Which of the following choices would allow Mrs. Wright to know that her students have employed mathematical reasoning to answer the questions?
Her students could justify their answers by showing different subtraction problems.
Which of the following is not a common type of invented strategy for addition and subtraction situations?
High-Low strategy
Which of the following tools is useful in developing relationships of numbers to 100 and beyond?
Hundreds chart
Which of the following is not a possible way in which to deal with a remainder in a division situation?
It is subtracted from the answer.
Connie had 5 marbles. Juan gave her 8 more. How many marbles does Connie have now?
Join Result Unknown 5 + 8 = ?
Connie has 5 marbles. Juan gave her some. She now has 13 marbles. How many marbles did Juan give her?
Join Change Unknown 5 + ? = 13
Connie had some marbles. Juan gave her 8 more marbles. Now she has 13 marbles. How many marbles did Connie have to start with?
Join Start Unknown ? + 8 = 13
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
In the problem, 5 + 6×3/2, what is the first operation which should be performed according to the order of operations?
Multiply
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.
A pre-kindergaten teacher is sittinf at a table with a small group of students. The teacher pours out a cup of blocks and ask a student to count the blocks with his pingers. The teacher is most likely assessing which skills?
One-to-one correspondednce
Which of the following is a common model to support invented strategies?
Open number line
Connie has 5 red marbles and 8 blue marbles. How many marbles does she have?
Part-part whole Whole Unknown 7 + 4 =?
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
Pairs of students take turns throwing a die. Each time the die is thrown, each student enters that number into one of four boxes he has drawn on his paper. ___ . ___ . ___ "After throwing the die four times, the students compare numbers. Whoever has the smallest four-digit number wins the game. This game will help students develop their understanding of:"
Place Value
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
An important early number concept is Part-Part-Whole. Identify the activity below that would provide children with experience in Part-Part-Whole.
Read the book Caps for Sale and have children use connecting cubes to make all combinations of the number 6.
Mr. Gomez plans to introduce the Aztec calendar below to his students. Introducing the Aztec calendar will help his students.
Recognize that different cultures have made contributions to the field of mathematics.
Which of the following statements is true about features of worthwhile tasks?
Relevant tasks include ones that are interesting to students and that address important mathematical ideas; they may come from literature, the media, or a textbook.
Which of the following is not a strategy for solving contextual problems?
Rely on locating key words in the problem.
Connie has 13 marbles. She gave some to Juan. Now she has 8 marbles left. How many marbles did Connie give Juan?
Separate Change Unknown 13 - ? =8
Connie has 13 marbles. She gave 5 marbles to Juan. How many marbles does she have left?
Separate Result Unknown 13 - 4 = ?
Connie had some marbles. She gave 5 to Juan. Now she has 8 marbles left. How many marbles did Connie have to start with?
Separate Start Unknown ? - 4 = 8
Which of the following reasons provides the best justification for why teaching through problem solving is effective for the struggling learner?
Students are able to pull from their knowledge base and use a strategy they like, which increases their chance of success and thereby motivates them to solve the problem.
Computational estimation refers to which of the following?
Substituting close compatible numbers for difficult-to-handle numbers so that computations can be done mentally
Ms. Dale asked her students to solve the following problem using a 4-step problem solving process: "Helen is helping her mother make aprons as Christmas presents for her six aunts. Helen is in charge of buying the buttons for the aprons at the craft store. Each apron needs eight buttons, and her mother wants an extra four buttons. How many total buttons should Helen buy?" As she was grading the students' work, Ms. Dale noticed Justin made the following mistake: ~1. How many buttons? -2. I will multipy the number of aprons by the numbre of buttons and add 4. -3. 6 aprons x 8 buttons = 46 buttons ~46+4=50 buttons~ -4. I multiplied 6 aprons and 8 buttons and got 46. Then i added the extra 4 and got 50. the answer is 50. How does this example demonstrate the importance of instituting a standard problem-solving process in a math classrooms?
Teachers can spot areas of student confusion and plan appropriate reteaching strategies.
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 is 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.
Based on your interpretation of implementing classroom discussions, which of the following teacher actions do you think best supports student learning?
The teacher hears an incorrect solution and asks students what they think about the idea.
Which of the following is a highly successful strategy for students solving subtraction situations?
Think Addition
What is the correct way to say 32 using base-ten language?
Three tens and two ones
A first-grade teacher wants to use manipulatives to demonstrate basic addition and how numbers are constructed. Which manipulative would be best suited for this lesson?
Unifix cubes
An example of an extension of students' knowledge of basic facts and place value to solving two-digit addition problems is the:
Up Over Ten strategy.
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.
Use this venn diagram to answer the question that follows. If various numbers were placed on this diagram according to their factors, where would the number 28 be placed?
a
A child with number sence is best defined as having:
a flexibility with thinking about numbers and their relationships.
When teaching computational estimation, it is important to:
accept a range of reasonable answers.
Multiples of 10, 100, 1000, and occasionally other numbers, such as multiples of 25, are referred to as ____________ numbers.
benchmark Benchmark numbers are special numbers that focus on ten-structured thinking, that is, flexibility in using the structure of tens in our number system. They are multiples of 10, 100, and 1000 (place value positions) and occasionally other special numbers, such as multiples of 25.
One-to-one correspondence allows young children to easily:
compare quantities.
One way to effectively model multiplication with large numbers is to:
create an area model using base-ten materials.
As reported by the National Mathematics Advisory Panel, what a 5- or 6-year-old child knows about mathematics not only predicts the child's future math achievement, but also forecasts:
future reading achievement.
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. Response Feedback: Producing an estimate is a difficult task for young children. They do not easily grasp the concept of "estimate" or "about." To support them, provide a range of options for them to select from. This will help them see that the term "about" can embrace a group of numbers and not a single focused answer. The more diverse the three choices of possible ranges, the easier it will be for students to make a decision on an initial estimation.
Young children tend to have more difficulty learning the relationship of:
less than.
Graphing activities are particularly valuable because they give children opportunities to:
make comparisons of numbers that have meaning to them.
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.
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 10 and some more.
Teachers and students should orally refer to the manipulatives for ones, tens, and hundreds as:
ones, tens, and hundreds.
The three components of relational understanding of place value integrate:
oral names for numbers, written names for numbers, and base-ten concepts.
The following bar diagram is an example of: 200 + 40 +9 +249 ____________________________________________ 5 1247 247 47 -1000 -200 - 45 _________ . ________ _______ 247 . 47 . 2
partial quotients
Proficiency with division requires understanding:
place value, multiplication, and the properties of the operations.
When introducing place value concepts, it is most important that base-ten models for ones, tens, and hundreds be:
proportional (model for a ten is 10 times larger than the model for a 1).
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. A reciter is a child who verbally counts using number words, but not always in the correct order.
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.
The following model (grid paper) can be used to represent:
the product of two 2-digit factors as the sum of partial products.
Computational estimation is best described as:
using easy-to-handle parts of numbers or substituting close compatible numbers for difficult-to-handle numbers so that computations can be done mentally or answers can be assessed for reasonableness.
