WorksheetsMathematics Teaching Ch.7-10 Test bank
Total questions: 56
Worksheet time: 28mins
What is the main goal of teaching mathematics to very young children according to the Learner Outcomes in Chapter 7?
To prepare them for advanced mathematical theories
To provide high quality number activities using a developmental approach
To focus solely on memorization of number sequences
To discourage the use of real-world activities in learning
Which of the following is NOT listed as a way to engage children in numeral writing and recognition?
Making numerals with clay
Using a calculator keypad as an instructional tool
Tracing numerals in sand
Writing them on the interactive whiteboard
According to the text, what is subitizing?
The ability to count objects one by one
Immediately recognizing a total number of objects in an organized collection without counting each one
A rote procedure for counting number sequences
The process of writing numbers from 1 to 120
What is an example of a rote procedure in early counting?
Subitizing
Counting the sequence of number words
Comparing quantities and describe relationships between numbers
Developing ways to connect mathematical ideas to the real-world
Which of the following is a research-based recommendation for high-quality learning activities in the first 6 years of life?
Limiting children’s experience and knowledge
Providing opportunities for children to explain their thinking as they interact with mathematical ideas
Avoiding the use of formal and informal experiences to strengthen children's problem-solving
Assessing children’s mathematical knowledge without considering strategies through observation and other informal practices
What is the key conceptual idea on which all other number concepts are developed according to the research-based learning trajectories?
The ability to count by ones
The meaning attached to the counting
The ability to perform addition and subtraction
The use of benchmark numbers
Verbal counting involves which of the following skills?
Producing a random string of counting words
Connecting the sequence in a one-to-one correspondence with objects in the set being counted
Counting the words in reverse order
Recounting the dots on a card
What is the purpose of using benchmark numbers 5 and 10 in learning?
To learn how to count by fives and tens
To solve complex algebraic problems
To use reference to solve different problems
To memorize the multiplication table
What does the part-part-whole concept help students understand?
How to break apart or build together a number without counting
How to count objects faster
How to perform complex calculations
How to memorize number facts
In the context of numbers 10 through 20, what pre-place-value concept should children be able to understand?
Being able to see 10 plus another number without having to think
Being able to count to 20 by ones
Being able to perform subtraction with numbers less than 20
Being able to write numbers from 10 to 20
What is the goal of missing-part activities in the learning material?
To teach students how to find the sum of two numbers
To help students identify the missing part of the whole
To encourage students to memorize addition facts
To practice counting objects in a set
According to the text, which of the following is NOT a common error or misconception in early number concepts?
Difficulty counting the teen numbers or decade numbers.
Writing the numeral backwards or reversing the digits in the teen numbers.
Using a calculator for simple addition and subtraction.
Not understanding the cardinality principle
What is the primary teaching tool to help children activate problem-solving strategies and gain a richer understanding of the operations, as mentioned in the section "Developing Addition and Subtraction Operation Sense"?
Multiplication tables
Contextual problems
Graphs and charts
Standard algorithms
Which standard-based development expectation is associated with K-2 students in the context of addition and subtraction?
Solving two-step problems using all four operations and developing an understanding of the relationship between multiplication and division
Expected to perform fluently with all operations using multi-digit number using strategies that consider place value and the application of the properties of the operations
Thinking about addition and subtraction situations involving adding to, taking from, putting together, and taking apart using increasingly sophisticated strategies
Explaining the interpretation of multiplicative situations as a comparison with a reference unit, solve multi-step word problems, interpret remainders, and learn algorithm for adding and subtracting multi-digit numbers.
Which of the following learner outcomes is related to the use of multiple representations to solve problems?
8.1 Demonstrate how to develop children’s skills in generalizing the problem structures with additive situations involving joining, separating, part-part-whole, and comparison where the unknown can be in any position.
8.2 Explain how students can apply the properties of the operations as strategies to either add or subtract.
8.3 Demonstrate how to develop children’s skills in generalizing the problem structures with multiplicative situations involving equal groups, comparison, area, and arrays where the unknown can be in any position.
8.5 Describe strategies for teaching students how to solve contextual problems.
Which of the following is an example of a contextual problem that helps students understand addition and subtraction?
Lou had 12 toy cars. Mia gave him 6 more. How many toy cars does Lou have altogether?
A rectangle has a length of 10 units and a width of 5 units. What is the area of the rectangle?
There are 4 apples and 3 oranges in a basket. How many pieces of fruit are there in total?
A train travels 60 miles in 2 hours. What is the speed of the train in miles per hour?
Which of the following is NOT a structure of addition problem?
Join
Separate
Part-part-whole
Comparison
What is a challenge for children when solving part-part-whole problems?
They can easily model it with a conceptual bringing together of quantities.
They know exactly how many counters to put down initially.
There is no action to model since it is a conceptual bringing together of quantities.
They are presented with too many strategies to solve the problem.
What does changing the number values in problems help students with?
It confuses students with too many numbers.
It gives them experience with a particular type of problem while keeping in line with their development.
It makes the problems easier to solve.
It helps students to avoid learning different strategies.
What is the purpose of using contextual problems in teaching students?
To make the problems more abstract and difficult.
To help students gain understanding by providing real world examples.
To limit the strategies that students can use.
To focus solely on the use of pronouns and names in problems.
Which of the following is a model-based problem for addition?
Using two different sets or groups to compare.
Thinking of addition as "take away."
Joining and separating in action situations.
Using physical representations such as words, pictures, and numbers to explain a subtraction problem.
What does the Commutative Property of Addition and Subtraction state about the order of addends?
The order of addends changes the answer.
The order of addends does not change the answer.
The order of addends is important for problem solving.
The order of addends affects the mastery of basic facts.
What are the three possibilities for the unknown in comparison problems where the comparison is based on one group being a particular multiple of the other?
Product, sum, difference
Product, group size, number of groups
Sum, group size, number of items
Difference, group size, number of groups
What does the Associative Property of Addition state about adding more numbers?
The sum changes when more numbers are added not matter what order.
The sum does not change when more numbers are added first.
The order in which numbers are added does not matter.
The sum only changes when numbers are added last.
In multiplication and division problem structures, what does the second factor tell us in equal-group problems?
The number of equal sets, groups, or parts.
The size of each set, group, or part.
The total number of items in all groups.
The difference between the groups.
What is the purpose of introducing symbolism in mathematics according to the learning material?
To make math problems more complex.
To help students understand that symbols represent something else.
To reduce the need for understanding context.
To focus solely on memorization of math facts.
What is the commutative property for multiplication?
The product remains the same when you multiply three numbers in any expression.
The array provides a clear picture that the two represent equivalent products.
The product changes when you change the order of numbers.
The array shows how to partition factors for division.
What does the associative property for multiplication state?
The product changes when you change the grouping of numbers.
The product remains the same when you change the grouping of numbers.
The product is always zero when you multiply numbers.
The product is always one when you multiply numbers.
According to the text, what should teachers focus on when teaching operations?
Sending the wrong message about doing mathematics.
Focusing only on the mathematical terminology.
Thinking about the answer before solving the problem.
Using large numbers in problems without strategies.
What is suggested to do with remainders in division problems?
Always round them up to the next highest whole number.
Discard the remainder.
Force the answer up to the next rounded whole number.
Think of remainders as "R 3" or "left over."
What is a model-based problem designed to do?
Confuse students with different operations.
Provide a visual and help with understanding.
Show students how to partition factors for division.
Teach students only about the structure of a problem.
Which of the following is a common misconception about addition and subtraction as mentioned in the document?
Students think that adding zero changes the number.
Students understand the commutative property of addition and subtraction correctly.
Students realize that subtraction always makes numbers larger.
Students know that the remainder must be included in the answer.
According to the document, by the end of which grade is multiplication and division fact mastery or automaticity often expected?
Grade 1
Grade 2
Grade 3
Grade 4
What is the three-phase strategy-based process mentioned in the document for developing fact fluency?
Derivation, memorization, and application
Addition, subtraction, and division
Illustration, justification, and reinforcement
Derivation, addition, and justification
What is the first phase in the developmental phases for learning basic facts?
Counting Strategies
Reasoning Strategies
Mastery
Guided Invention
Which strategy for teaching basic facts involves using story problems to improve students' accuracy and efficiency?
Memorization
Explicit Strategy Instruction
Guided Invention
Story problems strategy
What is a con of using memorization as an approach to teaching basic facts?
It does not work, showing a 2 of the developmental process
It supports student thinking
It does not work, showing a 2 of the developmental process
It takes more time to teach
Which approach to teaching basic facts is described as supporting student thinking and allowing them to choose a strategy?
Memorization
Explicit Strategy Instruction
Guided Invention
Story problems strategy
What is a reason NOT to use timed tests for assessing basic facts?
Timed tests do not assess the four elements of fluency
Timed tests help students think and choose a strategy
Timed tests are needed for students to master basic facts
Timed tests support student thinking
What is a disadvantage of the Guided Invention approach to teaching basic facts?
It is the easiest or most convenient to teach
It supports student thinking
It may be harder for students at lower levels
It helps students learn basic facts fast
According to the text, what is NOT recommended when teaching basic facts?
Involving families in the learning process
Using timed tests
Encouraging self-monitoring among students
Making fact practice enjoyable
What strategy is suggested to help students derive math facts?
Memorization of all facts in one session
Working on foundational facts first before moving to tougher ones
Public comparison of student mastery levels
Avoiding the use of technology
What is the role of technology in teaching basic facts, as mentioned in the text?
To limit the use of calculators
To provide immediate feedback and reinforcement
To replace the need for teachers
To encourage memorization of facts
What is the text's view on the use of calculators for mastering basic facts?
They should be used from the beginning
They should be used only after mastering the basic facts
They should never be used
They should be used based on the instructional goals of the day
What does the text suggest about making fact practice enjoyable?
It is not necessary for learning math facts
It should be done by turning math into a game
It should be avoided as it can distract from learning
It should be done only after all facts are memorized
According to Chapter 10, what is the foremost objective when integrating base-ten groupings with counting by ones?
To ensure that students can perform complex calculations.
To help students understand that grouping by tens is not just a rule that is followed, but also that any grouping can help, including all or some of the singles.
To make students memorize the number system.
To introduce the concept of fractions.
What are the two categories of concrete place value models mentioned in the text?
Proportional and non-proportional models.
Abstract and concrete models.
Digital and analog models.
Visual and auditory models.
What is a key role in making the connection between individual digits and numbers when integrating base-ten groupings with place-value notation?
The use of colors to differentiate numbers.
The physical coordination of digits for hundreds and thousands.
Language plays a key role in making these connections.
The ability to perform addition and subtraction.
Which of the following is an example of a non-proportional model?
A textbook illustration where ten is physically 10 times larger than one.
An abacus with same-sized beads on wires in different columns.
A set of blocks where each block represents a different number.
A digital number display.
What is the initial challenge for students when they start to see "ten" in base-ten groupings?
Understanding that "ten" can be both 10 ones and 1 ten.
Learning to count by tens instead of by ones.
Realizing that "ten" is the basis of our number system.
Recognizing the patterns in our number system.
What is the counting method that helps students understand the concept of grouping by tens?
Counting by fives
Counting by hundreds
Counting by tens
Counting by twos
Why might English Learners (ELs) become confused when learning place-value system?
Because they are not instructed to work together
Because the word grouping is frequently used
Because they may not understand the word grouping
Because the place-value system is not important
What is a characteristic of non-proportional models in teaching place value concepts?
Children can take the pieces apart or put them together
Children make sense of what they are doing
Children cannot make sense of what they are doing
Pieces are traded before 5 of one size have accumulated
What is a characteristic of pregrouped models in teaching place value concepts?
Children can take the pieces apart or put them together
Pieces are traded after 5 of one size have accumulated
Children may use them without really understanding what they are doing
Children always understand what they are doing
What do the cubes represent in the base-ten models activity?
Five single cubes form a bar of 5
Ten single cubes form a bar of 10
Ten single cubes form a bar of 100
Five single cubes form a bar of 10
What do the sticks represent in the base-ten models activity?
A bundle of five
A single stick of ten
A bundle of ten
Ten bundles of one
