Math Methods Final

Gabby has 1/2 quart of water. She wants to pour 1/6 quart each into small glasses. How many glasses can she serve?

3 Glasses

Katelynn believe that any division problem involving zero will have an answer of zero. Sabrina says that any division problem involving zero will be undefined. Using the missing factor approach (and an explanation) to help clarify the students' beliefs.

6/0= is what? and what X 0=6

Amy decided to treat her family and friends to a night at the movies to see the latest Avengers movie. A total of 13 people attended, some were adults and others were kids. The cost of an adult ticket was $10. While kids tickets were $7. If the total spent on admission to the movie was $109, how many kids attend the movie?

7 kids

In order to master multiplication facts involving eight, Brittany wants to use the double, double, double strategy. Which of the following equations models that strategy?

8y=2(2y x 2y)

Which if the following statements is always true?

A fraction a/b can be modeled using equal sized-segments modeled on a number line.

Which structure of multiplication is personified in the following problem: Any has four bags of apples, There are six apples in each bag. How many apples does amy have altogether?

Additive Structure

Which of the following is true regarding divisibility?

All numbers that are divisible by 6 must be even numbers

According to Van De Walle, why are fractions hard?

All of the above

Algebraic thinking and reasoning involves...

All of the above

Equivalent fractions...

All of the above

In an effort to increase her third grade students conceptual understanding of division, Harlee should:

All of the above

When teaching fractions, teachers should...

All of the above

Which of the following "big ideas" should Zoe, a third grade teacher, consider when teaching fractions.

All of the above

Which of the following are ways in which algebraic thinking can be modeled in elementary schools?

All of the above

Which of the following should teachers do when teaching growing patterns?

All of the above

Which of the following students is using thinking strategies for multiplication?

All of the above students are using effective thinking strategies.

A productive belief about teaching and learning mathematics is...

All students need to have a range of strategies and approaches from which to choose in solving problems.

When teaching basic facts, your text recommends that teachers...

Ask students to self monitor Focus on self improvement Limit practice to short segments.

Eliciting and using evidence of student mathematical thinking includes all but one of the following:

Asking students to make math drawings or use visual supports to explain and justify their reasoning.

When helping elementary students to develop a conceptual understanding of number properties, it is helpful to:

Build them into students explorations with number sentences and allow them to discuss their thinking

Which of the following is true regarding a second graders knowledge of multiplication?

By the end of second grade, students should master the foundations for multiplicative thinking including skip counting and mastery of addition facts.

Which interpretation of multiplication is personified in the following scenario: Heidi's basketball team uniforms had three different pairs of shorts, four different jerseys and two different pairs of socks. How many different uniforms does the team have?

Combination Multiplication

Brittany says, "I know that 5 X 3 is 15, I don't have to worry about 3 X 5 because it is 15," She demonstrated an intuitive understanding of what property?

Commutative Property of Multiplication

Which structure of subtraction is personified here: G walk from her parking spot to class is 1/4 of a mile. M walk is 5/8 of a mile to class. How much longer of a walk does M have?

Comparison Structure of Subtraction

The following question personifies which interpretation of remainders: Emeralds soccer league for children had thirty-severn children try out for three teams. If 11 players are allowed on each team, how many teams can be formed?

Dispose-The reminder needs to be disposed

Zoe solved 16X12 this ways: 16X12=16(10+2)=160+32=192. What property is illustrated by her work?

Distributive

What is a obstacle in teaching and learning mathematics?

Dominant Culture Beliefs

Which of the following students correctly explained 0 / A?

Emerald, who said it can be thought of as: What number multiplied by A would have a product of zero, which means the answer is zero.

In the area model for fractions what defines the parts?

Equal Area

Which interpretation of remainders is personified in the question that follows: Jamie can put 6 pictures on a page in her photo album. If she has 82 pictures from her 21st birthday party, how many pages will she need?

Extra-the problem requires us to have an extra package.

Which structure of division is personified in the following question: Macy, Nichole and Lindey shared 39 Barbie Dolls, How many did each person get?

Fair Sharing Division

Division problems is which the size of the set is unknown are referred to as:

Fair sharing division

Real life connections to algebra are only appropriate for students studying algebra in middle or high school.

Fale

Effective teaching single digit multiplication or division does not require teachers to teach for conceptual understanding.

False

If A is a whole number then A X 1= 1 is always true

False

It is important for students to recognize that, regardless of the whole, 1/2 is always bigger than 1/3/

False

Students do not develop algebraic thinking skills until they enter middle school.

False

The main difference between an algebraic expression and an algebraic equation, is that algebraic expressions involve symbols and an equal sign.

False

When multiplying mixed numbers by fractions you will always get a product that is larger than your original mixed number.

False

Zero divided by five can be interpreted as, "What number multiplied by zero produces an answer of five.:

False

Which of the following students is mathematically correct in her view of division?

Gabby, who says, "Two-hundred sixteen divided by three is 72, because 210 divided by three is 70 and 6 divided by three is 2, so I just added those two quotients together."

Which of the following students best described the meaning of 2 1/2 X 1 1/4

Hannah who stated: It can be interpreted as two full groups of one and one-fourth plus an additional half-group of one and one-fourth.

Which of the equations below matches the following statement made by Amy: For any multiplication problem, if you take half of one factor and multiply it by doubled the other factor you will get the same answer you would normally get if you just multiplied the two numbers.

If A x B= C then 1/2 A x 2 B= c

When comparing fractions...

If the numerators are the same, the fraction with the largest equal sized-pieces is the larger fraction.

Haley made the following conjecture: "Whenever I multiply a number by zero, the product is always zero," Her conjecture demonstrates an understanding of what property?

Multiplication property of zero, zero property of multiplication.

If you are viewing a typical hundreds chart representing whole numbers, what expression would describe the number directly below and one step to the left of your starting number?

N+9

The division problem 1/2 / 3 can be interpreted as...

One-half is what part of three?

Which of the following is NOT an interpretation for Division?

Peasant Divison

Which of the following should Gracie, a 3rd grade teacher, avoid when teaching?

Proceeding through multiplication facts in order from 0 to 9

Which of the following is NOT a way for teachers to elicit and use evidence of student mathematical thinking?

Providing students with opportunities to use their own reasoning strategies and methods for solving problems

Which of the following students statements is always correct regarding their response to this questions: Which is greater N+2 or 2N?

Raegan, who states the N+2 will be greater if N is a whole number less than 2.

Which structure of subtraction problems is demonstrated in the following scenario? D and E have 3 quarts of liquid mis. They use some of it on wednesday, how much do they have left?

Take away

Zoe stated the sum of any natural number and zero will always be zero. Which of the following properties does her statement reflect?

The conjecture is false for while numbers

Which of the following creates a fraction in any given figure?

The parts of the figure are the same size but different shapes.

Any given fraction can be interpreted as a unit fraction or the sum of unit fractions if the numerator and/or denominator is greater than zero.

True

Drills are ineffective intervention for fourth grade students who have not mastered their multiplication facts.

True

Estimation is an important skill because it helps students access the reasonableness of answers using mental computations.

True

Flexible methods of computation in multiplication and division involve decomposing and composing numbers in a variety of ways.

True

For students to generalize an operation or pattern, they must view several example and be attentive to what is happening mathematically in the problem.

True

Foundations of algebra begin with a strong understanding of arithmetic.

True

Fraction strips and cuisenaire rods are commonly used to show length models for fractions.

True

Functions describe in concrete ways the idea that for very input there is a unique output.

True

Geometric patterns make good examples for elementary students because the pattern is easy to see and students can manipulate the objects.

True

If K represents an odd number, then K+2 and K-2 are also odd numbers.

True

If you divide two fractions that are less than one, it is possible that the resulting quotient could be two.

True

In division, the divisor can be subtracted from the dividend in groups of any amount.

True

In multiplication, there is a direct relationship between the area of any given rectangle and the product of it dimensions.

True

In order for a set of elements to be considered a pattern, the core of the set must repeat.

True

In the set model for fractions, the whole is defined by whatever value is determined by one set.

True

One way to address common misconceptions in addition and subtraction of fractions is to openly discuss whether responses are correct and why.

True

Rounding, as an estimation strategy, is a way of changing numbers in the problem to make computations easier to compute mentally.

True

Symbolism, especially involving equality and variables, must be well understood conceptually for students to be successful in mathematics, particularly algebra.

True

There are an infinite number of fractions between zero and one.

True

Third graders are expected to interpret the product of 5X7 as the total number of objects in 5 groups of 7 objects each.

True

Two equivalent fractions are two ways of describing the same amount by using different sized fractional parts.

True

Unifex cubes can be used to model how mixed numbers can be decomposed into fractions greater than one.

True

Using compatible numbers in estimation refers to changing the numbers to one that would make the problem easier to compute mentally.

True

Using the hundreds chart, a student can show that every other multiple of four is also a multiple of 8.

True

When you multiply two numbers, you can split one number into two parts, multiply each part by the other number and add them together.

True

When developing a written record for modeling division it is important to:

Use place value columns to help ensure that quotients are accurate.

If Meleah thinks 455X8 as being more than 3200 but less than 4000 because 400X8 is 3200 the student is:

Using front end estimation to estimate the product.

When developing the standard algorithm for division, teachers should...

Utilize the process of recording explicit trades because it is more mathematically meaningful than the more common "Bringing down."

When teaching basic multiplication facts teachers should...

Work on multiplication facts over time.

Devin, a second grade student stated, "When you add a number to another number then subtract the number you added, ups will get the number you started with." Which number sentence describes her conjecture?

X+Y-Y=X