MATH 406 home chapter 11 & 12

More than 80% of all mathematical computations in daily life involve written computation and estimation, rather than mental computation.

2) False

All of the following are correct ways to decompose the number 500 EXCEPT:

4 hundreds. O tens, and 99 ones

The following is a pictorial model for an improper fraction. Which improper fraction matches the model?

4) 5/2

The place-value grid below contains a decimal. The decimal should be identified as:

43 and 7 hundredths

If you have 2/7 of a piece of chocolate, how many more pieces will be needed to make a whole?

5

According to your text, which of the following region models is easiest for children to partition?

?

Children tend to think of fractions as two whole numbers, the numerator and the denominator.

?

In the study of fractions, the concept of equivalence focuses on different representations of the same amount.

?

It is easier to compare two fractions that are represented by the same partitioning than two fractions that are represented by different partitioning.

?

The fraction c/d does NOT mean:

?

Which is NOT a correct way to divide 12 by 4?

?

Which of the following models would best illustrate the density property of fractions?

Not Are: Measurement

According to research, what percentage of instructional time is devoted to written computation?

Not: 10 - 30% Maybe 30-50

A student is given a problem that requires the addition of 236 and 349. The student student 6 + 9, which is 15: 30 + 40, which is 70; and 200 + 300, which is 500. The then adds 15, 70, and 500, and states that the sum is 585, This student's approach illustrates which strategy?

Not: Lattice addition

The shaded area in the following model illustrates what multiplication problem?

O3/5 x 4/5

A student is asked how 4 cookies could be divided evenly among 5 people. Which meaning of fractions is being emphasized?

Part-whole

A word problem indicates that in a classroom, there are 5 girls and 7 boys. The teacher and students represent this relationship as 5/7. Which meaning of fractions is being emphasized?

Ratio

Between any two fractions, there are an infinite number of fractions.

True

Children tend to use written computation even when they could use a more efficient method.

True

Different estimation strategies can work för the same problem.

True

In general, the amount of time spent on estimation has increased over time

True

Some countries use the comma for the decimal point.

True

The front-end estimation strategy will produce an answer that is always less than the actual.

True

Barry explained how he mentally solved the problem, 24 + 23. He said, "I added 20 plus 20 which makes 40, added 4 plus 3 which makes 7, and then added 40 plus 7 to get 47." Which mental computation strategy is Barry using?

adding from the ledt

A student solved the problem, 18 + 22 + 21 + 19 + 20, in the following manner: all the numbers are close to 20, therefore, 5 x 20 - 100. Which estimation strategy is he using?

clustering

Melissa explained how she mentally solved the problem, 36 + 23. She said, "I counted by tens, 36.46.56 and then counted by ones 57.58..59." Which mental computation strategy is Melissa using?

counting-on

Instructional goals for teaching computation include teaching children to:

develop competence with each of the computational methods determine the reasonableness ofa result 5) only B and C

Which of the following statements about the teaching of mental computation is not a recommendation?

encourage all students to use the same strategy for solving a problem

According to your text. which of the following should always be used to check the reasonableness of the result?

estimations

Some words used in connection with estimation include all of the following, except:

exact

According to your text, some countries say the denominator before they say the numerator.

false

To find equivalent fractions, you add the same number to both the numerator and denominator.

false

A student solved the problem, 132 + 222 + 348 + 435, in the following manner: 100 + 200 + 300 + 400. Which estimation strategy is he using?

front-end

All three meanings of fractions involve the idea of partitioning.

true

Which of the following is NOT true?

Between any two whole numbers, there is a whole number

Strong understanding of benchmark fractions such as 1/4, 1/3, and 1/2 can facilitate students':

Checking the reasonableness of computations with fractions

A circle is the easiest region model to partition.

False

According to your text, students who are proficient at written computations are also usually good estimators.

False

Students should be introduced to decimals only after they have mastered fractions.

False

The Common Core State Standards for Mathematics recommends that comparing fractions with different denominators should be a focus of grade 3.

False

The clustering estimation strategy is used to estimate a difference.

False

The long division algorithm familiar to Americans is also common throughout the developed world because mathematics is a universal language.

False

The parts of a region model must be congruent while the parts of an area model may not be congruent.

False

Jill has 2 feet of string. She wants to cut it into fourths. Which part-whole model will best illustrate this situation?

length

Jimmy explained how he mentally solved the problem, 11 + 12 + 19 18 He sald, "| added 11 and 19 to get 30 and added 12 and 18 to get 30. Finally, I added 30 and 30 together to get 60." Which mental computation strategy is Jimmy using?

making compatibles

Katrina explained how she mentally solved the problem, 37 + 44. She said, "I added 3 plus 37 which makes 40, and then added 40 to 40 which makes 80 and then added 1 more to get 81. Which mental computation strategy is Katrina using?

making tens

In regards to fraction symbols, which connection do most textbooks concentrate on?

model and symbol

A student is shown a rectangle divided into 5 equal sections. Two of ons are shaded, and the student is asked to identify the fraction that is indicated by the shaded region. Which meaning of fractions is being emphasized?

part-whole

Jenny has a circle that's been divided into six equal parts, She then shades in five of those parts. Which meaning of fractions does this best represent?

part-whole

Which is NOTa correct way to find 2/5 of 20?

partition the 20 into 2 equal groups and multiply the number in a group by 5.

When helping to develop students' understanding of fractions, which is the most appropriate developmental sequence?

portioning word counting symbols

A student is asked how 4 cookies could be divided evenly amount 5 people. Which mean of fraction is being emphasized?

quotient

Mrs. Lye took out a circle and divided it equally (same size and shape) into five sections. Which part-whole model best illustrates this situation?

region

All of the following are appropriate ways to use the calculator as a computational tool, except:

to facilitate a search for patterns