EC-6 Math

Which of the following are correct? Select all answers that apply. A.1.045 < 1.45 The ones place is the same so look at the tenths place. 1.45 is greater than 1.045. B.1.504 > 1.50400 The ones place is the same so look at the tenths place, hundredths, thousandths, etc. These numbers are equal as the zeros at the end of the number on the right do not affect value. C.-1.045 < -1.405 D.1.54 > 1.45 The ones place is the same so look at the tenths place. 1.54 is greater than 1.45.

A.1.045 < 1.45 B.1.54 > 1.45

If a number ends in zero, what number(s) can it be divided by? A.2 A number that ends in zero is even and therefore divisible by 2. B.9 The number may or may not be divisible by 8, depending on what numbers precede the zero. C.4 The number may or may not be divisible by 4, depending on what numbers precede the zero. D.5 A number that ends in zero (or 5) is divisible by 5.

A.2 D.5

Which of the following is not a rational number? A.π The value of pi (π) never ends and does not repeat, making it irrational. B.0 C.-9.86398 D.843

A.π

Which of the following is the product of 2 odd numbers and 1 even number, each of which is greater than 1? A.20 The prime factorization of 20 is 2 × 2 × 5 which is 2 even numbers and an odd number. B.30 The prime factorization of 30 is 2 × 3 × 5 which satisfies the need for 2 odd numbers and an even number. C.15 D.25

B.30 The prime factorization of 30 is 2 × 3 × 5 which satisfies the need for 2 odd numbers and an even number.

Which of the following sentences is true? A.All rational numbers are integers. B.Irrational numbers often include a symbol, such as square root or pi. Irrational numbers can not be expressed as a ratio of two integers and are thus often written with a symbol or radical. C.Whole numbers and natural numbers both begin with zero. D.Integers include all natural numbers, whole numbers, and their opposites. Integers are positive and negative counting numbers and zero.

B.Irrational numbers often include a symbol, such as square root or pi. C.Integers include all natural numbers, whole numbers, and their opposites.

Which of the following is the best way for elementary students to be introduced to rectangular arrays? A.Giving them sample problems with arrays B.Using manipulatives such as 10-blocks to create their own arrays This gives them an opportunity to explore the concept concretely before having to put it into practice. C.Watch an online video over arrays D.During math games, use an array as part of a question

B.Using manipulatives such as 10-blocks to create their own arrays This gives them an opportunity to explore the concept concretely before having to put it into practice.

Mrs. Brooks sets up a few math stations for her kindergarten students. One station has a 10-sided dice, a bowl of beads, and a recording sheet with a row of 3 boxes. When the students arrive at this station, they roll the dice and place that number of beads in the center box of their recording sheet. Then, they create one number to the left and one number to the right of the number on the dice, using the beads, in the other two boxes on their recording sheet. They record all 3 numbers the beads represent, then repeat the activity. Which of the following topics are the students most likely exploring in this station? A.spatial concepts B.one more and one less In one more and one less relationships students subtract one and add one to a number. C.benchmarking numbers D.part-part-whole In part-part-whole relationships, students explore that numbers can be made of two or more parts.

B.one more and one less

Marsha asked all 72 children at recess and only ⅙ said that their favorite ice cream flavor was strawberry. Which of the following expression can be used to determine the number of children who told her strawberry was their favorite? A. 72 × 16.66 B.72 × 0.33 C.72 × 0.166 The fraction ⅙ can be converted to a decimal by dividing 1 by 6 for 0.166. This multiplied by the total number of children (72) will provide a solution for the number of children picking strawberry. D.72 × 33

C.72 × 0.166

Mr. Sudu is a waiter. His total weekly earnings consist of a wage of $6 per hour plus approximately 15% in tips on his total sales for the week. One week Mr. Sudu worked 25 hours and had total sales of z dollars. Which of the following represents his total weekly earning in dollars, E, for that week? A.E=6z+25E=6z+25 B.E=0.15 \left( z+150 \right)E=0.15(z+150) C.E=0.15z+150E=0.15z+150 To find Mr. Sudu's earnings, multiply the percentage in decimal form (0.15) by the total sales in dollars (z) and add this to his wage of 150, which is the product of his hourly rate (6) and the number of hours he worked (25). D.E=25 \left( 0.15z+6 \right)E=25(0.15z+6) This equation multiplies the number of hours he worked (25) by his tips plus his hourly earnings.

C.E=0.15z+150

Which of the following comparisons between equations and inequalities is NOT true? A. Equations contain only one possible symbol between each expression (=), while inequalities can contain four possible symbols between each expression (<, >, ≤, ≥). B.Equations typically have only one solution that makes the equation true, while inequalities typically have a solution set, or range of values, that make the inequality true. C.Equations are solved using inverse operations while inequalities cannot be solved with inverse operations. This is false; both equations and inequalities can be solved using inverse operations to isolate the variable. D.An equation is a statement that two expressions are equal, while an inequality is a statement that two expressions are not equal. This is true; equations are two expressions that are equal, and inequalities are two expressions that are not equal.

C.Equations are solved using inverse operations while inequalities cannot be solved with inverse operations. This is false; both equations and inequalities can be solved using inverse operations to isolate the variable.

For a student with strong addition skills, which subtraction algorithm is most suited their skill set? A.Trade First( algorithm for subtraction. The numbers are aligned automatically so that you can concentrate on solving the operations for each column. Borrowing is animated step by step so you can see what happens. Borrowing over several columns is also supported.) B.Counting Up This method adds numbers to the smaller number to reach the larger number. C.Left to Right Subtraction(while you will need to do the regrouping from right to left, after you have gotten the regrouping together, you can do the subtraction either from right to left as in the standard algorithm or from left to right.) This method only uses subtraction as an operation. D.Same Change Rule(In a subtraction problem, the "same change" rule says that we can add or subtract both numbers by the same amount without changing the difference. For example, consider the difference between 10 and 6. The difference is 4, because 10-6=4.)

Counting Up

Mrs. Luna tried flipping her classroom to teach common denominators, having students watch a lecture at home and then doing the homework practice during class. Many students did not watch the entire video because they thought they had the concept down after the first example. If she tries this again, how should she change her approach? A.Give prizes for those who watch the entire video. B.Keep students inside during recess if they did not watch the entire video so they can catch up. C.Have students create the video. Students cannot create a video or teach a topic that they have not learned yet. D.Provide a notes outline that needs to be filled in as they watch the video. This approach helps them stay engaged while watching.

D.Provide a notes outline that needs to be filled in as they watch the video

Which of the following is the best way for elementary students to learn inverse operations? A.Use word problems to illustrate how inverse operations work. B.Read the definition and take notes about operation inverses. C.Give students a worksheet packet with progressively harder questions. D.Use a number line to illustrate adding and subtracting the numbers in a fact family. This allows students to visualize the concept and understand opposite operations. Fact families are an example of inverse operations on a simpler level. The facts 2+3=5 and 5-3=2 are inverses of each other because the student has to put 2 parts plus 3 parts to equal 5 parts and in the subtraction fact a student would have to begin with the total (which is the opposite) and then subtract 3 parts.

D.Use a number line to illustrate adding and subtracting the numbers in a fact family.

The Parent Teacher Organization at Douglass Elementary baked cookies. The ingredients to make each batch of cookies cost $3. Each batch made 20 cookies. The PTO sold each cookie for $0.50. They produced b batches of cookies, and sold every single one of them. What is a valid expression, in terms of b, for the profit that the PTO made for their cookie sale? A.[(0.5)(20) + 3]b The $3 should be subtracted, not added, because it represents how much the ingredients for each batch cost, so it gets taken away from their profit. B.[(0.5)(3) + 20]b C.[(0.5)(3) - 20]b D.[(0.5)(20) -3]b In general, Profit = Revenue - Expenses. The revenue that the PTO brought in from their bake sale was $0.50 for every cookie sold. There were 20 cookies in each of b batches of cookies made and sold. Therefore, there were a total of 20b cookies produced and sold. With each cookie selling for $0.50, the total revenue from the sale was 0.50 × 20b, which can also be expressed as (0.5)(20b) or (0.5)(20)b. The expense to produce the cookies was $3 for every batch. Therefore, expenses = 3b. Profit can now be expressed as the difference between revenue and expenses: (0.5)(20)b - 3b. The answer choices show b factored out, and so the answer [(0.5)(20) -3]b can be selected.

D.[(0.5)(20) -3]b

The teacher provides a word problem for her students: Sandra is making sandwiches for her family's camping trip. She has 72 slices of turkey, 48 slices of cheese, and 96 pieces of lettuce. What is the greatest number of sandwiches she can make if each sandwich has the same filling of turkey, cheese, and lettuce? Which of the following mathematical concepts is she most likely teaching in this lesson? A.greatest common multiple The greatest common multiple is not a real topic. B.least common multiple C.least common factor D.greatest common factor

D.greatest common factor

Which of the names below is not a proper classification for 48/3 A.natural B.whole C.integer D.irrational Irrational numbers can not be written as a fraction. Therefore, this number is not irrational.

D.irrational

Before teaching multiplication, a teacher reviews skip counting on a number line. Students use different colored markers to show counting by 2s, 5s, and 10s. After introducing multiplication, they review their number lines and connect the concept to the jumps. Why did the teacher return to the number line as she taught? A.This tied the warm-up to the exit ticket. B.This allowed students to connect prior knowledge to new concepts with a visual example. This method allows them to "see" multiplication. C.Students could add decorations if they already understood multiplication. D.It provided remediation for struggling students.

This allowed students to connect prior knowledge to new concepts with a visual example.

Students are asked to identify the answer to a problem without actually solving it. She asks them: What answer is best when given the expression: 1/10 × 7/60 ? 7/600 7/10 1 7/60 70/60 What concept does she want them to recognize? A.Multiplication tables B.Base-10 multiplication C.Cross-simplifying fractions before multiplying D.When 2 fractions are multiplied, the product is smaller than either original fraction When 2 fractions are multiplied, their product will always be smaller than the original number.

When 2 fractions are multiplied, the product is smaller than either original fraction