Math Content

What is the first step in solving this equation? 3(y + 4) - 2(3y - 1) = 103(y+4)−2(3y−1)=10

3y+12−6y+2=10

It took Julie ¾ of an hour to run 3½ miles. What is her average speed in miles per hour?

4 ⅔ miles per hour

Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip?

40 × .1 × 2

Bill went to the store to purchase new clothes for the upcoming school year. Bill purchased 8 shirts, 4 pairs of shorts, and 2 pairs of pants. If a single outfit consists of one shirt and either one pair of shorts or one pair of pants, how many outfits can Bill create with the clothes he purchased?

48

Which math expression is not represented by the array below?

48 × 1/8

Hailey's mom wants to help her practice using fractions. They decide to make their famous chocolate chip cookie recipe, but it will need to be tripled so that she will have enough for all of the third-grade students. The original recipe calls for 2 ½ cups of flour and ¾ cup of sugar. How much more flour than sugar does she need to make enough cookies for her grade?

5 1/4 cups

Asher makes $240 every pay period plus 15% on all sales. He determines his paycheck using the expression 240 + .15x. Which of the following is equivalent to Asher's expression?

5(48 + .03x)

Solve: [5(6+5) + 475]/{-3[3+ 7(5)] + 119}

106

Which of the following is the same as this expression? 1y + 8x -2 + 2x + 1 -3y1y+8x−2+2x+1−3y

10x−2y−1

The pictograph above displays data for sports equipment sold last Saturday at a certain sporting goods store. At this store, basketballs sell for $12, volleyballs sell for $15, and the total sales made last Saturday on the items shown in the pictograph was $212. If each soccer ball sold for d dollars, what is the value of d?

$10

What is the prime factorization of 36?

(2²) × (3²)

Solve: -4(3-5) + 2 -3[3+ 7(4)] + 8}

-2/17

If 6(3x+4) = 2(x+2) - 8, what is the value of x?

-7/4

Students are working on measurement principles. Kali measures a countertop in the classroom that is 5,743 mm long. Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm. How does the 3 in Kali's number compare to the 3 in Lauren's number?

1/100

Solve the following equation. Write the solution as a fraction in simplest form. 3(4x - 5) + 8 = 9(2x - 1)

1/3

If the number 180 is written as the product of its prime factors in the form a²b²c, what is the numerical value of a + b + c, where c = 5 and a and b do not equal 1?

10

Solve for a. 2a - 12 + a = 18

10

Which of the following is equivalent to the expression below? 2x+4y-3x+6

-x+4y+6

Which numbers are divisible by 2, 3, 6, and 7? Select all answers that apply.

1,260 252 2,772

Which of the following are correct? Select all answers that apply.

1.045<1.45

Lily wants to compare the ages of the children in her family. The table below shows the children's ages. Which of the following compares the children's ages correctly?

12 > 10 > 8

If \frac{1}{5}x + 3 = 651​x+3=6, what is the value of x?

15

Students are plotting improper fractions on a number line. Quincy places a fraction between the 5 and the 6 on the line. If the denominator is 3, which of the following could be the numerator?

17

Put these fractions, decimals and percentages in order from greatest to least: 15%, 0.34, 245%, 2 ¾, 1.5, 1/15

2 ¾, 245%, 1.5, 0.34, 15%, 1/15

Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½ inches. How much longer is the pencil than the pair of scissors?

2 ⅞ inches

Which expression can be used to solve the following word problem? Mrs. Bussey has planned a field trip for the third grade students. They have 2 buses and 49 people that need rides. There are also 2 coolers that will carry the lunches that need to be stored on the bus. On the morning of the field trip, 3 students are absent. How many people will be on each bus?

2/(49−3)​

Solve: [7(3 - 1)2 + (-8)]/{-3[3+ 6(½)] + 19}

20

Which expression can be used to solve the following word problem? John and Jose want to buy a pizza for dinner and then head to a movie. They will each pay for their movie ticket, which costs $12 each, and they will split the pizza cost of $9. John has $17 and Jose has $20. How much will Jose have left at the end of the evening?

20 - (9/2 + 12)

What is 19,968 rounded to the hundreds place?

20,000

What percent is represented by the shaded area of the decimal square?

24%

Simplify the expression: 4( 7x−3)

28x-12

When considering the addition problem 1/3 + 3/8, which of the following statements is true? Select all answers that apply.

3 and 8 are relatively prime The Least Common Denominator = 24

Consider the algorithm below: Step 1: Select a numerical value for n. Step 2: Subtract 4 from n. Step 3: Square the result Step 4: Multiply the result by 3 Step 5: End Which of the following is an equivalent algebraic expression?

3(n-4)2

If ⅙x-4=1 then x =

30

Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16

5x - 1 = 16

Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1)3x+2(3x-2)+5-2(2x+1)

5x-1

Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 113(2x+1)−5(x+4)=11

6x+3−5x −20=11

What is the value of the "7" in the number 432.0769?

7/100

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?

72 × 0.166

What percent is represented by the unshaded area of the decimal square?

76%

A teacher presents a right triangle to her class. She declares that the hypotenuse can be written as either 4x + 30 or as 6x + 14. Given this relationship, what is the value of x?

8

What is the value of the "8" in the number 17,436,825?

800

All of the following are equivalent to the number 16, except for which expression?

8^2

Which symbol most accurately reflects the relationship between the two numbers below? 0.8 ☐ 4/3

<

Which of the following sequences of steps will yield the valid solution for x to the equation -8 + 5x = 12?

Add 8 to each side of the equation, then divide by 5 on each side of the equation.

Which of the following sentences is true? Select all answers that apply.

All irrational numbers include a symbol such as square root or pi. Integers include all natural numbers, whole numbers, and their opposites.

Which of the names below is not a proper classification for 48/3?

irrational

The following word problem was given to Mr. Trout's fourth-grade class: The Hotel Vacay is hosting a Wintertime Brunch for families. Each child that attends gets to decorate a gingerbread house and use the ice slide 3 times. Every family gets 2 snowballs per person. If 108 people can be seated and there are an equal number of adults and children, how many gingerbread houses and snowballs do they need? Morgan solved the problem using this equation: 108/2 + 108 × 2 Julia solved the problem using this equation: 108 × 2 ½ Which child is correct?

Both children

For a student with strong addition skills, which subtraction algorithm is most suited their skill set?

Counting up

Mr. Jones has been teaching order of operations to his class and a group of students have mastered the concept quickly and easily. What would be the best way to offer them a challenge and increase the rigor of their lessons?

Introduce brackets and braces to go along with parentheses.

Jordan was simplifying the expression: 3x^{2}-4+8x-5x^{2}+63x2−4+8x−5x2+6. She simplified it to 8x^{2}+8x+108x2+8x+10, and then raised her hand to have her teacher check her work. Of the following, what is the best response from the teacher to Jordan?

Jordan is not correct. Every term has a sign to the left of it. When she combined 3x^{2}3x2 and -5x^{2}−5x2, she disregarded the sign of the 5x^{2}5x2 term and got 8x^{2}8x2 when she should have simplified it to -2x^{2}−2x2. She made the same mistake when adding the constants. She dropped the negative in front of the 4; -4 and 6 combine to 2.

A model of an equation is shown. What is the value of MM?

M=3

Bobby is buying gumballs for 7 of his friends. There are 51 gumballs before Bobby makes his purchase at the store. Bobby wants to give each of his friends the same amount of gumballs and not have any gumballs left. Which of the following approaches can Bobby use to find the greatest number of gumballs he can purchase to give his friends?

Make a list of the multiples of 7 and then purchase the highest multiple of 7 that is less than 51.

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?

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

Mrs. Marshall grades tests from the last unit and realizes most students are missing word problems because they do not identify the correct operation to use. They did demonstrate mastery on questions that provided the equation. How should she address this issue?

Provide a warm-up question each day and students must underline key terms that help decide what operation to use.

Miss Kelly has been teaching fractions and believes her students understand composing and decomposing fractions through the activities they have done. What activity would be best to informally assess their knowledge before moving on to the next lesson?

Provide a warm-up question that asks them to write one way to decompose 3/4

On a recent quiz in Mrs. Zehr's math class, the majority of students in the class incorrectly simplified the expression 2 \left( 3x-4 \right)2(3x−4), picking the answer choice 6x-46x−4. Of the following, which strategy for reteach would be the best course of action for Mrs. Zehr based on how her students answered this question?

Review the concept of the distributive property using real world examples: If a family meal at a fast food restaurant has 4 hamburgers, 3 chicken fingers, 2 fries, and 4 drinks, and someone orders 3 family meals, how many of each item will they receive? How can this be written mathematically using the distributive property?

Susan's second-grade class is studying fact families. Each student is purposefully assigned a fact card and asked to find other members of their family. Above are the cards received by 5 students. Students in the same fact family then work in a group to create fact family houses that are displayed at the school's Open House where parents come by to see the classroom and the student's work. Why is this an effective way to group students?

Students are discussing the concept before working on it.

Which sequence of steps, when completed, will solve the equation -3y + 4 = -2-3y+4=-2 ?

Subtract 44 from each side and then divide both sides by -3-3.

Mr. Harris assigns his students to create a factor tree of the products of a number. One student turns in the product factor tree of 32 shown here. Which of the following best describes the error in this factor tree?

The factor tree identifies the sums and not the product factors of many of numbers.

Jaylene is trying to solve the equation 5x+7=72. She raised her hand to get help from her teacher. When the teacher comes over, the following is written on her paper: Jaylene wants to know if her first step is correct. Of the following, which is the best teacher response to Jaylene?

The first step is incorrect; while subtracting 7 is the correct inverse operation, the subtraction property of equality states that in order to keep an equation balanced, you must apply the subtraction on both sides of the equal sign. She should also subtract 7 from 72.

The teacher provides a word problem for her students: Quacky Donald's Donuts sells glazed donuts in packages of six and donut holes in packages of 10. If Quacky Donald's Donuts sold the same number of glazed donuts and donut holes yesterday, what is the minimum amount of donut holes that Quacky Donald's Donuts sold? Based on the world problem above, which of the following concepts is the teacher most likely to teach in the lesson?

least common multiple

Mr. Yoder gave each of his students some Starbursts and some Skittles. He instructed the students to use the candy to set-up and solve multi-step equations, using the Starbursts to represent the x's, the Skittles to represent the constants, and different colors to represent positives and negatives. To solve the equations, students must determine how many Skittles are equivalent to one Starburst. Which of the following concepts is Mr. Yoder most likely working on with his students?

order of operations when solving equations

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?

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

For homework, Mr. Waters asked students to bring in 3 receipts from home. In class, they practiced rounding the prices of items and then totalling them to compare to the final price paid. What is the best reason this is good teaching method?

This makes connections between the classroom and the real world.

Which of the following is the best way for elementary students to learn inverse operations?

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

Which of the following is the best way for elementary students to be introduced to rectangular arrays?

Using manipulatives such as 10-blocks to create their own arrays

What is the next step in this lattice multiplication algorithm?

add the diagonals

Mr. Chappel hangs posters in each corner of the room with different names of number categories. One corner has a sign that says integers, another has a sign that says rational numbers, another says irrational numbers, and the last says whole numbers. Students are assigned a corner to start and on the first rotation they must add a definition to the sign. On the second rotation, they must add numbers that are examples to the sign. What should be the third rotation task?

adding a picture that helps students remember what is included in the number set

Which of the following situations might require the use of a common denominator? Select all answers that apply.

addition of fractions subtraction of fractions

What is the place value of the "9" in the number 6,587.9213?

tenths

What is x in terms of y for the equation: 74 - 6x = 9y

x = (9y -74) ÷ -6

Which of the following is not a rational number?

π

Students were asked to draw a picture representation of adding 2 fractions. What equation is represented by the picture below?

⅔ + ½ = 1 ⅙