Smarter Balanced Math Sample Questions: Grades 6-8

Last week we investigated several sample questions from the 3rd through 5th-grade band of math problems the students may encounter on the 2015 Smarter Balanced Assessment. This week, we will share some of the smarter balanced math sample questions released for grades 6-8:

(Note: the targeted grade level is indicated after each sample question number.)

Question #1 (6th grade):

Look at each expression. Is it equivalent to q1?

Select Yes or No for expressions A – C:

A) 6(6x + 4y) Yes No

B) 30(6x – 6y) Yes No

C) 12(x + 2y + 2x) Yes No

Explanation: Like the elementary level questions, students will need to understand that there is more than one possible “yes” answer (in this case, more than one equivalent algebraic expression), requiring test takers to truly understand factoring – along with having a strong sense of basic facts in order to multiply properly.

Question #2 (8th grade):

For each linear equation in the table, select whether the equation has no solution, one solution, or infinitely many solutions.

The following equations are given, and after each equation, students select “no solution”, “one solution”, or “infinitely many solutions”:

36x + 24 = 12(x + 2 + 2x)

x = x + 1

-12(x + 2) = -14x + 2

Explanation: This question exemplifies the increasing difficulty level of questions from grades 6 – 8, as “in grade 6 students generate equivalent algebraic expressions, in grade 7 these are expanded to include expressions with rational coefficients, and in grade 8 students use earlier strategies to solve increasingly complex equations” (from http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm).

Question #3 (7th grade):

The point on the number line shows the location of q37

Move each expression into a box to show its correct location on the number line.

(Students are then given the following expressions to place on the number line):

-3 ½ – 3 ½

-3 ½ – (-5)

-3 ½ + 3 ½

-3 ½ + (-5)

Explanation: For this problem, students must know how to add and subtract integers, along with understanding where each answer falls on the number line.

Question #4 (7th grade):

Different states have different sales tax rates. Three states have online calculators to compute sales tax on a purchase. Use the following steps to match each calculator with the correct state.

• Select Calculator A, B, or C.

• Enter a purchase price.

• Then select “Find Sales Tax” to compute the sales tax for that purchase price.

You may use the calculators as many times as you need to solve the problem to the right.

(Note: When students input a number for the purchase price and try out each calculator, they can see what the sales tax is for that particular calculator. For example, if a student inputs a $10 purchase price for “calculator A”, the sales tax shown is $0.63. They would then drag “Calculator A” to Kansas, with the 6.3% sales tax.)

Explanation: In this problem, students need to understand how to use the calculator tool, how to drag and drop, and they must also realize that there are more options than calculators to drag and drop too; in other words, some choices will not be used. Finally, this question is a reflection of real-world “online calculators” that people commonly use.

Question #5 (6th grade):

Jamal is filling bags with sand. All of the bags are the same size. Each bag must weigh less than 50 pounds. One sandbag weighs 57 pounds, and another sandbag weighs 41 pounds. Explain whether Jamal can pour sand from one bag to the other so that the weight of each bag is less than 50 pounds.

Explanation: In this question, students must explain their reasoning (by typing a response) regarding why they believe Jamal can or cannot pour sand from one bag to the other and still keep each bag’s weight under 50 pounds. This is a 1-point question, and to receive full credit, the scoring rubric requires that the student demonstrates “complete understanding … [and can provide] sufficient support for the conclusion (e.g., applying the mean, explaining how much weight would need to be transferred, or other valid supporting explanation)” (from www.smarterbalanced.org).

Conclusions and Recommendations:

Obviously, these questions are challenging since many of the tasks require multiple steps, sophisticated mathematical reasoning, and a firm knowledge of mathematical tools. Basic fact knowledge is still critical, yet students need to blend those skills with other concepts, and they will need to employ abstract reasoning as well.

Like the elementary sample problems, these questions also draw heavily from concepts students are expected to understand based on the Common Core Standards. Therefore, it is imperative that curriculum supervisors, principals, teachers, and any other related stakeholders have a clear understanding of those standards – and make appropriate instructional decisions in curriculum planning, textbook selection, lesson planning, etc.

It may seem like common sense, but it bears repeating: the more assessment, instruction, and instructional materials align, the greater chances students have for success. Moreover, teachers who are guided by the Common Core are naturally preparing their students for these tests, and they need not feel that they need to do “test prep” in such an isolated fashion. Of course, it still makes sense for teachers to help students become comfortable with the format of the test: typing answers, using the online tools and understanding the language of the directions.

If you are a teacher or parent in a Smarter Balanced state, feel free to share your comments about testing preparations for your child/children. We would love to hear from you!

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Julie Lyons