# help thinking of conceptual or open-ended Intro Algebra and Intermediate Algebra test questions

Like many other math teachers, I am teaching remotely in Spring term. I teach Math 60 (Intro Algebra) and Math 95 (Intermediate Algebra) at a community college. In the age of math solving technology (like Photomath), I want to create more conceptual or more open-ended test questions, so the student can't just point their phone at an equation and have the phone solve it for them. (Yes, I'm being quite cynical here!)

Here are some of the topics I teach:

1. Solve basic linear equations, like 8x + 5 = 6x - 5
1. Factoring
2. Add rational expressions, like 1/x + 1/(x+1)
3. Solve rational equations.

One idea I have is giving two different proposed solutions to an equation, like #1 above, where each proposed solution is either correct, has a small error, or has a big error.

Does anyone have any creative ideas?

• I have no advice. I can only lament about 8-grade stuff being taught in college. Ok, community college, but still a tertiary ed institution. Sigh. Mar 24, 2020 at 20:11
• @RustyCore Generally the way this works is that the students don't get any credit-toward-a-degree for these classes. So it's more of a nice service that the colleges offer rather than a sign of the degradation of society. Mar 24, 2020 at 20:40

I taught algebra at a community college for several years (recently switched to CS), and this was largely my goal for weekly quizzes (given in online multiple-choice format via Blackboard). Roughly half the questions were directly computational or symbolic manipulations, with the other half an attempt at being conceptual. I've taken my quiz source document for the intermediate algebra class and cut it down to most of the conceptual prompts/examples here:

Name the result of the operation. 1) The result of a subtraction operation is called a ____.

Identify the correct word. 2) Any written combination of numbers and operations (with no equal sign) is called a(n) ____.

Write the sentence as an equation, using n to represent the unknown number. 5) Eight times the difference of 12 and a number is -56.

Identify the false statement regarding signed numbers. 6) Select the statement regarding signed numbers which is false. A) adding a positive and a negative may result in a number of either sign B) multiplying two negatives results in a positive number C) multplying a positive and a negative results in a negative number D) adding two negatives results in a positive number

Characterize the set of numbers. 11) When a rational number is expressed in decimal notation, which of the following is not a possibility? A) an infinite, non-repeating decimal B) a terminating decimal C) a repeating decimal D) a non-terminating decimal

List all numbers from the given set that are of the indicated type. 12) Rationals in {9, -15, 0, (2/3), 0.overbar(5), 0.47, π}

Identify the property illustrated by the statement. 13) (4 ∙ 3) ∙ 2 = 4 ∙ (3 ∙ 2)

Find the inverse. 14) Find the multiplicative inverse of 3(8/9).

Analyze the form of the expression. 15) Why can we not say that this expression is "simplified"? 3((2/3)x + 8) + (6/15)x A) fractions not reduced B) parentheses not removed C) like terms not combined D) all of the above

Identify the incorrect rule of exponents. 16) According to the Fundamental Rule of Exponents, which of the following shortcuts on same-base powers is incorrect? A) exponents add powers B) multiplying adds powers C) division subtracts powers D) radicals divide powers

Identify the correct rule of distribution. 17) According to the General Distribution Rule, which of the following operations will distribute piecewise? A) exponents over addition B) radicals over subtraction C) radicals over multiplication D) exponents over subtraction

Identify the polynomial by its degree and number of terms. 21) 15s^2 + 9s + 6 A) quadratic monomial B) linear trinomial C) cubic binomial D) quadratic trinomial

Identify the well-defined real number. 31) Which of the following is well-defined as a real number? A) sqrt(-9) B) (6/0) C) 0 to power of ((-3)) D) (0/8)

Find any real number for which the rational expression is undefined. 32) (25x to power of ((2)) - 64/2x - 8)

Indicate the quadrant in which the point belongs. 46) (11, -7)

• Thanks for these suggestions. I came up with a few additional question outlines: 1. [Solve for x, or factor, or whatever.] Ron solved it this way. Draco solved it this way. Who is correct? Both? Neither? Explain why. 2. Create a binomial with a GCF of 8x, or create a linear equation whose solution is x= 4.
– Kara
Apr 1, 2020 at 3:12