One-Step Equations
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ISEE Lower Level: Quantitative Reasoning › One-Step Equations
Ava saves money and already has $8 in her jar. She wants $20 total, so $x + 8 = 20$. Subtract 8 from both sides to find $x$. What is the value of $x$ in $x + 8 = 20$?
8
12
18
28
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is x + 8 = 20, subtract 8 from both sides to find x = 12. In this specific problem, students encounter Ava's savings scenario where she has $8 and needs $20 total, requiring subtraction to find how much more she needs. Choice B is correct because 20 - 8 = 12, which accurately represents the solution after applying the correct inverse operation. Choice A (28) results from adding 8 + 20 instead of subtracting, while choices C (18) and D (8) represent other arithmetic mistakes. Teaching strategies include using visual models like number lines to show the relationship between parts and wholes, and encouraging students to think about what makes sense in the context of the problem.
Maya buys 4 notebooks for $3 each at school. She writes the equation $4x = 12$ for the total cost. Divide both sides by 4 to find $x$. Solve for $x$ in $4x = 12$.
3
8
16
48
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is 4x = 12, divide both sides by 4 to find x = 3. In this specific problem, students encounter the equation 4x = 12, which requires dividing both sides by 4 to solve for x. Choice C is correct because 12 ÷ 4 = 3, which accurately represents the solution after applying the correct inverse operation. Choice A (48) is incorrect because it results from multiplying 4 × 12 instead of dividing, while choice B (8) and choice D (16) represent other common arithmetic errors. Teaching strategies include practicing inverse operations through varied examples and reinforcing the concept of isolating the variable by performing the same operation on both sides of the equation.
Ella has $x$ stickers and gives away 5 stickers today. She still has 11 stickers, so $x - 5 = 11$. Add 5 to both sides to find $x$. If $x - 5 = 11$, what is $x$?
6
11
16
55
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is x - 5 = 11, add 5 to both sides to find x = 16. In this specific problem, students encounter Ella's sticker collection where she has 11 stickers left after giving away 5, requiring addition to find her original amount. Choice C is correct because 11 + 5 = 16, which accurately represents the solution after applying the correct inverse operation. Choice A (6) results from subtracting 11 - 5 instead of adding, while choices B (55) and D (11) represent multiplication errors or misunderstanding. Teaching strategies include using manipulatives like counters to model giving away and finding the original amount, reinforcing that addition undoes subtraction in equation solving.
Liam saves $5 each week for a new game. He writes the equation $5w = 35$ for his goal. Divide both sides by 5 to find $w$. Find the number that satisfies $5w = 35$.
7
30
40
175
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is 5w = 35, divide both sides by 5 to find w = 7. In this specific problem, students encounter Liam's savings equation 5w = 35, which requires dividing both sides by 5 to determine how many weeks (w) he needs to save. Choice B is correct because 35 ÷ 5 = 7, which accurately represents the solution after applying the correct inverse operation. Choice A (30) might result from subtracting 5 from 35, while choice D (175) comes from multiplying 5 × 35 instead of dividing. Teaching strategies include using real-world contexts like savings goals to make equations meaningful and encouraging students to verify their answers by substituting back into the original equation.
A recipe uses 6 cups of flour for one batch of muffins. You make 3 batches, so $3f = 18$ cups total. Divide both sides by 3 to find $f$. Solve for $f$ in $3f = 18$.
6
15
21
54
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is 3f = 18, divide both sides by 3 to find f = 6. In this specific problem, students encounter a recipe context where 3 batches use 18 cups total, requiring them to divide both sides by 3 to find the flour per batch. Choice A is correct because 18 ÷ 3 = 6, which accurately represents the solution after applying the correct inverse operation. Choice B (54) results from multiplying 3 × 18, while choice C (21) and D (15) represent other arithmetic errors or misunderstandings. Teaching strategies include using familiar contexts like cooking to make math problems relatable and emphasizing the importance of understanding what the variable represents in word problems.
A bus travels for 3 hours at the same speed. The total distance is 90 miles, so $3x = 90$. Divide both sides by 3 to find $x$. Solve for $x$ in $3x = 90$.
30
87
93
270
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is 3x = 90, divide both sides by 3 to find x = 30. In this specific problem, students encounter a bus traveling for 3 hours covering 90 miles total, requiring division to find the speed per hour. Choice A is correct because 90 ÷ 3 = 30, which accurately represents the solution after applying the correct inverse operation. Choice B (270) results from multiplying 3 × 90 instead of dividing, while choices C (87) and D (93) might come from subtraction or addition errors. Teaching strategies include using rate problems to reinforce the relationship between distance, speed, and time, and encouraging students to check reasonableness by verifying that 30 miles/hour × 3 hours = 90 miles.
Noah buys a toy for $9 and has $15 total. He writes $x + 9 = 15$ for his money. Subtract 9 from both sides to find $x$. What is the value of $x$ in $x + 9 = 15$?
4
6
9
24
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is x + 9 = 15, subtract 9 from both sides to find x = 6. In this specific problem, students encounter Noah's money situation where he spends $9 from his $15 total, requiring subtraction to find his original amount. Choice B is correct because 15 - 9 = 6, which accurately represents the solution after applying the correct inverse operation. Choice A (24) results from adding 9 + 15 instead of subtracting, while choices C (4) and D (9) represent other calculation errors. Teaching strategies include using money contexts to make equations concrete and teaching students to check their work by substituting the answer back into the original equation to verify that 6 + 9 = 15.
A smoothie recipe needs $x$ cups of yogurt plus 4 cups fruit. The total is 10 cups, so $x + 4 = 10$. Subtract 4 from both sides to find $x$. Solve for $x$ in $x + 4 = 10$.
2
4
6
14
Explanation
This question tests ISEE Lower Level quantitative reasoning skills: solving one-step equations for an unknown. Solving a one-step equation involves performing the inverse operation to isolate the variable. For example, if the equation is x + 4 = 10, subtract 4 from both sides to find x = 6. In this specific problem, students encounter a smoothie recipe where yogurt plus 4 cups of fruit equals 10 cups total, requiring subtraction to find the yogurt amount. Choice C is correct because 10 - 4 = 6, which accurately represents the solution after applying the correct inverse operation. Choice A (14) results from adding 4 + 10, while choices B (2) and D (4) might come from dividing or other calculation errors. Teaching strategies include using measuring cups or visual representations to make the problem tangible and reinforcing that subtraction undoes addition when solving equations.