claim 1 smarter balanced sample items high school - target i solve equations and inequalities in one...
TRANSCRIPT
![Page 1: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/1.jpg)
Claim 1Smarter Balanced Sample Items
High School - Target I
Solve equations and inequalities in one variable.
Questions courtesy of the Smarter Balanced Assessment Consortium Item Specifications – Version 2.0Slideshow organized by SMc Curriculum – www.ccssmathactivities.com
![Page 2: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/2.jpg)
Enter the value for x that makes the given equation true.
48 = x − 3
Question 1a
![Page 3: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/3.jpg)
Rubric: (1 point) The student enters the correct value for the variable x.
Answer: 51
Question 1a Answer
![Page 4: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/4.jpg)
Enter the value for x that makes the given equation true.
20x 5(6x + 4) = 4x 6
Question 1b
![Page 5: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/5.jpg)
Rubric: (1 point) The student enters the correct value for the variable x.
Answer: 1
Question 1b Answer
![Page 6: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/6.jpg)
Solve the inequality for n. 45 ≥ −15n
Question 2a
![Page 7: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/7.jpg)
Rubric: (1 point) The student enters the correct solution to the inequality.
Answer: n ≥ −3
Question 2a Answer
![Page 8: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/8.jpg)
Which inequality represents all possible solutions of 3n < 12?
A. n < 36
B. n < 4
C. n > 36
D. n > 4
Question 2b
![Page 9: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/9.jpg)
Rubric: (1 point) The student selects the correct option.
Answer: D
Question 2b Answer
![Page 10: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/10.jpg)
Solve the inequality for w.
2w + 17 13
Question 2c
![Page 11: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/11.jpg)
Rubric: (1 point) The student enters the correct solution to the inequality.
Answer: w 2
Question 2c Answer
![Page 12: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/12.jpg)
Evaluate the claim as True or False for each set of numbers. Claim: All members of the set are solutions for w in the given inequality.
20 − 5(6 + 4) ≥ 4 − 6 𝑤 𝑤 𝑤Decide if all members of each set are solutions. Click True or False.
Question 2d
![Page 13: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/13.jpg)
Rubric: (1 point) The student correctly matches true or false to each option.
Answer: F, F, F, T, T
Question 2d Answer
![Page 14: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/14.jpg)
Question 3a
![Page 15: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/15.jpg)
Rubric: (1 point each) The student enters the correct value for B.
Answers: Example 1: 2Example 2: 80Example 3: 100
Question 3a Answer
![Page 16: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/16.jpg)
Question 3b
Solve the given equation for x.
20xB=
![Page 17: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/17.jpg)
Rubric: (1 point) The student enters the correct equation.
Answer: x = 20B
Question 3b Answer
![Page 18: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/18.jpg)
Question 3c
Solve the given equation for x.
6x + Cx = 11
![Page 19: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/19.jpg)
Question 3c Answer
Rubric: (1 point) The student enters the correct equation.
Answer: 116
xC
=+
![Page 20: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/20.jpg)
Question 3d
![Page 21: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/21.jpg)
Question 3d Answer
Rubric: (1 point each) The student enters the correct solution.
Answer: Example 1: or 0.01Example 2: 25
1100
![Page 22: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/22.jpg)
Question 4a
![Page 23: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/23.jpg)
Question 4a Answer
Rubric: (1 point) The student enters the solution(s) to the equation.
Answer: and 3
5
3
5
![Page 24: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/24.jpg)
Question 4b
![Page 25: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/25.jpg)
Question 4b Answer
Rubric: (1 point) The student enters the solution(s) to the equation.
Answer: and i3
5 i3
5
![Page 26: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/26.jpg)
Consider the equation: x2 − 14x + 45 = 0
Part A: Drag numbers into the boxes to rewrite the equation in the form shown.
Part B: Use the Add Point tool to place a point for each solution on the number line.
Question 4c
![Page 27: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/27.jpg)
Rubric: (2 points) The student correctly rewrites the equation and correctly places both points on the number line (1 point) The student correctly rewrites the equation or correctly places both points on the number line(e.g., 7; 4; points at 5 and 9).
Answers:Part A: 7, 4Part B: 5 and 9
Question 4c Answer
![Page 28: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/28.jpg)
Part A: Drag and drop numbers from the list to enter an equivalent equation for 3x2 + 2x − 225 = 0 into the quadratic formula.
Part B: Use the Add Point tool to place a point for each solution on the number line.
Question 4d
![Page 29: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/29.jpg)
Rubric: (2 points) The student produces the correct quadratic formula and two correct values for n. (1 point) The student produces the correct quadratic formula or two correct values for n.
Answer:
Question 4d Answer
![Page 30: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/30.jpg)
Drag and drop numbers from the list to enter an equivalent equation for 2(x + 1)2 = −3 into the quadratic formula.
Question 4e
![Page 31: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/31.jpg)
Question 4e Answer
Rubric: (1 point) The student produces the correct quadratic formula.
Answer: ( ) ( ) ( )( )( )( )( )
24 4 4 2 5
2 2x
- ± -=
![Page 32: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/32.jpg)
Question 4f
Use the drop down menu to enter an equivalent equation for n2 −3n = 10 by factoring, and the solutions for n and n2.
![Page 33: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/33.jpg)
Rubric: (2 points) The student correctly factors the equation and provides the correct values for n. (1 point) The student correctly factors the equation or the student provides both values for n.
Answer: +1, +2, +1, 5; 2, +5
Question 4f Answer
![Page 34: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/34.jpg)
Which equation has no real solutions?
A. 4x2 + 4x − 24 = 0
B. x2 + 4x + 16 = 0
C. 5x2 + 3x − 1 = 0
D. 3x2 − 4x + 1 = 0
Question 5a
![Page 35: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/35.jpg)
Rubric: (1 point) The student selects the correct option.
Answer: B
Question 5a Answer
![Page 36: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/36.jpg)
What are the solutions for the given equation?
x2 + 4x + 16 = 0
A. x = −2 ± 4i √3
B. x = −2 ± 2 √3
C. x = −2 ± 2i √3
D. x = −2 ± 4 √3
Question 5b
![Page 37: Claim 1 Smarter Balanced Sample Items High School - Target I Solve equations and inequalities in one variable. Questions courtesy of the Smarter Balanced](https://reader035.vdocuments.us/reader035/viewer/2022062500/5697c00a1a28abf838cc7b2c/html5/thumbnails/37.jpg)
Rubric: (1 point) The student selects the correct option.
Answer: C
Question 5b Answer