End-of-Unit Assessment

1.

These four numbers are plotted on a number line: $\text{-}\frac {2}{3}, \frac{5}{8}, \text{-}\frac {3}{5}, \text{-}\frac {1}{2}$

From left to right, which is the correct ordering on the number line?

A.

$\text{-}\frac {1}{2}, \text{-}\frac {3}{5}, \text{-}\frac {2}{3}, \frac 5 8$

B.

$\text{-}\frac {1}{2}, \text{-}\frac {3}{5}, \frac 5 8, \text{-}\frac {2}{3}$

C.

$\text{-}\frac {2}{3}, \text{-}\frac {3}{5}, \text{-}\frac {1}{2}, \frac 5 8$

D.

$\text{-}\frac {3}{5}, \text{-}\frac {2}{3}, \text{-}\frac {1}{2}, \frac 5 8$

Answer:

$\text{-}\frac {2}{3}, \text{-}\frac {3}{5}, \text{-}\frac {1}{2}, \frac 5 8$

Teaching Notes

Students who select choice A have listed the negative fractions in the reverse order. Students who select choice B have listed all fractions in increasing order by magnitude, ignoring signs. Students who select choice D may have ordered the fractions based on their sign and their numerator.

2.

Diego’s dog weighs more than 10 kilograms and less than 15 kilograms.

Write two inequalities to describe the minimum and maximum values of $w$ , the weight of Diego’s dog in kilograms.

Answer: $w>10$ (or $10<w></w></span>) and <span class="math">\(w<15$ (or $15>w$ )

Teaching Notes

Watch for students who may have a misunderstanding of “minimum” or “maximum” in this situation. Students who reverse the order of the symbols may have a misunderstanding about the meaning of the inequality.

3.

Select all the numbers that are a common multiple of 4 and 6.

A.

1

B.

2

C.

10

D.

12

E.

24

F.

40

G.

60

Answer: D, E, G

Teaching Notes

Students who select choice A or B may have confused common multiples for common factors. Students who select choice C may have calculated $4+6$ and have a deep misunderstanding. Students who select choice F may have only found multiples of 4.

4.

Select all the true statements.

A.

Point

A

is at the opposite of 5.

B.

Point

B

is the opposite of point

E

.

C.

Point

C

is at

|\text-2|

.

D.

Point

D

is at

|1|

.

E.

Point

E

is the opposite of point -2.5.

F.

Point

F

is at

|\text-6|

.

Answer: A, D, E, F

Teaching Notes

Students who select choice B may not understand that the opposites must both be the same distance from 0. Students who select choice C may have ignored the absolute values lines.

5.

Which temperature is warmer: -2 degrees Celsius or -5 degrees Celsius?
Write an inequality to express the relationship between -2 and -5.
On the number line, graph all the temperatures that are warmer than -2 degrees Celsius.

Answer:

-2 degrees Celsius
$\text -2 > \text -5$ or $\text-5<\text-2$
Graph has an open circle at -2 and an arrow pointing to the right.

Minimal Tier 1 response:

Work is complete and correct.
Acceptable errors: No arrow on the graph, provided that the graph extends all the way to the right on the number line.
Sample:

$\text{-}2$ degrees Celsius
$\text{-}5 < \text{-}2$
Graph includes an open circle at -2 and extends fully to the right.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Graph has a closed circle or no circle at -2; answers to the first two parts are incorrect but consistent with one another.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: No graph; graph does not start or end at -2; graph has multiple errors including a closed circle at -2 and an arrow pointing to the left; work in the first two parts shows a lack of understanding about negative numbers.

6.

Draw polygon $ABCDEF$ in this coordinate plane given its vertices $A (\text -2,\text -3)$ , $B (0,\text -3)$ , $C (0,1)$ , $D (3,1)$ , $E (3,3)$ , and $F (\text -2,3)$ .

A coordinate plane with the origin labeled "O". Both axes have the numbers negative 5 through 5 indicated.

Answer:

Minimal Tier 1 response:

Work is complete and correct.
Sample: Polygon drawn as above. Vertices do not need to be marked as discrete points or labeled.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: One or two vertices are incorrect; vertices are correct but connected in the wrong order, for example, $A$ to $C$ to $B$ ; the points $A$ and $F$ are not connected, though the rest of the sides of the polygon are present.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Consistent errors, such as reversing the $x$ - and $y$ -coordinates; several missing vertices; vertices are plotted but the sides of the polygon are not.

Teaching Notes

Watch for students drawing just the vertices and not the polygon or not connecting point $F$ to point $A$ to complete the polygon.

7.

Lin spent a day hiking. This graph shows her elevation (in meters) at some different times. Negative values of $x$ represent the number of hours before noon, and positive values of $x$ represent the number of hours after noon.

<p>Coordinate plane, origin O, horizontal axis, x, labeled by ones, vertical axis, y labeled by twos. Points marked at (negative 5 comma 10), (0 comma 3), and (2 comma negative 2).</p>

What was Lin’s elevation at noon? Explain your reasoning.
At 10:00 a.m., Lin’s elevation was 70 meters. Add this point to the graph.
At 1:00 p.m., Lin was at sea level. Add this point to the graph.
Did Lin’s elevation increase or decrease between 7:00 a.m. and 2:00 p.m.? Explain your reasoning.
Lin’s elevation decreased from 2:00 p.m. to 3:00 p.m. Add a point to the graph that shows her possible elevation at 3:00 p.m. Explain your reasoning.

Answer:

30 meters. Sample reasoning: An $x$ -coordinate of 0 represents noon, and the point $(0,30)$ is on the graph.
The graph should include the point $(\text{-}2,70)$ .
The graph should include the point $(1,0)$ .
Lin’s elevation decreased. Her elevation changed from 100 meters to -40 meters.
Sample response: A point at $(3,\text{-}50)$ is graphed; Lin climbed downward, so her elevation will be more negative. A correct point will be $(3,y)$ with $y < \text{-}40$ .

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification.
Sample:

30, because the point $(0, 30)$ is on the graph
$(\text{-}2,70)$ plotted
$(1,0)$ plotted
Decreased. She went down 140 meters.
$(3,\text{-}50)$ plotted. Lin dropped further, so the new point is lower.

Tier 2 response:

Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
Sample errors: Misinterpretation of the y-axis scale so that each grid line is treated as one unit (or ten units); one problem part is incorrect.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: Does not understand that the zero mark is noon, but otherwise, interpretation of points shows understanding; $x$ - and $y$ -coordinates are consistently reversed.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: Work does not show understanding of the relationship between points on the graph and the situation.

Teaching Notes

Students plot points and interpret the meaning of points in all quadrants in context. They will need to think carefully about the meaning of the numbers on both axes, especially the $x$ -axis—this has time relative to noon, with negative numbers being before noon and positive numbers being after.