End-of-Unit Assessment

1.

These four numbers are plotted on a number line: $\text-\frac45$ , $\frac12$ , $\frac18$ , $\text-\frac34$

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

A.

$\frac12$ , $\frac18$ , $\text-\frac34$ , $\text-\frac45$

B.

$\text-\frac45$ , $\text-\frac34$ , $\frac12$ , $\frac18$

C.

$\text-\frac34$ , $\text-\frac45$ $\frac18$ , $\frac12$

D.

$\text-\frac45$ , $\text-\frac34$ , $\frac18$ , $\frac12$

Answer:

D

Teaching Notes

Students who select choice A have listed the fractions in the reverse order. Students who select choice B may believe that unit fractions with larger denominators are bigger than fractions with smaller denominators. Students who select choice C may have had trouble with the non-unit fractions or may have forgotten that “more negative” numbers are smallest.

2.

Select all the numbers that are a common multiple of 8 and 12.

A.

96

B.

80

C.

48

D.

32

E.

24

F.

20

G.

4

Answer:

A,C,E

Teaching Notes

Students who select choice B or D may have only found multiples of 8. Students who select choice F may have calculated $8+12$ and have a deep misunderstanding. Students who select choice G may have confused common multiples for common factors.

3.

Select all the true statements.

A.

Point $A$ is at $|\text-6|$

B.

Point $B$ is at the opposite of -4.

C.

Point $C$ is at $|\text-2.5|$

D.

Point $D$ is at the opposite of -3.

E.

Point $E$ is the opposite of point $B$ .

F.

Point $F$ is at $|6|$ .

Answer:

C,D,E

Teaching Notes

Students who select choice A may have ignored the absolute value lines. Students whole select choice B may have located -4 and not the opposite of -4.

4.

A youth size small T-shirt is designed to fit children who weigh between 43 and 55 pounds.

Write an inequality to describe $w$ , the weight of a child who has outgrown the small
T-shirt.
Write an inequality to describe $y$ , the weight of a child who is not ready for the small
T-shirt yet.

Answer:

$55<w></w></span> or <span class="math">\(w>55$
$y<43$ or $43>y$

Teaching Notes

Watch for students who may have a misunderstanding of “outgrown” or “not ready” in this situation. Students who reverse the order of the symbols may have a misunderstanding about the meaning of the inequality.

5.

Which elevation is higher: 8 feet below sea level or 13 feet below sea level?
Write an inequality to express the relationship between -8 and -13.
On the number line, graph all the elevations that are higher than 8 feet below sea level.

Answer:

8 feet below sea level
$\text-8 > \text-13$ or $\text-13<\text-8$
Graph has an open circle at -8 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:
- 8 feet below sea level
- $\text-8 > \text-13$
- Graph includes an open circle at -8 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 -8; 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 -8; graph has multiple errors including a closed circle at -8 and an arrow pointing to the left; work in the first two parts shows a lack of understanding about negative numbers.

6.

Draw polygon $UVWXYZ$ in this coordinate plane given its vertices $U(1,2)$ , $V(4,5)$ , $W(\text-1,5)$ , $X(\text-3,3)$ , $Y(\text-3,\text-4)$ , and $Z(1,\text-2)$ .

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, $X$ to $Z$ to $Y$ ; the points $U$ and $Z$ 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 $Z$ to point $U$ to complete the polygon.

7.

This graph shows the temperature (in degrees Celsius) at different times during one winter day. Negative values of $x$ represent the number of hours before noon, and positive values of $x$ represent the number of hours after noon.

What was the temperature at noon? Explain your reasoning.
At 3:00 p.m., the temperature was $7 ^\circ \text{C}$ . Add this point to the graph.
At 8:00 a.m., the temperature was $\text-1 ^\circ \text{C}$ . Add this point to the graph.
Did the temperature increase or decrease between 8:00 a.m. and noon? Explain your reasoning.
From 4:00 p.m. to 5:00 p.m., it got colder. Add a point to the graph that shows a possible temperature at 5:00 p.m. Explain your reasoning.

Answer:

10 degrees Celsius. Sample reasoning: An $x$ -coordinate of 0 represents noon, and the point $(0,10)$ is on the graph.
The graph should include the point $(3,7)$ .
The graph should include the point $(\text-4,\text-1)$ .
The temperature increased. The temperature changed from -1 to 10 degrees Celsius.
Sample response: A point at $(5,1)$ is graphed; It got colder, so the temperature will be lower than 4 degrees Celsius. A correct point will be $(5,y)$ with $y<4$ .

Minimal Tier 1 response:

Work is complete and correct, with complete explanation or justification.
Sample:
- 10 degrees Celsius, because the point $(0,10)$ is on the graph
- $(3,7)$ plotted
- $(\text-4,\text-1)$ plotted
- Increased. It went up 11 degrees Celsius.
- $(5,1)$ plotted. A correct point will be $(5,y)$ with $y<4$ .

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; 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.