Mathematics 6
Items to Support Formative Assessment
Unit 1: The Number System
6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants
of the coordinate plane. Include use of coordinates and absolute value to find distances between
points with the same first coordinate or the same second coordinate.
6.NS.C.8 (Pre-Assessment problem)
On a map, Shanti’s house is located at (-5, 6), Clarksville Middle School is located at (-5, -4), and
Clarksville Elementary school is located at (4, -4).
a. How far is Shanti’s house and Clarksville Middle School?
b. What is the distance between Clarksville Middle School and Clarksville Elementary school? Show a
different method than the strategy you chose in Part a.
Solution:
Graphing method-use graph paper and plot points, students can count the units to arrive at the answers.
Distance from Shanti’s house to Clarksville Middle School is |6| + |-4|= 10
Distance from Clarksville Middle School to Clarksville Elementary School is |-5|+ |4| = 9
6.NS.C.8 (Post-Assessment Problem)
Jose drew the points A (5, 2), B (3, -3), C (3, 4), and D (-1, 2). Jose says that the distance between A
and D is 4 and the distance between B and C is 7.
Plot all four points and justify if Jose is correct or incorrect in his thinking.
Solution:
I plotted the points and counted from point A (5, 2) to point D (-1, 2) and it was 6 spaces. Jose was not
correct when he said that the distance was 4.
Jose was correct when he said that it was 7 spaces from point B (3, -3) to C (3, 4).
6.NS.C.8 (Short Answer)
When an archaeologist finds a site to dig they have to be organized and precise with their plan. Grids are
often used to help maintain accuracy and consistency. When something is found it is located on the grid
and given a number. The location of an object is as important as the object. To begin, the archeologist
selects a point at the dig site to serve as the origin. From that point they mark the grid with 1-meter squares.
When an artifact is found in a square the ordered pair is recorded. Use coordinate grids to locate the
following objects: a burial site at (5, 4), a spear at (5, -5), a awl at (-2, -5), a effigy at (-2, 4). What is the
distance for the following:
• From the Burial Site to the Effigy
• From the awl to the effigy
• From the Burial Site to the spear.
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Solutions:
From the Burial Site to the Effigy (5, 4) to (-2, 4) so 5 + -2 = 7 meters
From the awl to the effigy (-2, -5) to (-2, 4) so -5 + 4 = 9 meters
From the Burial Site to the spear (5, 4) to (5, -5) so 4 + -5 = 9 meters
6.NS.C.8c Shape Distance
1. How far on the coordinate plane has the original rectangle been moved? Use what you know about
distance and the coordinate plane to explain your answer.
2. How far on the coordinate plane has the original triangle been moved? Use what you know about
distance and the coordinate plane to explain your answer.
3. Can your distance be a negative number? Why or why not? What math skills tie closely with this
question?
Solutions:
1. The rectangle moved 6 units to the right. Students may say they counted or identified coordinate pairs.
2. The triangle moved 7 units down. Students may say they counted or identified coordinate pairs.
3. No, a distance itself cannot be a negative number. The skill of absolute value best defines this.
6.NS.C.8 Game A Twist on Battleship – How to Play:
1. Distribute the A Twist on Battle Ship - Game Board Resource Sheet to each student. Have
students draw 3 quadrilaterals on the top coordinate plane. Note: quadrilaterals can be horizontal,
vertical, or diagonal. Coordinate pairs for vertices should contain only whole numbers.
2. Students should then find a partner to play against.
3. After the ships have been positioned, the game proceeds in a series of rounds.
4. In each round, each player's turn consists of announcing a target coordinate in the opponents' grid,
which is to be fired upon.
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product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
If one of the ship’s vertices does not occupy that point, then place a  on that coordinate.
So you are marking the shots you have fired.
b. If one of the ship’s vertices does occupy the coordinate, then the ship takes a hit. If the
ship takes a hit then place an X on that coordinate.
The player's opponent announces whether or not the shot hit one of his or her ships and then takes
a turn.
When all of the vertices of a ship have been hit, the ship has been sunk. After all of one player's
ships have been sunk, the game ends and the other player wins.
a.
5.
6.
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product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
6.NS.8 A Twist on Battleship – Game Board Resource Sheet
This board is for
the location of
my ships.
This board is to
track hits “X” and
misses “O” on my
opponent’s ships.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.