• GRADE 4 SUPPLEMENT

GRADE 4 SUPPLEMENT
Set C5 Geometry: Coordinate Systems
Includes
Activity 1 Coordinate Place Four C5.1
Activity 2 Dragon’s Gold C5.7
Independent Worksheet 1 Coordinate Dot-to-Dots C5.13
Independent Worksheet 2 Robot Programs C5.15
Independent Worksheet 3 Pirate James & His Robot C5.17
Independent Worksheet 4 Rosa’s Robot C5.19
Skills & Concepts
H use coordinate systems to specify locations and shapes on a grid with ordered pairs
H describe paths from one point to another point on a grid
H multiply 1- and 2-digit numbers by 10 and 100
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Bridges in Mathematics Grade 4 Supplement
Set C5 Geometry: Coordinate Systems
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Set C5 Geometry: Coordinate Systems
Set C5 H Activity 1
ACTIVITY
Coordinate Place Four
Overview You’ll need
Coordinate Place Four is a game in which players take H Coordinate Place Four Game Board (page C5.6, run a
turns placing markers on a grid by identifying ordered class set and 1 copy on a transparency)
pairs. The object of the game is to be the first to place H 12 red and 12 blue game markers
4 markers in a horizontal, vertical, or diagonal line, while
H overhead pen
blocking the other player from doing so. A more chal-
lenging version of the game involves being first to form H game markers (each student will need 12 markers in a
a square with 4 markers on the board. The teacher intro- single color)
duces Coordinate Place Four to the whole class, and then H helper jar containing a popsicle stick for each child
students play the game in pairs. with his/her name on it
Skills & Concepts
H use coordinate systems to specify locations and
shapes on a grid with ordered pairs
Instructions for Coordinate Place Four
1. Display the Coordinate Place Four overhead. Give students a few moments to examine the game
board quietly. Then explain that you are going to play a new game with the class. The game will help
them learn to locate positions on a grid by naming coordinates, which are ordered pairs of numbers, or
in this case, ordered pairs of letters and numbers. Illustrate the idea of coordinates by placing a game
marker at one of the intersections on the grid. Ask students to identify the location of the marker as pre-
cisely as possible.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Coordinate Place Four
6
5
4
3
2
1
0
A B C D E F
Team 1 Team 2
( _____, _____ ) 1 ( _____, _____ ) 7 ( _____, _____ ) 1 ( _____, _____ ) 7
( _____, _____ ) 2 ( _____, _____ ) 8 ( _____, _____ ) 2 ( _____, _____ ) 8
© The Math Learning Center ( _____, _____ ) 3 ( _____, _____ ) 9 ( _____, _____ ) 3
Bridges
( _____, _____ ) 9 in Mathematics Grade 4 Supplement • C5.1
( _____, _____ ) 4 ( _____, _____ ) 10 ( _____, _____ ) 4 ( _____, _____ ) 10
( _____, _____ ) 5 ( _____, _____ ) 11 ( _____, _____ ) 5 ( _____, _____ ) 11
Set C5 Geometry: Coordinate Systems
Activity 1 Coordinate Place Four (cont.)
Students It’s up in the third row.
The marker is over from the beginning of the grid.
It’s in the B column.
It’s at B, 3.
2. On the overhead or at the board, write the ordered pair, or coordinates, that describes the location of
the marker, and explain the notation to the class.
(B, 3)
Teacher We can describe the location of the marker very precisely by telling which column and
which row it’s in. We write the letter of the column first (B), and then the number of the row (3).
B and 3 are the coordinates of the marker. Since we write them in order, they are also called an
ordered pair.
3. Move the game marker to several other points on the grid, and ask students to report the ordered pair
that gives the location of the marker each time. Then give each student a copy of the game board blackline.
Write several ordered pairs on the board, and ask the children to place their finger on each as you go.
(C, 3) (B, 6) (E, 0) (F, 6)
4. Explain that in the game of Coordinate Place Four, you will take turns with the class to place markers
on the grid. The first team to place 4 markers in a horizontal, vertical, or diagonal row wins the game. It
is fair to block the other team from getting 4 in a row. Tell the students that you will use the blue mark-
ers, and they will use the red. Explain that a team has to record the coordinates they want on one of the
lines below the grid before they can place a marker. Then take the first turn.
Teacher Here are the coordinates I want for my first marker. (Teacher records B, 2 and places a
blue marker there).
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Coordinate Place Four
6
5
4
3
2
1
0
A B C D E F
Team 1 Team 2
B 2
( _____, _____ ) 1 ( _____, _____ ) 7 ( _____, _____ ) 1 ( _____, _____ ) 7
( _____, _____ ) 2 ( _____, _____ ) 8 ( _____, _____ ) 2 ( _____, _____ ) 8
( _____, _____ ) 3 ( _____, _____ ) 9 ( _____, _____ ) 3 ( _____, _____ ) 9
( _____, _____ ) 4 ( _____, _____ ) 10 ( _____, _____ ) 4 ( _____, _____ ) 10
C5.2 • Bridges in Mathematics Grade 4 Supplement
( _____, _____ ) 5 ( _____, _____ ) 11 ( _____, _____ ) 5 ( _____, _____ ) 11 © The Math Learning Center
( _____, _____ ) 6 ( _____, _____ ) 12 ( _____, _____ ) 6 ( _____, _____ ) 12
Set C5 Geometry: Coordinate Systems
Activity 1 Coordinate Place Four (cont.)
5. Have students pair-share ideas about where the class should place their first red marker. After they
have had a minute to talk it over, pull a stick from your helper jar to select a student to take a turn for
the class. Ask the rest of the students to remain silent as their classmate records the ordered pair on the
overhead and places the marker in the corresponding location.
6. Take turns with the class recording ordered pairs and placing markers. Block the class at the first op-
portunity, and explain your thinking as you do so.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Coordinate Place Four
6
5
4
3
2
1
0
A B C D E F
Team 1 Team 2
B 2
( _____, _____ ) 1 ( _____, _____ ) 7 D 4
( _____, _____ ) 1 ( _____, _____ ) 7
C 1
( _____, _____ ) 2 ( _____, _____ ) 8 D 5
( _____, _____ ) 2 ( _____, _____ ) 8
D 3
( _____, _____ ) 3 ( _____, _____ ) 9 ( _____, _____ ) 3 ( _____, _____ ) 9
( _____, _____ ) 4 ( _____, _____ ) 10 ( _____, _____ ) 4 ( _____, _____ ) 10
( _____, _____ ) 5 ( _____, _____ ) 11 ( _____, _____ ) 5 ( _____, _____ ) 11
( _____, _____ ) 6 ( _____, _____ ) 12 ( _____, _____ ) 6 ( _____, _____ ) 12
Teacher I got a little nervous that you might try to make a vertical row of 4. Can you see why I
put my marker on (D, 3)?
Students So you can block us.
Let’s block Mrs. Sayles on our next turn.
Oh, I know where to put our next marker! I hope she pulls out my stick next!
7. Continue to take turns with the class until one team has placed 4 markers in a row, or until both
teams have used all 12 of their markers. If neither team has been able to place 4 in a row by the time all
the markers have been used, call it a draw, erase the overhead, and play the game again.
8. When students understand how to play Coordinate Place Four, have them each play the game with a
partner. Each pair will need one game board (have them set the second one aside for now), and 24 game
markers (12 each in two different colors). Have pairs flip a coin or play Rock, Paper, Scissors to decide
which partner will go first. Circulate as children are playing the game to visit with them about their
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • C5.3
Set C5 Geometry: Coordinate Systems
Activity 1 Coordinate Place Four (cont.)
strategies for winning, and to give assistance as needed. If some pairs finish before others, have them
use the other partner’s game board to play a second time.
Extensions
• Introduce a more challenging version of Coordinate Place Four during the same instructional period
or at some other time. This version is played the same as the original, but the object of the game is to
be the first team (or the first player) to place 4 game markers in a square. The completed games be-
low illustrate some of the ways in which squares can be formed on the grid.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency. Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Coordinate Place Four Coordinate Place Four
6 6
5 5
4 4
3 3
2 2
1 1
0 0
A B C D E F A B C D E F
Team 1 Team 2 Team 1 Team 2
A 5
( _____, _____ ) 1 ( _____, _____ ) 7 D 3
( _____, _____ ) 1 ( _____, _____ ) 7 A 1
( _____, _____ ) 1 ( _____, _____ ) 7 E 5
( _____, _____ ) 1 ( _____, _____ ) 7
E 5
( _____, _____ ) 2 ( _____, _____ ) 8 B 3
( _____, _____ ) 2 ( _____, _____ ) 8 C 3
( _____, _____ ) 2 ( _____, _____ ) 8 E 2
( _____, _____ ) 2 ( _____, _____ ) 8
B 3
( _____, _____ ) 3 ( _____, _____ ) 9 B 1
( _____, _____ ) 3 ( _____, _____ ) 9 A 3
( _____, _____ ) 3 ( _____, _____ ) 9 C 1
( _____, _____ ) 3 ( _____, _____ ) 9
D 1
( _____, _____ ) 4 ( _____, _____ ) 10 D 4
( _____, _____ ) 4 ( _____, _____ ) 10 A 5
( _____, _____ ) 4 ( _____, _____ ) 10 C 5
( _____, _____ ) 4 ( _____, _____ ) 10
E 1
( _____, _____ ) 5 ( _____, _____ ) 11 C 4
( _____, _____ ) 5 ( _____, _____ ) 11 B 4
( _____, _____ ) 5 ( _____, _____ ) 11 B 5
( _____, _____ ) 5 ( _____, _____ ) 11
A 1
( _____, _____ ) 6 ( _____, _____ ) 12 ( _____, _____ ) 6 ( _____, _____ ) 12 B 2
( _____, _____ ) 6 ( _____, _____ ) 12 ( _____, _____ ) 6 ( _____, _____ ) 12
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Coordinate Place Four
6
5
4
3
2
1
0
A B C D E F
Team 1 Team 2
C5.4 • Bridges in Mathematics Grade 4 Supplement 5 )
C
( _____, _____ 1 ( _____, _____ ) 7 D 1
( _____, _____ ) 1 ( _____, _____ ) 7
© The Math Learning Center
A 3
( _____, _____ ) 2 ( _____, _____ ) 8 D 3
( _____, _____ ) 2 ( _____, _____ ) 8
Set C5 Geometry: Coordinate Systems
Activity 1 Coordinate Place Four (cont.)
INDEPENDENT WORKSHEET
Use Set C5 Independent Worksheet 1 to provide students with more practice using coordinate systems
to specify locations on a grid with ordered pairs.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • C5.5
Set C5 Geometry: Coordinate Systems Blackline Run a class set and one copy on a transparency.
Coordinate Place Four
6
5
4
3
2
1
0
A B C D E F
Team 1 Team 2
( _____, _____ ) 1 ( _____, _____ ) 7 ( _____, _____ ) 1 ( _____, _____ ) 7
( _____, _____ ) 2 ( _____, _____ ) 8 ( _____, _____ ) 2 ( _____, _____ ) 8
( _____, _____ ) 3 ( _____, _____ ) 9 ( _____, _____ ) 3 ( _____, _____ ) 9
( _____, _____ ) 4 ( _____, _____ ) 10 ( _____, _____ ) 4 ( _____, _____ ) 10
( _____, _____ ) 5 ( _____, _____ ) 11 ( _____, _____ ) 5 ( _____, _____ ) 11
( _____, _____ ) 6 ( _____, _____ ) 12 ( _____, _____ ) 6 ( _____, _____ ) 12
C5.6 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
Set C5 Geometry: Coordinate Systems
Set C5 H Activity 2
ACTIVITY
Dragon’s Gold
Overview You’ll need
Dragon’s Gold is a game in which players take turns rolling H Dragon’s Gold (page C5.11, run a class set and 1 copy
a die and moving the designated number of spaces on a on a transparency)
coordinate grid. There are gold coins of different values H Dragon’s Gold: Blank (page C5.12, optional, run as
placed on some of the coordinate points, and five of the needed)
points are marked with stars that allow a player to multiply
H dice dotted or numbered from 1–6 (1 for each pair of
his or her score for a turn by 10. The object of the game is
students)
to get the highest score in 5 turns. The teacher introduces
Dragon’s Gold to the whole class, and then students play H red and blue game markers
the game in pairs. H helper jar containing a popsicle stick for each child
with his/her name on it
Skills & Concepts
H Student Math Journals or scratch paper
H use coordinate systems to specify locations and
shapes on a grid with ordered pairs
H describe paths from one point to another point on a grid
H multiply 1- and 2-digit numbers by 10 and 100
Instructions for Dragon’s Gold
1. Display the Dragon’s Gold overhead. Give students a few moments to examine the game board quietly.
Then explain that you are going to play a new game with the class. The game will help them practice
naming coordinates, and learn to describe paths from one point to another point on a grid.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Dragon’s Gold
6 25
5 28 13
4 6 16
3 9 12
2 24 15
1 18 7 36
0
Start ŸA B C D E F
Red t eam Blue t eam
1 _________________________________ 1 _________________________________
2 _________________________________ 2 _________________________________
3 _________________________________ 3 _________________________________
© The Math Learning Center Bridges
4 _________________________________ 4 _________________________________ in Mathematics Grade 4 Supplement • C5.7
5 _________________________________ 5 _________________________________
Total Score ________________________ Total Score ________________________
Set C5 Geometry: Coordinate Systems
Activity 2 Dragon’s Gold (cont.)
2. Explain that in the game of Dragon’s Gold, each team places a red or a blue marker on the coordinates
(A, 0) to start. Teams take turns rolling a die numbered 1–6 and moving their game marker that many
spaces on the grid. Teams have to stay on the grid lines as they move from one point to the next; they
can move their marker forward, backward, or sideways, but not diagonally. A team collects the value of
any gold pieces they land on along the way. If a team lands on a star during their turn, they get to mul-
tiply their total for that turn by 10. If they land on 2 stars during a single turn, they get to multiply their
total for that turn by 100.
3. After you have explained the game rules, give students each a copy of the game board. Then ask one
of them to roll the die so you can demonstrate the process.
Teacher Let’s do a demonstration run together. Jose, will you please roll the die for us? What did
we get? 5? Okay, we’re going to start on (A, 0). We get to move 5 spaces because we rolled a 5. We
have to move along the grid lines, so moving 1 space would mean we could get to (A, 1) and collect a
gold piece worth 18 points, or (B, 0) where we couldn’t collect anything.
Sari Couldn’t we go from (A, 0) up to (B, 1)?
Teacher Nope. Why not?
Students Because you have to stay on the lines.
You can’t go diagonal in this game, only up, down, and sideways.
But Jose rolled a 5. We get to move 5 spaces, not just 1.
4. Have students pair-share ideas about some of the possible paths they could take, given the number
their classmate just rolled. Which path would result in the highest score? Ask them to use their own
game boards to plan the best path. After they have had a minute or two to talk, ask a volunteer to share
his or her idea with the class by telling you how to move the marker. Trace the suggested path with an
overhead pen so everyone can see it.
Max We think you can get the highest score if you move the marker up 3 spaces and over to the
right 2 spaces.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Dragon’s Gold
6 25
5 28 13
4 6 16
3 9 12
2 24 15
1 18 7 36
0
Start ŸA B C D E F
Red Team Blue Team
1 _________________________________ 1 _________________________________
C5.8 • Bridges in Mathematics Grade 4 Supplement
2 _________________________________ 2 _________________________________ © The Math Learning Center
3 _________________________________ 3 _________________________________
4 _________________________________ 4 _________________________________
Set C5 Geometry: Coordinate Systems
Activity 2 Dragon’s Gold (cont.)
Students Wow! If you go Max’s way, you land on a star.
So we’d have 18 + 9 is 27, and then we’d get to multiply 27 by 10. That’s 270 points, just for one
turn!
We have a different idea that gets more points.
So do we! Can we show?
If you go over to the right 4 and up 1, you can get 360 point because it’s 36 × 10.
There’s an even better way. If you go up 2 and over to the right 3, you land on 18 and a star and 24.
That’s 42 × 10 which is 420 points!
5. After students have had a chance to discuss some of their ideas, erase the overhead. Place a red and
a blue game marker near the start point at coordinates (A, 0). Take your turn first so students have the
benefit of seeing the game in action once more before it is their turn. Roll the die, decide on the best
path, and record it on the board so the students can see it.
Teacher I am going to play as the red team today, and you will all work together as the blue team.
Here I go. I rolled a 3. Let me think for a minute. Okay, here’s the path I am planning to take. I think
I can get the most points this way. Put your thumbs up if you agree.
Mrs. Nolan’s Paths
Start at (A, 0). Move up 3 spaces.
6. Move your marker according to the plan you just recorded. Work with input from the class to record
an equation for your turn on the overhead. Then have a volunteer roll the die for the class. Ask students
to work in pairs to determine the path that will yield the highest score for their team. Let them know
that it is okay if they land on the same coordinates as you. When they have had a minute or two to work,
pull a stick from your helper jar to choose a student to share his or her plan with the class. Record the
proposed path on the board so everyone can see it, and then have the student move the marker accord-
ingly. Work with input from the class to record an equation for their first move.
Set C5 Geometry: Coordiante System Blackline Run a class set and one copy on a transparency.
Dragon’s Gold
6 25
5 28 13
4 6 16
3 9 12
2 24 15
1 18 7 36
Kids’ Paths 0
Start ŸA B C D E F
Start at (A, 0). Move up 1 space, to the right 4