Coordinates on the Plane: a week of ready-to-teach maths

Five days of lessons for Year 6 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus Coordinate hunt boards, a Quadrant tour board with its move cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the Coordinate hunt boards for Day 2 and the Quadrant tour board and move cards for Day 3, one set for each pair.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. For Day 1, tape two crossing lines on the floor as axes, if you have the space.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: the x-axis and the y-axis are two number lines that cross at zero, so they carry negative numbers too and split the plane into four quadrants. A point is an ordered pair, x first: (−3, 2) is 3 left and 2 up. When a point moves, right and left change x, and up and down change y, by exactly the size of the move.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

Words to watch

The origin is (0, 0), where the axes cross. Quadrants are numbered I, II, III and IV anticlockwise from the top right. A point on an axis has a 0 in its pair and sits in no quadrant. A translation slides a point or shape without turning it; a reflection flips it over a line such as an axis.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 builds the four-quadrant plane; Day 2 plots and reads points in it; Day 3 moves points and tracks how their coordinates change; Day 4 moves whole shapes; and Day 5 puts it all to work on a map. It builds on the Year 5 grid coordinates in the first quadrant (AC9M5SP02) and on this year’s integers on a number line (AC9M6N01). It leads to the Year 7 work of plotting relationships from tables of values on the Cartesian plane (AC9M7A05).

Materials for the week (one trip)

• For Day 1: masking tape for a floor plane, and sticky notes.
• For Days 2 and 3: the cut-out boards and move cards, one set for each pair, and a counter each.
• For Day 4: rulers and coloured pencils.
• All week: grid paper for extra plotting.

Words for the word wall

Cartesian plane, x-axis, y-axis, origin, quadrant, coordinates, ordered pair, x-coordinate, y-coordinate, positive, negative, translate, reflect, vertex

Dear families

This week in maths, Year 6 uses coordinates in all four quadrants of a Cartesian plane, including negative numbers, and describes how a point’s coordinates change when it moves.

Try this at home

• Draw two crossing axes on paper. Take turns calling a point, such as (−2, 3), for the other to plot.
• Pick a starting point and give a move, such as 4 left and 1 down. What are the new coordinates?
• Play a simple battleships game on a grid from −5 to 5.
• Ask your child why (3, 2) and (2, 3) are different points.

Points we plotted

Fill one row a day. Write a point, its quadrant, and where it lands after a move you choose.

Printed from the free seegongsik Coordinates on the Plane teaching pack · seegongsik.com/au/y6/space/AC9M6SP02/pack

Four quadrants

The x-axis and the y-axis are two number lines that cross at zero, the origin. Carried on past zero they hold negative numbers, to the left and below, and split the plane into four quadrants, numbered I to IV anticlockwise from the top right. The signs of a point give its quadrant; a point with a 0 in its pair lies on an axis, in no quadrant. Children build the plane and sort points by their signs.

We are learning to

• extend both axes past zero to make a plane with four quadrants,
• name the quadrant of a point from the signs of its coordinates,
• recognise points that lie on an axis.

Success criteria

• I can say which quadrant (−3, 5) is in, and why.
• I can explain why (0, −4) is not in any quadrant.

You need

The worksheet, one per child, masking tape for two crossing axes on the floor, and sticky notes numbered −5 to 5.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the floor plane; start Session B with Parts A and B.

Watch for these ideas

• Numbering the quadrants clockwise, or starting in the wrong corner.
• Reading the y-axis numbers as negative going up.
• Putting a point with a 0 in its pair into a quadrant.

Answers

• Part A: −6 to 6 along both axes, left to right and bottom to top; I top right, II top left, III bottom left, IV bottom right.
• Part B: I (3, 5), (4, 2); II (−2, 4), (−6, 3); III (−5, −1), (−1, −6); IV (6, −3), (2, −2), (5, −5); on an axis (0, 4), (−3, 0), (0, 0) ((0, 4) on the y-axis, (−3, 0) on the x-axis, (0, 0) is the origin).
• Part C: (1) any pair with −4 first and a negative second number, such as (−4, −2); (2) IV; (3) no, it is the origin, on both axes.

Four quadrants

A. Finish the plane

B. Sort the points

(3, 5); (−2, 4); (−5, −1); (6, −3); (0, 4); (−3, 0); (−1, −6); (4, 2); (−6, 3); (2, −2); (0, 0); (5, −5)

C. Signs

1. Write a point in quadrant III with an x-coordinate of −4. ______________

2. A point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in? ______

3. Is (0, 0) in a quadrant? What is it called? ________________________________

Plot and read

A point is named by an ordered pair: the x-coordinate first, across from the origin, then the y-coordinate, up or down. (−3, 2) means 3 left and 2 up; swap the numbers and you have a different point. Children plot points in all four quadrants, read the coordinates of points already plotted, fix order mistakes, and play Coordinate hunt.

We are learning to

• plot a point in any quadrant from its ordered pair,
• read the coordinates of a plotted point, x first,
• explain why the order of the pair matters.

Success criteria

• I can plot (−5, −3) and (3, −4) correctly.
• I can read the coordinates of a point in quadrant II.

You need

The worksheet, one per child, sharp pencils, and the Coordinate hunt boards (cut-outs), one for each child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the reading in Part B.

Watch for these ideas

• Going up or down first, so (−3, 2) lands at (2, −3).
• Counting the lines from the edge of the grid instead of from the origin.
• Plotting a point with a 0 in a square instead of on the axis.

Answers

• Part A: A 4 right and 3 up, in I; B 2 left and 5 up, in II; C 5 left and 3 down, in III; D 3 right and 4 down, in IV; E 2 down, on an axis; F 4 left, on an axis; G 1 left and 1 down, in III; H 5 right and 1 up, in I.
• Part B: P (2, −5), Q (−3, 3), R (−6, −2), S (5, 4), T (0, 3), U (−4, −5).
• Part C: (1) Kai swapped the order: (−3, 2) is 3 left and 2 up; (2) (4, −1); (3) no: (5, 0) is on the x-axis, in no quadrant.

Plot and read

C. Fix the mistake

1. Kai plotted (−3, 2) by going 2 left and 3 up. What went wrong? ______________________________

2. Ari read a point that is 4 right and 1 down as (−1, 4). What should it be? ______________

3. Jo says (5, 0) is in quadrant I. Is Jo right? Why? _______________________________________

Moving points

When a point moves, its coordinates change by the move: right adds to x and left takes from x; up adds to y and down takes from y. Moving (2, 3) 4 left lands on (−2, 3), across the y-axis in quadrant II. Children work out where points land, find the move between two points, and play Quadrant tour.

We are learning to

• work out a point’s new coordinates after a move,
• describe the move from one point to another,
• explain which coordinate a move changes, and by how much.

Success criteria

• I can move (3, −4) 6 left and 2 up and name the new point.
• I can find the move from (1, 4) to (1, −2).

You need

The worksheet, one per child, and the Quadrant tour board and move cards (cut-outs) with a counter for each child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the moves to find in Part B.

Watch for these ideas

• Changing the wrong number: moving left and changing y.
• Counting from 2 to −2 as 2 steps instead of 4, by skipping zero.
• Thinking a move left always makes the x-coordinate negative.

Answers

• Part A: (−2, 3) (II); (−1, 3) (II); (−3, −2) (III); (−2, −3) (III); (−2, −3) (III); (0, 0) (the origin).
• Part B: 6 down; 5 right; 5 right and 5 up; 5 left and 4 up.
• Part C: (1) (x − 3, y + 2); (2) x stays the same, y goes down by 7; (3) any move of more than 1 left and more than 1 down, such as 3 left and 2 down.

Moving points

A. Where does it land?

B. Find the move

C. The rule

1. A point (x, y) moves 3 left and 2 up. Its new coordinates are (x ____ 3, y ____ 2).

2. A point moves from (−2, 5) to (−2, −2). What happens to each coordinate? ______________________

3. Give a move that takes (1, 1) into quadrant III. ______________________________________

Shapes on the plane

A shape on the plane is fixed by its corners. Slide a shape and every corner moves by the same amount, so every corner’s coordinates change in the same way; reflect it in the y-axis and every x-coordinate changes sign, while a reflection in the x-axis changes every y. Children slide a triangle across quadrants, reflect a rectangle in each axis, and find missing corners.

We are learning to

• plot a shape from the coordinates of its corners,
• slide a shape and work out its new corners,
• describe how a reflection in an axis changes the coordinates.

Success criteria

• I can slide a triangle 6 left and 4 down and list its new corners.
• I can say what happens to (5, 3) when it is reflected in the y-axis.

You need

The worksheet, one per child, a ruler, and two coloured pencils.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the reflections in Part B.

Watch for these ideas

• Moving only one corner, or moving each corner a different amount.
• Changing the sign of the wrong coordinate in a reflection.
• Joining corners out of order, which crosses the sides.

Answers

• Part A: A (−5, −2), B (−2, −2), C (−5, 1).
• Part B: in the y-axis P (−2, 1), Q (−5, 1), R (−5, 3), S (−2, 3); in the x-axis P (2, −1), Q (5, −1), R (5, −3), S (2, −3); the y-axis changes the sign of x, the x-axis the sign of y.
• Part C: the square (−3, −2); the rectangle (−4, 3).

Shapes on the plane

What happens to the coordinates in each reflection? ______________________________________________

C. Missing corners

1. Three corners of a square are (−3, 2), (1, 2) and (1, −2). The fourth corner is ______________

2. Three corners of a rectangle are (−4, −1), (2, −1) and (2, 3). The fourth corner is ______________

Map it

Coordinates are an address system. A park map drawn on a four-quadrant grid gives every place a pair, and every route becomes a move: right or left first, then up or down. Children read places on the map, describe routes as moves, follow walks to find where they end, and solve coordinate puzzles, then play the self-check quiz.

We are learning to

• read the coordinates of places on a map in four quadrants,
• describe a route between two places as a move,
• use coordinates and moves to solve problems.

Success criteria

• I can describe the route from the Gate to the Pond as a move.
• I can find where a walk of 7 right and 1 up from the Playground ends.

You need

The worksheet, one per child, and the Quadrant tour boards from Day 3 for early finishers.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the puzzles in Part C and the quiz.

Watch for these ideas

• Describing a route by counting squares along a winding path instead of as one move across and one up or down.
• Taking the start from the end the wrong way round, so the move points backwards.
• Mixing up “units from the y-axis” (the x-coordinate) with “units from the x-axis” (the y-coordinate).

Answers

• Part A: Gate (0, −6), Playground (−4, 3) II, Pond (3, 4) I, Cafe (5, −2) IV, Toilets (−5, −3) III, Lookout (−1, 5) II, Bike rack (2, −4) IV; the Gate is on the y-axis.
• Part B: (1) 3 right and 10 up; (2) 10 right and 1 up; (3) the Pond; (4) the Toilets.
• Part C: (1) (−3, 4); (2) (−1, −5); (3) (3, 0), (−3, 0), (0, 3) and (0, −3).

Map it

B. Routes

1. From the Gate to the Pond, the move is ____________________________

2. From the Toilets to the Cafe, the move is ____________________________

3. Start at the Playground and walk 7 right and 1 up. Where are you? ______________

4. Start at the Bike rack and walk 7 left and 1 up. Where are you? ______________

C. Puzzles

1. A point in quadrant II is 3 units from the y-axis and 4 units from the x-axis. What is it? ______________

2. A new seat goes where the Lookout would be if it were reflected in the x-axis. Where is the seat? ______________

3. Write four points that are each 3 steps from the origin along an axis. ______________________________

Coordinate hunt

Print one sheet for each pair and cut it in half: each player gets a ships board and a calls board.

How to play

1. Secretly mark three ships on your ships board: 2, 3 and 4 points long, on grid points next to each other in a straight line.
2. Take turns to call a pair, x first. Your partner says hit or miss; mark the call on your calls board.
3. A ship sinks when every point is hit. The first to sink all three of the other player’s ships wins.

Quadrant tour

Teacher note: the 24 cards are 12 moves and their opposites, so the deck never drifts one way. A card changes x by its left or right number and y by its up or down number, nothing else.

What we know: Coordinates on the Plane

Work on your own. Show your thinking if you can.

Answers and marking guide

Answers

1. Quadrant II.
2. Any pair with both numbers negative, such as (−2, −5).
3. M (3, −2), N (−5, −4).
4. (−4, 5), in quadrant II.
5. (−1, 3).
6. 6 right and 2 down.
7. (−5, −3).
8. (−2, −1).

A quick three-level guide

Eight questions, four ideas. A child at standard plots and reads points in all four quadrants and says how a move changes each coordinate.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: the four quadrants, plotting and reading, moving points, shapes on the plane, and problems on a map.