Positions and Pathways: a week of ready-to-teach maths

Five days of lessons for Year 2 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out 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. Cut out the two card sheets once; the arrows, tokens and grid map are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and when.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

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 model answers, so you can walk in and teach it.

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 lesson can also split into a short warm-up and a main session if your timetable runs small blocks.

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 finds places by their neighbours; Day 2 pins them down with a grid; Day 3 follows a pathway; Day 4 plans and gives one; and Day 5 reveals what a map really is and has children draw their own. It builds on giving and following directions in Year 1, and it opens the way to grid references and coordinates in the years ahead.

Materials for the week (one trip)

• From the classroom: scissors, pencils or crayons, this pack printed.
• From home or the craft box: a few counters, buttons or bottle tops to use as place tokens, and a little sticky tape.
• Cut out once, use all week: the arrow cards, the place tokens and the grid map in this pack. No maths equipment to buy.

Dear families

This week in maths, Year 2 learns to find places on a map, describe where things are, and follow and give simple directions. It is all about reading a familiar space drawn flat on a page.

Try this at home

• Draw a map of your bedroom from above, as if the roof came off. Mark the bed, the door and one more thing.
• Play I-spy with position words: it is next to the fridge and below the clock. Take turns.
• Say the way from the front door to the kitchen before you walk it: how many steps, then which way to turn.
• On a walk or a shopping trip, follow a simple map together and name the next turn out loud.

My maps and paths this week

Fill one row a day. Tick when you have found a place and followed a path.

Printed from the free seegongsik Positions and Pathways teaching pack · seegongsik.com/au/y2/space/AC9M2SP02/pack

Find the place on the map

Children find places on a map of a space they know and say where each one is, using the everyday position words next to, between, above and below. There is no grid yet: position is told by neighbours, the way we point things out in real life.

We are learning to

• find a named place on a simple map of a space we know,
• say where a place is using next to, between, above and below,
• give a clue for a place so a friend can find it.

Success criteria

• I can find a place on the map when a friend describes it.
• I can describe where a place is with a position word.

You need

A simple map you sketch on the board, or the classroom itself. The place tokens (cut-out sheet 1), one set per pair. The worksheet, one per child. Coloured pencils help.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the class map. Start Session B with a quick clue swap, then move to the worksheet.

Watch for these ideas

• Using next to for places that are only near: next to means side by side, sharing an edge.
• Reading above and below as bigger and smaller, rather than higher and lower on the map.
• Giving a clue that fits more than one place: a good clue points to just one.

Answers

• The sandpit is between the slide and the swing. The tree is above the sandpit.
• The tree is next to the gate. The swing is below the pond.
• Clues and the child’s own map vary: check each clue points to exactly one place.

A map of the park

Here is a map of a park, seen from above. Use the words next to, between, above and below to finish each sentence.

Finish the sentence

The sandpit is between the ______ and the ______.

The tree is above the ______.

The ______ is next to the gate.

Draw a ring around the swing. The swing is ______ the pond.

Draw and describe

Draw a map of your own classroom from above. Mark two things you know.

On my map, the ______ is next to the ______.

Across, then down

The same familiar map gets rows and columns, so a place can be said exactly with no pointing at all. The habit underneath is the permanent one: name the column from the left first, then the row from the top.

We are learning to

• count columns from the left and rows from the top,
• say where a place is as a column and a row,
• find a place when I am told its column and row.

Success criteria

• I can say the column first, then the row.
• I can find a place from its column and row.

You need

The grid map (cut-out sheet 2) and the place tokens (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the token game. Start Session B with the grid check.

Watch for these ideas

• Saying the row before the column, or counting rows from the bottom instead of the top.
• Counting the grid lines instead of the spaces between them.
• Starting the count from zero: the first column and the first row are number one.

Answers

• Column 3, row 1 is the pond. Column 4, row 2 is the seat.
• The sandpit is column 2, row 2. The bin is column 1, row 3. The kiosk is column 4, row 1.
• Table: pond is 3 and 1; seat is 4 and 2; sandpit is 2 and 2; bin is 1 and 3; kiosk is 4 and 1.

Name the spot

This park map has columns and rows. Count columns from the left and rows from the top. Say the column first, then the row.

Read the grid

What is in column 3, row 1? ______

What is in column 4, row 2? ______

Write the column and the row

Your own spot

Choose one thing on the map. Write: the ______ is in column ______, row ______.

Walk the pathway

A list of directions is a journey written down before it happens. Children follow one, one step at a time, and find that the destination stays unknown until the last step. Order matters, and each arrow does exactly one thing.

We are learning to

• follow a list of directions one step at a time,
• move up, down, left and right on a grid map,
• find where a pathway ends.

Success criteria

• I can follow a pathway step by step.
• I can say where the pathway ends.

You need

The grid map (cut-out sheet 2), the place tokens and the arrow cards (cut-out sheet 1), one set per pair. A counter or button for the walker. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the floor walk. Start Session B on the worksheet grid.

Watch for these ideas

• Moving two squares for one arrow, or sliding diagonally: one arrow is one straight step.
• Reading up as down: on this map up moves toward the top.
• Losing their place halfway: a finger on the grid keeps the count honest.

Answers

• Up, up, up from the gate lands on the slide.
• Right, right, up, up from the gate lands on the sandpit.
• To walk back from the slide to the gate: down, down, down.

Follow the pathway

On this grid, up goes toward the top and down toward the bottom; left and right go sideways. One arrow is one square. Start on the named square and trace each pathway with your finger.

1. Start at the gate. Follow: up, up, up. Ring where you land, and write it: ______
2. Start at the gate. Follow: right, right, up, up. Write where you land: ______
3. You followed up, up, up to reach the slide. Write the steps to walk back to the gate: ______

Make your own

Start on any named square. Write a pathway of three arrows, then walk it. Where does it end? ______

Plan the pathway

Giving directions is the inverse skill, and it comes with a built-in check: walk your recipe in your head, square by square, and see where it truly ends. Children discover that two different pathways can reach the same goal, and that a plausible one can miss by a single square.

We are learning to

• give a list of directions from a start to a goal,
• check a pathway by walking it square by square,
• find more than one pathway to the same place.

Success criteria

• I can write directions that reach the goal.
• I can check my pathway by tracing it.

You need

The grid map (cut-out sheet 2), the arrow cards and the place tokens (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the first checked route. Start Session B by finding a second way.

Watch for these ideas

• Writing the goal instead of the steps: directions are the moves, not the destination.
• Forgetting to count squares, so the path lands one square short or long.
• Believing a plan without walking it: the check is what catches a miss.

Answers

• Gate to the sandpit, one good way: right, right, up, up.
• A different way to the sandpit: up, up, right, right. Any pathway that ends on the sandpit is correct.
• Gate to the kiosk: right, right, right, right, up, up, up. Any pathway that ends on the kiosk is correct.

You give the directions

Write the arrows that walk from the start to the goal. Use up, down, left and right, one arrow for each square. Then trace your path to check it lands on the goal.

1. From the gate (column 1, row 4) to the sandpit (column 3, row 2). Write your arrows.

2. Now find a different way from the gate to the sandpit.

3. From the gate to the kiosk (column 5, row 1).

Did it land?

Trace each pathway with your finger. Tick the ones that reached the goal, and fix any that missed.

A map from above

The deepest idea in the unit is the quietest: a map is not a picture of what a place looks like, it is the place seen from straight above, flattened to outlines. Once a child sees the table become a rectangle and the rug a patch, every map they meet makes sense.

We are learning to

• see that a map shows a space from straight above,
• match a real thing to the shape it makes on a map,
• draw a simple map of a space I know and mark places on it.

Success criteria

• I can explain that a map is the view from straight above.
• I can draw a map and mark places and a path on it.

You need

Paper and coloured pencils. The worksheet, one per child. The grid map and place tokens from the cut-outs can help children plan before they draw.

Lesson flow (about 50 minutes)

Two half-sessions instead? End Session A after the map is drawn. Start Session B with the map swap and directions.

Watch for these ideas

• Drawing things as they look from the side (a chair with legs) instead of from straight above.
• Making the map a picture rather than a plan: a map keeps the positions, not the detail.
• Leaving out the door or a landmark, so a set of directions has nowhere to start.

Answers

• Maps vary. Check the view is from above (shapes and outlines), the door is marked, and the described position and path match the drawing.
• The Year 2 Space strand is now complete: shapes classified, positions found, and pathways walked, planned and drawn.

Draw your map

A map shows a place from straight above, as if the roof came off. Draw a map of your classroom or your bedroom. Mark the door and three things you know.

Say where things are

On my map, the ______ is next to the ______.

The ______ is between the ______ and the ______.

Give a path

Write the directions to walk from the door to your bed or your desk. Use up, down, left and right.

From the side or from above?

A map draws a house (a) from the front, or (b) from straight above. Circle the one a map uses: a or b.

Arrow cards and place tokens

Cut out the cards. Lay arrow cards in a row to build a pathway, one arrow for each square. Put place tokens on the grid map to make your own park. On this map, up moves toward the top.

Arrow cards

Place tokens

Teacher note: the arrows match the pathways on screen, where up moves toward the top of the map. Four of each arrow is enough for the longest pathway in the pack.

The grid map

This is your park grid: five columns across and four rows down. Place tokens on it, then walk a pathway with a counter, one square for each arrow. Count columns from the left and rows from the top.

Pathway strip

Lay your arrow cards here in order to record a pathway, one card in each box.

Teacher note: the grid map is the same one used on the worksheets, so the floor game and the pages match.

What we know: Positions and Pathways

Use the park map below. Work on your own. Show your thinking if you can.

1. The swing is between the ______ and the ______.
2. The swing is below the ______ and above the ______.
3. The sandpit is in column ______ and row ______.
4. Write what is in column 3, row 1: ______
5. Start at the gate. Follow: down, right, right. Write what you land on: ______
6. You walked down, right, right to get there. Write the steps to walk straight back to the gate: ______
7. Write directions to walk from the gate to the sandpit: ______
8. True or false: a map draws a place as if you look straight down from above, like the roof came off. ______

Answers and marking guide

Answers

1. the pond and the seat.
2. below the tree and above the slide.
3. column 3, row 3.
4. the bin.
5. the seat (gate, down to the pond, right to the swing, right to the seat).
6. left, left, up.
7. one good way is down, down, right, right. Any pathway that ends on the sandpit is correct.
8. true.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say where and how, the column before the row.

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: find a place, read the grid, follow a path, give directions, and map from above.