Grade by Grade
E. Spatial Sense · 3D Objects, Directions and Measurement

Giving and Following Directions

E1.4 A1About 35 minutes
Learning goals
  • I can follow directions with several steps that include distances and turns.
  • I can give clear directions to get from one place to another.
  • I can make quarter turns and half turns to the right or left.
  • I can check directions and fix a mistake.

Words to know

direction
The way something is facing or moving: up, down, left, right, forward or backward.
distance
How far it is from one place to another. We can measure it in steps, squares on a grid, or metres.
quarter turn
One fourth of a full turn. A quarter turn right is like the minute hand moving from 12 to 3.
half turn
Half of a full turn. After a half turn you face the opposite way.
full turn
A turn all the way around, until you face the same way you started.
map
A drawing of a place as seen from above. A legend tells what the symbols mean.

Remember from Grade 2

In Grade 2 you described where things are, made maps with a legend, and made quarter turns and half turns.

This year your directions get more exact. You will say how far to go (the distance) and which way to turn, step by step, like a GPS in a car!

Let's start with a robot game

Pretend a friend is a robot. A robot only does exactly what you say. If you say "Go to the fridge", the robot doesn't know how! You must say:

"Walk forward 4 steps. Make a quarter turn to the left. Walk forward 2 steps."

Good directions have three things: which way you are facing at the start, how far to go, and which way to turn.

start:facing upquarter turnrightquarter turnlefthalf turn(turn around)
Turning from facing up. A quarter turn right makes you face right. A quarter turn left makes you face left. A half turn makes you face the opposite way.

Turns

  • A quarter turn right turns the same way the hands of a clock move. A quarter turn left turns the other way.
  • Two quarter turns in the same direction make a half turn. After a half turn you face the opposite way.
  • Four quarter turns make a full turn. You end up facing the same way you started.

A turn does not move you to a new spot. You stay in the same place and change the way you face.

H = homeS = schoolL = libraryP = parkR = rinkG = storepondHLSPRG
A map of a town on a grid. Each letter is a place. The legend tells which place each letter stands for. The blue squares are a pond.

Using a grid map

On this map, we move from the middle of one square to the middle of the next. "Forward 3" means move 3 squares in the direction you are facing.

In real life, each square might stand for a distance, like 1 block or 100 metres.

Worked example

Example 1: Follow the directions

Start at Home (H), facing right. Follow these directions:

  1. Forward 3 squares.
  2. Quarter turn left.
  3. Forward 3 squares.
  4. Quarter turn right.
  5. Forward 4 squares.

Where do you end up?

  1. Start at H, facing right. Forward 3: you pass 2 squares and land on L (library).
  2. Quarter turn left: you were facing right, so now you face up.
  3. Forward 3: you move up 3 squares and land on S (school).
  4. Quarter turn right: you were facing up, so now you face right.
  5. Forward 4: you move right 4 squares and land on P (park).

You end up at the park (P). You visited the library and the school on the way.

H = homeS = schoolL = libraryP = parkR = rinkG = storepondHLSPRG
The path from Example 1: from Home to the library, up to the school, then right to the park.
Worked example

Example 2: Give directions

You are at the park (P), facing right. Give directions to the rink (R). Stay out of the pond!

  1. The rink is 3 squares down and 1 square left of the park.
  2. You are facing right. To face down, make a quarter turn right.
  3. Go forward 3 squares. Now you are in the bottom row, just right of the rink.
  4. To face left, make another quarter turn right. Then go forward 1.
  5. Check the path: it goes down the right side of the map, far from the pond.

Quarter turn right, forward 3, quarter turn right, forward 1. You reach the rink.

Turns depend on the way you face

"Turn right" does not always mean "go toward the right side of the map". If you are facing down the map and make a quarter turn right, you will face left on the map! Turn the page, or turn your body, to check.

Worked example

Example 3: Find the mistake

Zoe starts at the library (L) facing right. She wants to go home. She says: "Forward 3." Where does she end up? Fix her directions.

  1. Facing right from L, forward 3 moves her to the right, onto R (rink). That's the wrong way!
  2. Home is to the left of the library. She must turn around first.
  3. A half turn makes her face left. Then forward 3 brings her to H.

Fixed directions: Half turn, forward 3. She reaches home.

Thinking like a mathematician

After you write directions, test them. Put your finger on the start and follow each step exactly. Fixing mistakes is part of being a good problem solver.

Just for fun

Why did the robot end up right where it started?

Someone told it to make a quarter turn right four times. Four quarter turns make one full turn!

Hands-on activity

Treasure hunt at home

You need: a small "treasure" (a toy or a mitten), paper and a pencil.

  1. A grown-up hides the treasure while you close your eyes.
  2. The grown-up gives you directions from a starting spot, such as: "Face the fridge. Walk forward 5 steps. Quarter turn right. Walk forward 3 steps. Look down."
  3. Follow the directions exactly. Did you find the treasure?
  4. Now you hide it and write directions with distances (steps) and turns.
  5. Test your directions yourself before giving them to someone.
  6. Extra: draw a map of the room on grid paper and mark the path.

Math talk: "Which steps in the directions were the most important? What happens if one step is wrong?"

H = homeS = schoolL = libraryP = parkR = rinkG = storepondHLSPRG
Use this map for the practice questions. Move from the middle of one square to the middle of the next.

Your turn

1

Start at Home (H) facing up. Go forward 3. Where are you?

2

Start at the library (L) facing right. Go forward 3. Where are you?

3

Start at the school (S) facing down. Go forward 3. Where are you?

4

You are facing up and make a half turn. Which way are you facing now?

5

You are facing right and make a quarter turn left. Which way are you facing now?

6

Start at the store (G) facing right. Go forward 3. Where are you?

7

How many quarter turns make a full turn?

More practice: warm-up

1

How many quarter turns make a half turn?

2

You face left and make a half turn. Which way do you face?

3

Does a turn move you to a different square?

4

Start at H facing right. Forward 1. Which square are you on?

5

Which letter is the park on the map?

More practice: on your own

1

Start at the rink (R) facing up. Forward 3, quarter turn right, forward 1. Where are you? Did you go through the pond?

2

Write directions from H to S. Start facing up.

3

Start at S facing right. Ben says: "Quarter turn right, forward 3." Where does he end up?

4

Start at the park (P) facing left. Forward 4, quarter turn left, forward 3. Where are you?

5

If each square on the map stands for 100 metres, how far is it from H to L going straight across?

Challenge

1

Find the fewest squares you can move to go from H to P. (You can only move up, down, left or right.)

2

Write directions from the store (G) to the rink (R) that avoid the pond. Start facing right.

3

Mo starts at L facing up. He makes a quarter turn right, then another quarter turn right, then goes forward 3. Where is he? What is a shorter way to say his turns?

Check your understanding

Quiz

1.

You are facing up. You make a quarter turn right. Which way are you facing?

2.

How many quarter turns make a half turn?

3.

After a half turn, you face ...

4.

On the town map, start at H facing right. Go forward 3. Where are you?

5.

Which set of directions is the most complete?

6.

If each square is 100 m, how far is a path of 4 squares?

For parents and teachers

Big idea: Children give and follow multistep directions that include distances and half and quarter turns (Ontario E1.4). Checking and fixing directions builds problem-solving and reasoning (strand A1).

Common difficulties:

  • Left and right after turning. When your child is facing down the page, "turn right" goes toward the left side of the page. Let them rotate the paper or stand up and turn their body.
  • Counting the starting square. "Forward 3" means 3 moves, not counting the square you start on.
  • Forgetting the starting direction. Directions only work if you know which way you face at the start.

How to help: On a walk, take turns giving directions: "Walk 20 steps, then turn left at the stop sign." At home, play the robot game. Hold your child's hand near roads; practise only in safe places.