Minds On

On the grid

Explore the following MathXplosion video entitled “On the Grid.” In this video, Eric discusses how to read maps with gridlines to locate objects.

Consider the following questions as you explore the video.

  • What is different about the horizontal and vertical axes?
  • How does Eric read coordinates or locations on the grid?
  • What does Eric say is the purpose of using a map with gridlines?

When you are ready, press each question to reveal the answer.

Answer: Horizontal axis is letters. Vertical axis is numbers.

Answer: Eric reads coordinates horizontally first (letter first) and vertically second (number second).

Answer: The purpose of using a map with gridlines is to show relative distance between objects.

Grid challenge

Using the following image, describe the movements the farmer might make while doing their daily chores. They have just fed the ducks at the duck pond. What else do you think the farmer will do today? Maybe they will collect the watering can from the barn before watering the cornfield. Next, they might tend to the horses or check on the windmill. Consider the farmer’s path as they do their chores, and record their steps using a voice recorder, speech-to-text, or writing tool.

There is a farm arranged in an 11 x 8 grid. The vertical axis is numbered 1 to 11, from the bottom to the top. The horizontal axis is labelled A to H, from left to right. There is a duck pond that spans from A1 to C1 and A2 to C2. The farmer stands at square C2 facing south toward the duckpond. To the right of the farmer, a cornfield spans from E1 to H1, and E2 to H2. There is a field of wheat stretching from D4 to F4, with a scarecrow at D4. A horse is standing on squares A5 and B5, and a small house appears on squares G5 and H5. Another horse is standing across squares A7 and B7. In the top left area, a windmill stands at B9. There is a barn on squares D9 and E9 and a watering can at F9. 2 squares to the right of the watering can, at H9, there is a tractor facing east.

What words did you use to describe movement and direction?

When you are ready, press ‘Answers’ to reveal some examples of possible answers to this grid challenge.

  • The farmer might want to fetch the watering can at F9. To get there from the duck pond (C2), the farmer can go up 6 spaces, right 3 spaces, and up 1 space.
  • Next, the farmer may need to water the cornfield. To get to the cornfield from F9, the farmer can go down 7 spaces (to F2).
  • From the cornfield, the farmer may want to check on the horses. The farmer can go up 1 space, left 4 spaces, and up 2 spaces (to B5).
  • Next, the farmer might go to the barn to return the watering can. From B5, they can go right 1 space, up 3 spaces, right 2 spaces, and up 1 space (to E9).

Action

Giving directions

Distance

When giving directions, it is important to describe the distance that needs to be traveled. You can use numbers and units to do this.

The following are some examples:

  • two metres (units)
  • five steps (numbers)
  • one kilometre (units)
  • three blocks (numbers)

Brainstorm

Brainstorm

Can you think of any other words that describe distance?

Turns

Most directions require movement in more than one direction.

Words to indicate a change in direction might be:

  • left
  • right
  • clockwise
  • counterclockwise
  • up
  • down

Brainstorm

Brainstorm

Can you think of any other words that indicate a change in direction?

Let’s explore some of these turns in more detail.

Clockwise

Clockwise means to turn to the right.

A clock with an arrow going from 12 towards 1. This is the direction a clock would turn.

Counterclockwise

Counterclockwise is the opposite of clockwise. It means a turn to the left.

A clock with an arrow going from 12 towards 11. This is the opposite direction a clock
						would turn.

Half-turn and quarter-turn

To make turns more exact or precise, and ensure we provide directions to the correct location, you can add the words half-turn and quarter-turn.

A half-turn turns an object back towards the way they were coming from.

For example, front to back.

A quarter-turn can be right (clockwise) or left (counterclockwise).

Questions

Respond to these questions about turns using a method of your choice:

  • Why do you need to indicate whether a quarter-turn is to the right or left?
  • Why don’t we need to describe a whole-turn or three-quarter-turn when giving directions?

When you are ready, press ‘Answers’ to reveal some possible responses.

Answer: We need to indicate right or left with quarter-turns so we can know which way to turn.

Answer: A whole-turn doesn’t change the position of the object because it’s right back to where it started. We don’t usually indicate a three-quarter turn because instead we talk about quarter turns.

Direction challenge

Explore a segment from following Look Kool episode entitled “Mapping.”

In the video, Hamza explored a 4 by 4 grid labeled ABCD on the y-axis, and 1 2 3 4 on the x-axis.

A grid that is 4 rows and 4 columns. The y-axis is labelled ABCD and the x-axis is
						labelled 1 2 3 4.

To travel from A1 to C4, we could give the following directions:

  • start at A1
  • move right three spaces
  • move up two spaces

Since there aren’t any obstacles, we could also provide the direction to move up and then right:

  • start at A1
  • move up two spaces
  • move right three spaces

Your turn

What directions would you give to get from D3 to A2?

Use the following Ten Frame to make your directions. This Frame is the same as the grid we explored, but the y-axis and x-axis aren’t labelled.

Your task is to place the arrows on the grid to make directions for getting from D3 to A2.

Giving and following directions

Let’s return to the farm grid that we explored in the Minds On section.

The following image displays the farm grid again.

There is a farm arranged in an 11 x 8 grid. The vertical axis is numbered 1 to 11, from the bottom to the top. The horizontal axis is labelled A to H, from left to right. There is a duck pond that spans from A1 to C1 and A2 to C2. The farmer stands at square C2 facing south toward the duckpond. To the right of the farmer, a cornfield spans from E1 to H1, and E2 to H2. There is a field of wheat stretching from D4 to F4, with a scarecrow at D4. A horse is standing on squares A5 and B5, and a small house appears on squares G5 and H5. Another horse is standing across squares A7 and B7. In the top left area, a windmill stands at B9. There is a barn on squares D9 and E9 and a watering can at F9. 2 squares to the right of the watering can, at H9, there is a tractor facing east.

Using the grid of the farm, answer the following questions by choosing the best answer.

Consolidation

Make your own instructions

Create a list of instructions (directions) to get from a starting point to an end point.

You must also create an alternate pathway to get to the same end point.

Be sure to include movement words such as half-turns and quarter-turns in your instructions.

You can use the following fillable and printable Grid Map document to create your instructions. If you’d prefer, you can use the Farm Map template and add any items you would like. You can also create a set of detailed instructions to a scenario of your choosing.

Record your directions using a method of your choice.

There is a farm arranged in an 11 x 8 grid. The vertical axis is numbered 1 to 11, from the bottom to the top. The horizontal axis is labelled A to H, from left to right. There is a duck pond that spans from A1 to C1 and A2 to C2. The farmer stands at square C2 facing south toward the duckpond. To the right of the farmer, a cornfield spans from E1 to H1, and E2 to H2. There is a field of wheat stretching from D4 to F4, with a scarecrow at D4. A horse is standing on squares A5 and B5, and a small house appears on squares G5 and H5. Another horse is standing across squares A7 and B7. In the top left area, a windmill stands at B9. There is a barn on squares D9 and E9 and a watering can at F9. 2 squares to the right of the watering can, at H9, there is a tractor facing east.

Think about your learning

  • How is understanding directions helpful in your life?
  • Is it important to have alternate (other) routes planned? Why or why not?
  • How can you improve your ability to make effective directions?

Reflection

How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

Now, record your ideas about your feelings using a voice recorder, speech-to-text, or writing tool.

Press ‘Discover More’ to extend your skills.

Harmony Honey Farms

It’s time to play a game! You will now access Harmony Honey Farms.

Questions

After playing, respond to the following questions. Record your ideas using a method of your choice.

  • What special words did you use to get the tractor to the beehive? These words describe movement.
  • List the movement words you used to complete the label design on a chart or in an audio recording

Lazy River

Play the TVO mPower game Lazy River to design a lazy river circuit.

Take a screen capture of your finished work if possible.

Now, create directions to describe the path the tubes take in your river.

Imagine the width of each square you place is 1 metre long, and include the number of metres the tube travels forward before a turn.

Use the following vocabulary to describe turns:

  • half-turn
  • quarter-turn
  • clockwise or right
  • counterclockwise or left

Is there another way to get to the lazy river? Revise if needed.