This is a level 3 link geometry activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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specify locations using grid references

FIO, Geometry and Measurement Link, Map Mysteries, page 22

Classmate

In this activity, students use grid references to solve a puzzle and to play a

variation on the Battleships game.

#### Activity

Ensure that your students know that co-ordinates are number pairs, used to specify the location of points on a grid (or points in a plane). They are arranged with the value from the x-axis (horizontal axis) first and the value from the y-axis (vertical axis) second. So the point (2, 3) is found 2 steps along from the origin (0, 0) and 3 steps up. To check that your students understand this, ask them to tell you what the co-ordinates are for the “D” of “Dog kennel” on the map in the student book (17, 9).

Some students will find the language of Jake’s poem quite difficult. Avoid going through it line by line and explaining what it means. This would rob the students of the excitement that comes from working it out for themselves. Put the students into small mixed-ability problem-solving groups of three or four and let them puzzle their way through it, asking for teacher help only when they need it. Tell them to keep the secret when they learn it so that others can discover it for themselves.

When they have circled the letters identified by the co-ordinates, the students should start with the letter E and count on to the next circled letter, making note of the “distance” (number of letters) from the first to the second. They then count from the second circled letter to the third, and so on, noting the distance each time.

When they reach the end of the alphabet, they loop back to the beginning (like this: ... W X Y Z A B C D ...), stopping when they reach the letter D (the last “3”). When they add the distances together, they should get 1 + 6 + 2 + 4 + (4 x 3) = 25.

The solution to the riddle hinges on the three mathematical words in the second line of the final stanza: co-ordinate, factors, and square:

• Co-ordinate was introduced and explained at the beginning of this activity in the usage “a pair of co-ordinates”; here it is being used in a different and unusual way, as a verb meaning “write as a pair of co-ordinates”.

- The students will have met the word factors before but may have forgotten what it means. Factors are numbers that are whole-number divisors of another number. For example, 1, 2, 3, 4, and 6 are all factors of 12 because they divide into 12 without remainder. In the case of Jake’s riddle, the students need to find the factors of the “special number” referred to. There are in fact two pairs of factors, but only one pair gives the co-ordinates of a point that lies on the map.
- Square is being used here to mean a “square number”, not a geometrical square. If your students don’t know this meaning of the word, give it to them when they need it, not at the beginning. Here are the first four square numbers:

#### Game

The treasure game is an adaptation of the traditional Battleships game. The main differences are that in the traditional game, the grid references consist of a number and a letter (for example, 5H) and define cells, not points.

The rules are as follows:

- The game is for two players or two teams of two.
- Each person or team has a map showing where treasure is hidden. The islands are the same for each player, but the treasure is in different locations.
- Players take turns at guessing where the treasure is hidden on their opponent’s map.
- Each time a player makes a guess, the other player says “miss” or “hit”. If it is a hit, the other player tells the first player which letter they hit (but not which treasure). Using their empty map, the first player records a dot for a miss or the letter for a hit.
- A player tells the other when they have successfully excavated (hit all the letters of) a particular treasure.
- Players keep taking turns until the treasure has been located and excavated.
- Points are awarded for each successful excavation, depending on the nature of the treasure and who found it first. See the student book for the scoring system.

To conclude this activity, use questions such as these to promote reflective thinking:

• Where have you seen grid references used in real life? (Map books, graphics in newspapers, crosswords, orienteering courses, seating arrangements …)

• Grid references don’t always use two numbers, but sometimes letters and numbers, such as A3. Why might this be? (Perhaps to make it easier for people to interpret if they don’t know how to read co-ordinates. There is less chance of confusion.)

#### Answers to Activity

If you unjumble the letters given by the co-ordinates, you will get these words:

To find exactly which of the flax bushes the treasure is under, you will need to work out the rest of the poem yourself! (When you’ve worked it out, you will have the

co-ordinates of the correct flax bush. You’ll know that you have got it right without an answer to tell you!)**Game**

A game involving co-ordinates.