Cross Off

Years K - 8

Summary

Children create their own number line and then explore it in a game situation by using their own addition and subtraction exercises. One student starts the investigation with a 'sum', then the other continues from that answer. A running record is also kept on paper and on the calculator. The person who can't move loses. The challenge is new every time because the starting equation will vary, also the limits of the number line can change, so the activity is suitable for threading.

Materials

  • Scrap paper
  • Large digit cards 0 - 20
    (and perhaps others as below)
  • One calculator per pair
This student is about to press = to record the second equation.

Acknowledgement

This activity derives from the work of Lynne McClure, a Scotland-based consultant who works throughout the UK. It is used here with permission.

Procedure

Lynne never tells children the rules of a game. Instead she uses an animation and expects the children to tell her what they think the rules are, or she 'trains' one student first then acts out the game on the board with her helper; again the children are expected to work out the rules of the game.

You can try this approach with this animation for Cross Off:

  • PDF file - left click to start from within the web page, or right click to save to your computer then double click to start.
  • Use keyboard arrows to change slides.
  • From within the web page, use Home to return to first slide then show the slides again.
  • If using the saved version in your computer using arrows will loop the slides back to the start.
Another approach is to hand out large digit cards from 0 to 20 and ask children to line up in order 'with the smallest at this end'. Choose two other children to play the game on the whiteboard using this human number line as a model. 		 

Content

  • addition facts beyond 10
  • addition facts to 10
  • decimal calculations
  • fraction calculations
  • mathematical conversation
  • number line - ordering, operations
  • numeral recognition
  • operations - whole number
  • place value
  • problem solving
  • properties of zero
  • recording - calculator
  • recording - written
  • subtraction
  • writing numerals

Player A writes an addition or subtraction of two numbers from the line so that the answer is also a number on the line. For example: 3 + 2 = 5:

  • 3 and 2 crouch down and can't be used again
  • 5 raises their card high in the air
  • Player A writes their equation on the whiteboard
Player B has to begin their addition or subtraction with 5 and the other two numbers they use must be available on the number line. For example: 5 - 1 = 4.
  • 5 and 1 crouch down and can't be used again
  • 4 raises their card high in the air
  • Player B writes their equation on the whiteboard
Play continues like this until one player can't take a turn and loses (or whatever other rules the students have created by studying the animation).

Having acted out the game invite students to return to their seats. On the whiteboard, sketch a number line from 0 - 20 (with arrowheads at each end) and from the record kept by Players A and B, invite some children, in turn, to come out and cross off the numbers in the order they were played. Circle a number (as in the photo above) when it is the answer. As this happens on the board, all students keep a running record on their calculator.

Students now play a tabletop model of the game by first sketching a number line on scrap paper. They write their equation as above and also keep a running record on the calculator.

Variations & Extensions

  1. Rather than play a competitive game between two, work as a team (and classroom community) to try to cross off the most numbers before the game is blocked.
  2. Change the rules, for example, so an addition must be followed by a subtraction and vice versa.
  3. How can zero be used?
  4. Change the number line limits:
    • What happens if we use a line from -10 to +10?
    • What happens if we use a line from 1 to 3 and mark it in tenths?
    • What happens if we use a line from 0 to 5 and mark it in quarters?


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Calculating Changes ... is a division of ... Mathematics Centre