Dot to Dot

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Purpose

This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.

Achievement Objectives
NA5-3: Understand operations on fractions, decimals, percentages, and integers.
Student Activity

 

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Specific Learning Outcomes

find fractions of whole numbers (Level 4)

add fractions

multiply fractions

Description of Mathematics

Number Framework Links
Use this activity to:
• help students consolidate and apply their knowledge of equivalent fractions (stage 7)
• develop confidence in students who are beginning to use advanced multiplicative strategies (stage 7).

Required Resource Materials

1 or 2 classmates

Photocopy of Gameboard copymaster

FIO, Level 3-4+, Proportional Reasoning, Book One, Dot to Dot, page 10

Activity

Game

This variation on an old game will motivate students to apply their knowledge and strategies to calculations involving fractions. The challenge of devising a winning strategy will encourage them to come back and play the game again.

This game could become a valuable addition to your repertoire of practice and maintenance activities suitable for independent use.

Most of your students are likely to have met and played the traditional version of this game. When explaining the rules for this version, highlight the key difference that the player who completes a square does not get an extra turn. This means that the emphasis moves from completing as many squares as possible to trying to complete the squares that are worth most points. Some squares are worth very little; others are worth a lot.

Note that “of” appears as an operator in a number of squares. Compare the questions that use “of” with those that use the “x” sign. The game reinforces the fact that both operators have an identical effect.

After the students have played the game a couple of times, get them to discuss strategy. Questions such as these will focus the discussion:

  • Which squares are worth most?
     
  • Is it more important to try for squares that are worth most or ones that you are sure to get correct?
     
  • Which operation gives the most points?
     
  • Which squares did you find most difficult?

If players can’t agree on an answer, they could ask a classmate or consult the answers master.

You may need to discuss with your students how they will total their points. It may be simplest if each player keeps a running total. Most of the answers are easily added whole numbers. The fractions will be a little more difficult, and if students have trouble with them, you could suggest that they record them as they win squares, but leave the addition until the end of the game. As this game is about learning to add and multiply fractions, players should not use  calculators!

Activity

There is plenty of scope here for students to create their own game boards, using fraction problems that are within their range of understanding. The game board copymaster has no subtractions or divisions. Students could make a game that includes one or both of these operations.

You may like to make up further game boards yourself, at different levels of difficulty. If you make them as masters and copy them as needed, you will get good value out of the time spent.

Answers

Game
A game for practising adding and multiplying fractions
Solution:

Activity
Game boards will vary.

Attachments
DotToDot.pdf225.83 KB
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Level Five