Decimal maze - Department of Education and Training



Task Description

This activity helps students to develop number sense of the four key operators (+ - x ÷) when applied to decimals, in an engaging and thought-provoking board game.

Students play in pairs taking turns moving a single counter around a maze board. They each start with the number 100 and are given a choice of moves to make with associated mathematical functions to perform on the number (using a calculator). A separate running total is maintained on each student's calculator throughout the game. The player with the highest number when the counter reaches the finish is the winner. In playing this game, the common misconception that multiplying always makes a number bigger and dividing always makes it smaller is challenged. It brings into play estimation skills, ICT skills and involves development of strategies to ensure the opponent ends up with a lower score.

Materials

• Decimal Maze Game Board & Instructions

• A four-function calculator per player

• One counter per pair

Key Mathematical Concepts

• Estimation of division, multiplication, addition and subtraction of decimal numbers mentally.

• Multiplication and division by a number less than one.

Using the Activity

• Introductory whole group discussion – revising how to add, subtract, multiply and divide decimal numbers using a calculator.

• Initial explanation of the game rules may include a brief demonstration of how to play if necessary. Students should be encouraged to estimate the possible moves prior to choosing which move they will make.

• Playing the game.

• Debrief of the game. This can include reflection, discussion or sharing the successful strategies used. What did students discover about dividing, multiplying, adding or subtracting a decimal number? Were there any patterns in this? The teacher could pose the question "what will happen if you divide by a number less than 1 (e.g. 0.9)?" to prompt further thought if necessary. This can be a good moment to establish/discuss multiplying and dividing by numbers larger and smaller than one.

• Play the game again to consolidate ideas learned (this can be done during the same session or returned to later).

• The game takes approximately 10 minutes to play.

Prerequisite Knowledge

Students should be familiar with decimal numbers, and have some understanding of how to add, subtract, multiply and divide them. Students should also be competent using a four-function calculator.

Links to VELS

|Dimension |Standard |

|Working Mathematically (Level 2) |They use place value to enter and read displayed numbers on a calculator… they use a four-function |

| |calculator… to check the accuracy of mental and written estimations. |

|Number (Level 3) |They estimate the results of computations and recognise whether these are likely to be |

| |over-estimates or under-estimates. |

|Number (Level 3.75) |Recognition that multiplication can either enlarge or reduce the magnitude of a number |

| |(multiplication by fractions or decimals). |

|Number (Level 4) |They add, subtract, and multiply fractions and decimals (to two decimal places) … They use estimates|

| |for computations and apply criteria to determine if estimates are reasonable or not. |

Assessment

When evidencing knowledge at VELS level 3.75, students will be able to explain that multiplying by a number less than one results in a smaller number, whilst multiplying by a number greater than one results in a larger number, and that the converse is true for division. Students will apply this knowledge to develop effective strategies to achieve a large number at the end of the game.

Students will also be able to successfully use a four-function calculator for this activity.

Teacher Advice

Some teachers in the trial suggested that a session on calculator use prior to the activity could be useful. Some teachers also found the discussions within the classroom were critical to the success of using this activity as a learning tool for decimal division and multiplication.

Some teachers found drawing diagrams of division by decimals (e.g. 6 ÷ 0.5), and using language like ‘how many halves are there in 6?’ was needed to help students understand the concepts.

Potential Student Difficulties

In the trial, some students were unfamiliar with how to use a calculator, and others keyed in the wrong information.

Some students found the concepts of decimal division and multiplication difficult in the trial.

Feedback

87% of the 85 students who trialled this activity reported that they learned some new mathematics as a direct result. One student described it as an ‘easy way to learn and it was fun’.

Most student feedback demonstrated a clear understanding of the key mathematical concepts investigated throughout this task.

All teachers in the trial reported that their lessons had gone well and that their set goals had been met.

Example 1

Provides evidence of student working at VELS Level 3.75

[pic]

This student has identified that dividing by 0.9 results in the largest increase in a number on the game board. The concept that multiply and divide are inverse functions has been clearly understood, and that both multiplying and dividing can enlarge or reduce a number.

Example 2

Does not provide evidence of student working at VELS Level 3.75

[pic]

This student is not comfortable with decimal places, and has incorrectly computed division by a number less than 1. He/she considers that dividing and subtracting will always make a number smaller, and did not recognise the significance of the observation that multiplying by a number less than 1 reduced the value.

Example 3

Provides evidence of student working at VELS Level 3.75

[pic]

This student has clearly identified that multiply and divide are inverse functions. He/she understands that multiplying does not always increase a number, and dividing does not always decrease it.

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