TUTOR GUIDE
Title: WORMS AND LADDERS GAME Entry Level THREE
MATHS CONCEPTS COVERED:Standards Ref:
C1
C2 / Add and subtract three- digit numbers
Solve practical problems involving multiplication and division by 2, 3, 4, 5 and 10
Using a calculator
PROCESS SKILLS COVERED:
Representing
Analysing / · Apply addition, subtraction, multiplication or division to obtain answers to simple problems that are clear and routine
· Using simple checking procedures
Interpreting
FUNCTIONAL MATHS BARRIERS ADDRESSED:
· Applying mathematical procedures correctly
· Choosing how to check answers
TASK BRIEF:
· Description of task
This is a board game for two or three players designed to develop and consolidate skills in using reverse calculations or alternative calculations to check answers to questions.
Preparing learners to play the game
- Ensure learners understand how to check answers to simple additions and subtractions
[e.g. 4 + 6 = 10 and 18 – 12 = 6] by carrying out reverse calculations [i.e. 10 – 6 = 4 and 12 + 6 = 18].
- Ensure learners are familiar with and ÷ as symbols for division.
- Ensure learners understand how to check answers to simple multiplications and divisions
[e.g. 3 x 5 = 15 and 10 ÷ 2 = 5] by carrying out reverse calculations [i.e. 15 ÷ 5 = 3 and 2 x 5 = 10].
- Ensure learners understand how to check answers to multiplications and divisions by carrying out repeated additions
- [e.g. 48 ÷ 3 = 16 can checked by repeatedly adding 16: 16 + 16 + 16 = 48].
Making up the game
- Photocopy the game board to A3 size in colour
- Make up five sets of cards as follows:
· 10 + and – cards with questions numbered 1 to 10 and 1 (point) on the reverse side
· 10 + and – cards with questions numbered 11 to 20 and 2 (points) on the reverse side
· 10 + and – cards with questions numbered 21 to 30 and 3 (points) on the reverse side
· 10 x and ÷ cards with questions numbered 1 to 10 and 2 (points) on the reverse side
· 10 x and ÷ cards with questions numbered 11 to 20 and 3 (points) on the reverse side
Rules for playing the game
The aim of the game is to earn as many points as possible.
- Shuffle the 1-point + - cards and place in a pile with the questions face down
- Repeat for the 2-point + - cards, the 3-point + - cards, the 2-point x ÷ cards and the 3-point x ÷ cards.
- Start the game by putting one counter for each player inside the start box.
- Take it in turns to throw the die and move your counter around the board according to the score on the die.
- If you land on a square containing the bottom of a ladder, you instantly move up to the square containing the top of the ladder.
- If you land on a square containing the end of a serpent, you instantly move down to the square containing the head of the serpent.
Landing on a pink square
- If you land on a pink ‘+ or – ‘ square, you must pick up a ‘+ or –‘ card: these have either an adding question with an answer or a subtracting question with an answer on them.
- You can choose a card from the top of the 1-point pile, the 2-point pile or the 3-point pile, depending on how difficult you want your question to be.
- Once you have chosen a card, your job is to work out whether the answer is right or wrong: to do this, you must check the answer by writing down and working out a reverse calculation
[you can do this on a mini whiteboard or on paper].
- Use a calculator only if you need to double check answers.
- Find the appropriate question number on the Add and Subtract Answer Sheet and see if your checking method agrees with one of the checking methods on it.
- If you are correct, you earn the number of points shown on the back of the card.
- Use the score sheet to record the points you earn [one player can record all the points for all players during the game if you prefer].
- If you land on a pink ‘x or ÷ ‘ square, you must pick up a ‘x or ÷‘ card: these have either a multiplying question with an answer or a dividing question with an answer on them.
- You choose a card from the top of the 2-point pile or the 3-point pile, depending on how difficult you want your question to be.
- Once you have chosen a card, your job is to work out whether the answer is right or wrong by checking the answer using a reverse calculation.
- Use a calculator only if you need to in order to double check answers.
- If you have chosen a 3-point question, you can also check the answer by working out an appropriate repeated addition if you prefer.
- Find the appropriate question number on the Multiply and Divide Answer Sheet and see if your checking method agrees with one of the checking methods on it.
- If you are correct, you earn the number of points shown on the back of the card.
- Use the score sheet to record the points you earn.
The game ends when one of the players passes over the Finish square.
When this happens, the points for each player must be added and the winner is the player with the highest score.
· Teaching and Learning Strategies
The primary aim of the game is develop skills in using reverse calculations as a means of checking.
The question cards are subdivided into 1 point cards, 2 point cards and 3 point cards in order to allow for differentiation between learner skill-levels in the game.
The 3-point multiplication and division question cards allow learners to choose repeated addition as an alternative method of checking answers to questions. The rationale behind this is that:
- Learners choosing a 3-point card may be more likely to have the skill-level to think about a second method of checking
- Questions such as 12 x 4 = 48 may lead to learners attempting to divide by a two-digit number when using reverse checking [i.e. 48 ÷ 12 = 4]; candidates may find working out 12 + 12 + 12 + 12 more accessible.
Checking methods on the multiplication and division answer sheet do not involve repeated additions with more than five numbers added together. If learners do add more than five numbers to check an answer, they may still be awarded the points, as long as the checking method is correct [e.g. when checking 36 ÷ 9 = 4, learners have worked out 4 + 4 + 4 + 4+ 4 + 4 + 4 + 4 + 4].
The multiplication questions have been designed so that any division occurring during checking does not involve decimals.
Repeated subtraction has not been included in the design of the game; tutors may choose to alter the game to include this as valid method of checking division questions if this is appropriate to their learners.
The game is purposely designed for a maximum of three players to:
- reduce boredom
- enable learners to work on calculations together as one small group.
When monitoring the game, tutors should ask learners open questions to prompt them into working out how to check answers for themselves.
Tutors should also encourage learners who are not engaged with working out checks to get involved with working with other players who are: this gives them opportunities to practice checking techniques further and to explain how to check questions to other learners.
The use of mini whiteboards means that players can try out checks and then share them with others more easily.
Learners often prefer using mini whiteboards to show their calculations as they can quickly erase mistakes and edit their working out as the discussion develops.
Entry Three