This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.
A PDF of the student activity is included.
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use place value strategies to solve addition problems
FIO, Link, Number Sense, Book One, Aiming High, paes 4-5
Photocopy the game board copymaster provided at the back of this booklet to give each student a recording sheet for the game.
This game is a great way to strengthen place value understanding and to devise some problem-solving strategies involving addition.
Explain the rules to the students through a short demonstration. Emphasise the rule that does not allow them to change the place of the number once it has been entered as well as the rule that it is important to enter a number on every turn. These are vital rules to encourage them to develop a strategy other than trial and error.
After the students have played a few games, increase the pace at which the dice is thrown. The increase in frequency of the throws may force them to change their strategies because they are no longer being given sufficient time to do an exact addition as they go.
Discuss possible strategies, such as starting high by using the first few throws to a score of about 900 and then concentrating on placing the remaining throws in the tens and ones to get the last 100 points. Alternatively, they could try starting low for the first six throws in the ones column and then use the last four throws to try to get near the target.
Have the students list the strategies they use and keep a tally of the winning ones to see which one gives the best results.
Question 1 in this activity poses a problem that involves finding the score nearest to the target number by looking at differences. Have the students discuss strategies that are easy and efficient for them to use in finding the differences.
They may choose to do a counting-on strategy for Tama’s score to build it up to 1 000. For example, 978 plus 2 makes 980 and plus 20 makes 1 000. So Tama is 22 away from 1 000. For Leila, they may just subtract 1 000 from 1 021 to find the difference of 21.
The use of a partial number line could help the students to see why Leila is closer to 1 000 than Tama. For example:
In question 2, you may need to encourage the students to make a list of all the possible results for Mere. This would show that Mere could end with a total ranging from 987 to 992 if she put the dice score in the ones place. With 987 (a 1), she would lose, and with 988 (a 2), she would tie. But if she throws a 1 or a 2, she
could put them into the tens place and make a total of 996 or 1 006.
Question 3b encourages the students to discuss the chances of making exactly 500. They could use a continuum with four or five descriptors or a number line to 100 and place the exact score of 500 somewhere along the line and discuss their reasons for the placement. For example:
“I placed it here because you could get exactly 500, but you would be very lucky to throw the numbers you would need at the end.”
The students could then keep a tally of 100 games played by the class and see how many times a score of 500 was achieved.
Extend the game by using two dice for each throw, with the students placing each of the two digits in any of the ones, tens, or hundreds places for every turn. This will encourage further strategies, such as rounding, to keep a running total.
Other ways to extend the challenge level include adding a thousands column and changing the target to 10 000 or adding a tenths column and keeping the target at 1 000.
Answers to Activities
A game using place value and addition
1. a. Strategies will vary. One possible strategy is to use large numbers first (hundreds and tens) until your total is in the nine hundreds and then use tens and ones only.
b.–2. Strategies will vary.
1. Leila wins because she is closer to 1 000 than Tama. (Tama is 22 less than 1 000, and Leila is 21 more.)
2. If Mere puts her last throw in the correct column, she has a 6 out of 6 chance of winning the game. (To win, she needs to put 1 or 2 in the tens column or 3, 4, 5, or 6 in the ones column.)
3. a. Strategies will vary.
b. It is possible to get exactly 500, but only if players get exactly the numbers they need at the end.