Growth Point 6

Addition and Subtraction Growth Points activities

The tasks listed on the following pages are rich tasks from various sources that may be used with multi-level groups or students who are working at a particular level.

6. Extending and applying addition and subtraction using basic, derived and intuitive strategies

Given a range of tasks (including multi-digit numbers), can solve them mentally, using the appropriate strategies and a clear understanding of key concepts.

Top table

Materials: None.

Activity: Students are placed into groups and appoint a recorder for each group. This person then records the street number of the home of each student. Working as a team, each group sums the street numbers, using an appropriate mental strategy. Class discussion can follow about the highest table total in the class. Is there a highest possible total? Is there a lowest possible total? How can they be sure?

Related key ideas: Properties of addition, combining, partitioning

Variation:

• Students find the median of street numbers for their table.

• I have a street and all the houses add up to x. What numbers could the houses have been?

• Can you place the houses on a number line? What do you notice about the way they are spread?

• If these were the only houses in the street, which house would be in the middle?

I went shopping and I bought...

Materials: Cards made from junk mail catalogues with priced items.

Activity: Place the cards face-down in the centre of the table. Students are given a spending limit for ‘shopping’. Note that the limit may vary with the type of catalogues used (e.g. supermarket catalogue with a $25 limit or a hi-fi catalogue with a $5,000 limit).

Students take turns to turn one card face-up and see what they bought when they went shopping. Students need to keep an exact total of what they spend until they reach their spending limit.

Once their limit is reached, students continue to turn the top card over, and they may trade one (or more) of their purchased items for the new one, provided they remain under their limit. After each purchase or trade, they must re-establish their total spending.

Related key ideas: Properties of addition, properties of subtraction, combining, partitioning, separation, comparison.

Variation: Students look at the items on up-turned cards. What are the possible combinations of items you can buy with your limit? What is the greatest amount of items you can buy? What is the smallest amount of items you can buy when spending all your limit? What do you notice about the cost of the items in each of these groups?

Heads high, tails low

Materials: Two dice, a coin, paper to record scores.

Activity: Each student commences this game with a score of 250. Students take turns to roll the two dice, and use the numbers to make a two-digit number. For instance, if you roll 2 and 5, you can opt to make 25 or 52. Once this two-digit number is determined, students toss the coin. If it lands as heads, they add this two-digit number to their total, and if it lands as tails they subtract it. The aim of this game is to be the first to reach either 0 or 500.

Related key ideas: Properties of addition, properties of subtraction, combining, partitioning, separation, comparison.

Variation: Students record their thinking as they go using a number line.

Race to the edge

Materials: One game card per pair, one dice labelled + 8, – 8, + 12, – 12, + 16, – 16, coloured pencil or counters for each student.

Activity: Each student begins the game in the centre of the board, on the square marked 50. Students take turns to roll the dice, and calculate their new total. For instance, a student starts at 50 and rolls 8, so can move to the square marked 58. However, students can only move to this total if it is adjacent (in any direction) to their current square. If there is no adjacent square with this total, play passes to the partner. Students track their progress across the game card by colouring or placing a counter over the squares they land in. The aim of the game is to be the first student to reach an edge of the square.

Related key ideas: Properties of addition, properties of subtraction, combining, partitioning, separation, comparison.

Variation: Students can move from an edge back into the centre 50 square.

Three-digit throw

Materials: Three dice for each pair.

Activity: Students draw a table with hundreds, tens and ones columns. They then take turns to roll the three dice. Make and record the highest possible number, and the lowest possible number using the three dice. Find the difference between these two numbers. Students keep a running total of their differences and progressively add these together. The winner is the first student to reach a total score of 1000.

Related key ideas: Properties of subtraction, partitioning, separation, comparison.

Salute you

Materials: Playing cards

Activity: Students place a card on their forehead without looking at it. Their partner then doubles that number that has been raised (e.g. if a student raised 7, the partner calls out 14). The student then needs to work out which card they have raised to their forehead (e.g. ‘I have a 7 because it is half of 14’).

Related key ideas: Properties of addition, properties of subtraction

Variation: Salute two cards to make a two-digit number.

Change the function that the partner is performing (e.g. instead of doubling, use +/– 1 or +/– 10).

Let's go shopping

Materials: Supermarket catalogue.

Activity: Students choose five items from a recent supermarket catalogue and round each item to the nearest dollar. They are then assigned $100 for shopping. Their task is to spend exactly $100, or as close to it as possible. What is the combination of quantities of these five items that gives a total closest to $100? Share ideas and results.

Related key ideas: Properties of addition, properties of subtraction.

Variation: Increase total from $100 or include more than five items, or make limitations such as choosing at least two of each item.

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