Numbers and the number system
Swap to order
Solving mathematical problems
Challenge
You will need:
For example: Shuffle a set of 0–9 digit cards. Place the 10 cards, face up, in a row.
8 3 6 0 4 5 1 7 2 9
Complete the statement below by swapping two cards. p For example: < 5 3 6 0 4 < 8 1 7 2 9 Now complete the statement below by swapping two cards. The two numbers must be different from the numbers you swapped in the previous statement. For example: p > 9 3 6 0 4 > 8 1 7 2 5
• set of 0–9 digit cards • any two additional 0–9 digit cards, for example 4 and 7
Repeat the above process twice more until you have written six different statements: three using the ‘less than’ symbol, and three using the ‘greater than’ symbol.
Numbers and the number system
What are the number sequences? Challenge halleng g
235 500
2750 75
235 200 235 000
24 150 215 150
7950
–50
2350
6950 2550
235 300 245 150
29 150
235 600
235 400 0
27 150 25
265 150
3950
2650
4950
–75
225 150 25 150
Solving mathematical problems
26 150 9950
2450
2950 23 150
–25 5950
2850 235 100
These 42 numbers are from six different number sequences. Each sequence has seven numbers.
205 150
Identify the six number sequences, writing the numbers in order, from smallest to largest.
235 150
8950 255 150 50 28 150
Then for each sequence, look at the seven numbers and write the number that comes before the first number, and the number that comes after the last number.
Record all the statements you make.
Think about …
Then order your 12 numbers, from smallest to largest.
Think about … Remember, you can’t use the same number twice. All 12 numbers must be different.
Remember, you’re alternating between statements, using the ‘less than’ and ‘greater than’ symbols. 8
What if ? What if you use 12 digit cards and complete the statements below?
Which digits are the same among certain sets of numbers? Which digits are different? What does this tell you?
What patterns can you spot in the different sets of numbers?
> < Write six different statements: three using the ‘greater than’ symbol, and three using the ‘less than’ symbol. Record your statements, then order the 12 numbers, starting with the smallest.
When you’v e finished, tur n to page 80.
What if ? What is the rule for each sequence? Using those same six rules, write another six similar number sequences. Make sure each sequence has seven numbers. Rewrite your list of 42 numbers so that they are all mixed up and give them to a friend. Can they identify your six number sequences, writing the numbers in order from smallest to largest?
When you’v e finished, tur n to page 80. 9