Double Double Boil and Bubble
We are practising doubling numbers with 2 or more digits.
Exercise 1 – W or Nothing!
What to do
1) Use your doubling strategies to double these numbers
2) Do the problems in your head
3) Record the answers
1) 2 (2) 12 (3) 42
4) 3 (5) 23 (6) 34
7) 4 (8) 44 (9) 84
10) 5 (11) 65 (12) 125
13) 7 (14) 27 (15) 47
16) 6 (17) 36 (18) 56
19) 9 (20) 19 (21) 59
22) 8 (23) 38 (24) 68
25) 67 (26) 75 (27) 175
28) 93 (29) 95 (30) 99
Describe a doubling strategy and share this idea with your partner.
How could you use this idea to halve a number? Try it!Exercise 2 – Seeing DDouble on the 100s BBoard
You need a hundreds chart (maybe several) and two counters.
What to do
1) Use your doubling strategies to double these numbers
2) Double each number and place a counter on the hundreds board showing BOTH the number and its double.
1) 21 (2) 13 (3) 48
4) 32 (5) 24 (6) 39
7) 42 (8) 45 (9) 54
10) 53 (11) 69 (12) 154
13) 72 (14) 74 (15) 79
16) 64 (17) 37 (18) 55
19) 92 (20) 18 (21) 58
22) 83 (23) 39 (24) 63
25) 62 (26) 71 (27) 575
28) 91 (29) 96 (30) 98
Moving down and moving across…what do you notice?
How could you use this idea to halve a number? Try it!Exercise 3 – Seeing DDoubles on the NNumberline
You need a numberline from 1 to 100, two counters and some floor space.
What to do
1) Use your doubling strategies to double these numbers
2) Double each number and place a counter on the numberline showing BOTH the number and its double.
1) 22 (2) 26 (3) 28
4) 31 (5) 33 (6) 37
7) 14 (8) 43 (9) 45
10) 51 (11) 57 (12) 58
13) 61 (14) 71 (15) 81
16) 16 (17) 76 (18) 86
19) 77 (20) 87 (21) 97
22) 78 (23) 88 (24) 98
25) 15 (26) 17 (27) 19
28) 94 (29) 394 (30) 994
How far is the doubled number from zero?
How could you use this idea to halve a number? Try it!Exercise 4 – Dice Doubles with Two Digits
You need two different coloured decagon dice with 0 to 9 on them.
You need one or two partners.
What to do
1) Use your doubling strategies to double the numbers
2) Choose one colour for tens digit and the other for the ones digit. Toss the dice and say the number. First person to say the correct double wins.
First to 5 wins the game.
Game Score SheetExercise 5 –Dice Doubles with Three Digits
You need three different coloured decagon dice with 0 to 9 on them.
You need one or two partners.
What to do
1) Use your doubling strategies to double the numbers
2) Choose one colour for hundreds digit, another colour for the tens digit and another colour for the ones digit. Toss the dice and say the number. First person to say the correct double wins.
First to 5 wins the game.
Game Score SheetExercise 6 – Big Double Trouble
What to do
1) Use your doubling strategies to double these numbers
2) Do the problems in your head
4) Record the answers
1) 222 (2) 244 (3) 245
4) 322 (5) 350 (6) 375
7) 425 (8) 450 (9) 475
10) 500 (11) 555 (12) 590
13) 707 (14) 207 (15) 407
16) 667 (17) 616 (18) 166
19) 999 (20) 919 (21) 599
22) 888 (23) 388 (24) 688
25) 697 (26) 679 (27) 967
28) 976 (29) 796 (30) 769
What is your favourite doubling strategy?
Double Double Boil and Bubble
Teacher’s Notes
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (Mikes Investigation Sheet link) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.
Number Framework domain and stage:
Multiplication and Division – Early Additive, Advanced Additive, Advanced Multiplication
Curriculum reference:
Number Level 4
Numeracy Project book reference:
These exercises and activities follow from a teaching episode based on Book 6 page 25 and Book 6 page 40. Extra teaching episodes are described with the exercise notes below.
Materials:
• Multilink blocks
• 100s chart and flipblock 100s board
• counters
• calculator
Prior Knowledge. Students should be able to:
• explain 1x2 = 2
• double any two digit number
During these activities students will meet:
• placevalue
• multiples of 2
Background:
Further information to back up what they will meet:
• FIO Books – Check Number Books for doubling activities.
• Digistore Activities – See http://www.nzmaths.co.nz
• National Archive of Virtual Manipulatives (via Google)
Comments on these exercises
In exercises 1,2,3 and 6 some attempt to structure the problems to encourage use of other answers, two more and two less, close to ten strategies. Doubling is a very powerful skill, and possibly the most important following counting, that students must aquire early. The first three exercises cover all numbers from 2 to 99.
Exercise 1
Teaching lessons preceeding this exercise could include:-
• single digit doubling,
• shifting through 10, 100 and beyond,
• doubling near 10, 100, 1000
• doubling 25, 50, 75
• modelling doubling as adding same number twice and two groups the same
Exercise 2
Teaching lessons preceeding this exercise could include:-
• modelling on the 100s board that 24 for example is down 2 rows and across 4 when doubled becomes down 4 rows and across eight.
• discuss what happens at the tens change, place value.
• link halving to doubling.
• discuss and model what happens when numbers go over 100
Students are also learning how to halve when they learn how to double.
Exercise 3
Teaching lessons preceeding this exercise could include:-
• modelling on the number line and linking length as distance from the zero to twice the length or as same length again.
• the halving could be modelled as a folded reflection
Exercise 4
Check students can use the dice to randomly generate two digit numbers.
Exercise 5
Check students can use the dice to randomly generate three digit numbers.
Exercise 6
Teaching lessons preceeding this exercise could include:-
• revision of doubling with shifts through 10 and 100 and beyond.
Practice excercises with answers (.pdf for whole file, .doc for parts)
Double Double Boil and Bubble – Answers
Exercise 1
1) 4 (2) 24 (3) 84
4) 6 (5) 46 (6) 68
7) 8 (8) 88 (9) 164
10) 10 (11) 130 (12) 250
13) 14 (14) 54 (15) 94
16) 12 (17) 72 (18) 112
19) 18 (20) 38 (21) 118
22) 16 (23) 76 (24) 136
25) 134 (26) 150 (27) 350
28) 186 (29) 190 (30) 198
Exercise 2
1) 42 (2) 26 (3) 96
4) 64 (5) 48 (6) 78
7) 84 (8) 90 (9) 108
10) 106 (11) 138 (12) 308
13) 144 (14) 148 (15) 158
16) 128 (17) 74 (18) 110
19) 184 (20) 36 (21) 116
22) 166 (23) 78 (24) 126
25) 124 (26) 142 (27) 1150
28) 182 (29) 192 (30) 196
Exercise 3
1) 44 (2) 52 (3) 56
4) 62 (5) 66 (6) 74
7) 28 (8) 86 (9) 90
10) 104 (11) 114 (12) 116
13) 122 (14) 142 (15) 162
16) 32 (17) 152 (18) 172
19) 154 (20) 174 (21) 194
22) 156 (23) 176 (24) 196
25) 30 (26) 34 (27) 38
28) 188 (29) 788 (30) 1988
Exercise 6
1) 444 (2) 488 (3) 490
4) 644 (5) 700 (6) 750
7) 850 (8) 900 (9) 950
10) 1000 (11) 1110 (12) 1180
13) 1414 (14) 414 (15) 814
16) 1334 (17) 1232 (18) 332
19) 1998 (20) 1838 (21) 1198
22) 1776 (23) 776 (24) 1376
25) 1394 (26) 1358 (27) 1934
28) 1952 (29) 1592 (30) 1538