Using Materials

Problem: Freddo the frog lives at number 28 on the number line. He wants to visit his friend at number 81. How far does he have to jump to get there? Stick the large number line on the board and record 28 + ? = 81.

Suggest Freddo will first jump to 30 because it is a “nice” or “tidy” number. Show this jump with an arrow and ring the jump of 2. Discuss how far Freddo has to go. Some  students will jump by tens to 80 then go 1 more. Some will jump 50 then 1 more, and a  few will jump 51 directly to 81. Show these jumps with arrows and ring the numbers. In all cases focus attention on the ringed numbers always giving the answer 53. Discuss which way is best. The students now do individual work with you observing their methods.

Examples. Give the students the first sheet from Material Master 5-12 and get them to  write the following 7 problems down against each number line. 39 + ? = 61, 48 + ? = 81, 57 + ? = 85, 29 + ? 78, 18 + ? = 60, 27 + ? = 93, 36 + ? = 90

The students do the problems then discuss the answers back as a whole group.

Using Imaging

Problem: Solve 18 + ? = 73

Draw a large empty number line on the board and discuss where to place the 18 and 73. Without adding 30, 40, 50, 60 and 70 to the empty number line discuss how to jump from 18 to 20 then to 73 in two steps. So the only numbers on the number line are 18, 20 and 73. Record the answer 55.

Examples. Get the students to turn over their sheet to use the empty number lines. It has 7 empty number lines. Get them to write the following 7 problems down against each number line; 29 + ? = 62, 58 + ? =93, 27 + ? = 86, 29 + ? = 78, 48 + ? = 70, 29 + ? = 83, 46 + ? = 83

Using Materials

Problem: “Ana goes Christmas shopping. She spends $345.60 on toys for her children and comes home with $208.95. How much money did she have to start with?”

Write ? – 345.60 = 208.95 on the board. Have the students cut a strip of paper, representing Ana’s unknown starting amount.

Cut off a piece and write $345.60 on it.

Discuss what goes on the other piece. (Answer: $208.95.)

Discuss what the starting amount must have been. (Answer: $345.60 + $208.95 = $554.55.)

Examples: Word stories and recording for: ? – 345 = 789

? – 456 = 102

? – 67.9 = 43.19

? – 67 = 90

? – 1 000 = 3 000

? – 200 = 560 ...

Using Imaging

Examples: Imagine the strips to solve these problems: Word stories and recording for:

? – 200 = 600

? – 220 = 230

? – $7.90 = $3.10

? – 111 = 238

 ? – 10 000 = 4 500 ...

Using Number Properties

Examples: Don’t use calculators for the fraction problems. Word stories and recording for:

? – 212.98 = 600.0034

? – 200.08 = 45.89

? – 7.9909 = 3.1091

 ? – 10 = 3/4

? – 2 1/3 = 1/3

? – 0.04 = 0.0009 ...

Understanding Number Properties:

a and b stand for any numbers: â–¡ – a = b. How would you work out

the number to put in the box? (Answer: I would work out the answer to a + b.)

Each player rules up a column for “tens” and a column for “ones”. The aim of the game is to get a total as close to 100 as possible. The student tosses a dice and decides whether the number will be put in the ones or the tens place. For example, if a four is thrown, it could either be 40 or four. The dice is rolled a total of seven times. All seven numbers must be used. The total of all the columned numbers may exceed 100, but the students will need to decide which player has got closer to 100.

Extension Activity

Use larger numbers and decimals for the target numbers. Vary the number of throws and what the thrown number can represent, such as:

Closest to 1 000: 10 throws of hundreds, tens, or ones.

Closest to 10: 10 throws of ones, tenths, or hundredths.

Closest to 1: 10 throws of tenths, hundredths, or thousandths
 

Preliminary Knowledge

The students need to know 10 hundreds make 1 thousand and vice versa, and 10

thousands make 1 ten thousand and vice versa.

Using Materials

Problem: The Bank of Mathematics has run out of $1000 notes. Alison wants to

withdraw $2315 in $1, $10 and $100 dollar. How many $100 notes does she get?

Examples. Repeat for: $2601, $3190, $1555, $1209, $2001, $1222, $2081….

Using Imaging

Problem: Tickets to a concert cost $100 each. How many tickets could you buy if you  have $3215?

Write $3215 on the board. Shield 3 one thousands, 2 one hundreds, 1 ten and 5 ones.

Ask the students what you can see. Discuss how many hundred dollar notes you could  get by exchanging the thousands. Discuss which notes are irrelevant (the ten and the ones).

Shielding and Imaging only: Examples. Find the number of hundreds in:

$1608, $2897, $2782, $3519, $3091, $4000….

Using the Number Properties

Examples. Find the number of hundreds in: 3459, 8012, 9090, 6088, 3280, 5823,

7721, 2083….

Challenging examples. Find the number of hundreds in: 13 409, 28 002, 78 370, 12

088, 45 290, 82 356, 21 344….

Find the number of tens in: 3709, 8002, 8579, 5208, 4829, 82 333, 12 897, 30

897, 89 000, 50 890

Using Materials

Problem: “Ray has $34, and he gets $25 for a birthday present. How much money does Ray have now?”
Record 34 + 25 on the board or modelling book. The students model 34 and 25 using the chosen materials and group the ones and tens.
Discuss the answer and record 34 + 25 = 59 on the board or modelling book.
Examples: Word stories and recording for: 45 + 22 52 + 13 42 + 25 35 + 43
53 + 25 43 + 22 ...

Using Imaging

Shielding and Imaging Only: Examples: Word stories and recording for: 14 + 43
31 + 25 23 + 41 24 + 25 32 + 26 38 + 21 13 + 41 25 + 23
44 + 24 ...
 

Using Number Properties

Examples: Word stories and recording for: 87 + 12 73 + 26 24 + 52 16 + 62
81 + 17 ...
Challenging examples: The students will need to understand the meaning of three-digit
numbers to do these: 241 + 21 342 + 44 643 + 21 27 + 210 303 + 44
25 + 510 ...