Transcript x 10 - A Learning Place

x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
ones
÷ 10
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
ones
÷ 10
3
4
1
3
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
ones
÷ 10
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
ones
÷ 10
Place Value 20
Fractions and Decimals 11
x 10
thousands
x 10
hundreds
÷ 10 =
tens
÷ 10
÷ 10
x 10
ones
÷ 10
tenths
÷ 10
1
10
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
x 10
ones
÷ 10
tenths
1 ÷ 10 4
Place Value 20
Fractions and Decimals 11
Investigation:
1. At least once a week, draw a multiplicative place value chart to tenths
from memory.
2. Explain to a friend that you are multiplying by 10 to get the value of
the column on the left.
3. Explain to a friend that you are dividing by 10 to get the value of the
column to the right.
Reflection: Why is the value of the column to the right of the ones
column, tenths?
Problem Solving
What number is missing from this place value chart?
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
x 10
ones
÷ 10
tenths
1 ÷ 10 4
1
4
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
tens
÷ 10
x 10
x 10
ones
÷ 10
tenths
1 ÷ 10 4
1
.4
decimal point
dec means 10
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
x 10
ones
÷ 10
.
tenths
0 ÷ 10 4
0
.4
Place Value 20
Fractions and Decimals 11
Investigation:
1. Gather examples of points (dots).
2. Investigate if they are decimal points.
For example,
in time, the colon is sometimes recorded as a dot. Is the dot a decimal point? Are we
multiplying and dividing by 10?
the dot dividing the seconds from the fractions of seconds when timing races. Is the
dot a decimal point? Are we multiplying and dividing by 10?
in AFL, scores are recorded using a dot. Is the dot a decimal point? Are we multiplying
and dividing by 10?
the dot between the dollars and cents. Is the dot a decimal point? Are we multiplying
and dividing by 10?
Reflection: What is a decimal point?
Problem Solving
Is this dot a decimal point? $5.25 Why?
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
x 10
ones
÷ 10
.
tenths
÷ 10
1
. 1
.
0 1
Place Value 20
Fractions and Decimals 11
Investigation:
1. Draw a multiplicative place value chart to tenths.
2. Select a card and place it in the tenths column.
3. Record the number with and without the zero in the ones place.
4. Explain that the number’s value is still ‘tenths’.
For example, select
Record the number as 0·4 and as ·4, explaining
that the value is still 4 tenths or
𝟒
𝟏𝟎
.
Problem Solving
Jill recorded a number as 0·7 and Jerry recorded a number as ·7
Do both numbers have the same value? What is the value?
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
tens
÷ 10
x 10
x 10
ones
÷ 10
tenths
1 ÷ 10 0
1 = 1 one
1 = 10 tenths
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
tens
÷ 10
x 10
ones
tenths
1 ÷ 100 ÷ 10 0
10 = 1 ten
10 = 10 ones
10 = 100 tenths
Place Value 20
Fractions and Decimals 11
x 10
thousands
hundreds
÷ 10
x 10
x 10
1
tens
÷ 10
0
x 10
ones
÷ 10
tenths
0 ÷ 10 0
100 = 1hundred
100 = 10 tens
100 = 100 ones
100 = 1000 tenths
Place Value 20
Fractions and Decimals 11
Investigation:
1. Draw a multiplicative place value chart to tenths.
2. Select a card and place it in the ones place.
3. Describe your number of ones using standard and non-standard place value as a number
of ones and as a number of tenths.
4. Place your card in the tens place.
5. Describe your number of tens using standard and non-standard place value as a number
of tens and as a number of tenths.
6. Place your card in the hundreds place.
7. Describe your number of hundreds using standard and non-standard place value as a
number of hundreds and as a number of tenths.
Reflection: How can we describe ones, tens and hundreds as tenths?
Problem Solving
Alex recorded a number as 5 tens.
Mike recorded a number as 500 tenths.
Did they both record the same number?
Place Value 20
Fractions and Decimals 11
x 10
thousands
x 10
hundreds
tens
÷ 10
÷ 10
x 10
x 10
ones
÷ 10
.
tenths
1 ÷ 10 4
.
1. 4 = 1
1.4 = 14 tenths
1. 4 =
1 4 = 1 one + 4 tenths
4
10
14
10
Place Value 20
Fractions and Decimals 11
Investigation:
1. Draw a multiplicative place value chart to tenths.
2. Select cards to make a number with ones and tenths.
3. Describe your number using standard and non-standard place value.
4. Record tenths as both fractions and decimals.
For example,
3.2 = 3 ones + 2 tenths, 3.2 = 32/10
3.2 = 32 tenths, 3.2 = 32/10
Reflection: How can we describe numbers with tenths using standard and nonstandard place value?
Problem Solving
7.3 is equal to:
(a) 7 tenths and 3 ones
(b) 7 ones and 3 tenths
(c) 73 ones
Problem Solving
7.3 is equal to:
7
(a) 3
10
3
10
(b) 7
(c) 73
Problem Solving
6.8 is equal to:
(a) 68 tens
(b) 68 ones
(c) 68 tenths
Place Value 20
Fractions and Decimals 11
x 10
thousands
x 10
x 10
hundreds
tens
÷ 10
÷ 10
1
x 10
ones
÷ 10
.
12.4 = 1 ten + 2 ones +
12.4 = 12 ones + 4 tenths
12.4 = 12
12.4 = 124 tenths
12.4 =
.
tenths
2 ÷ 10 4
12 4 = 1 ten + 2 ones + 4 tenths
4
10
4
10
124
10
.
12.4 = 5 ones +
12 4 = 5 ones + 77 tenths
77
10
Place Value 20
Fractions and Decimals 11
Investigation:
1. Draw a multiplicative place value chart to tenths.
2. Select cards to make a number with tens, ones and tenths.
3. Describe your number using standard and non-standard place value.
4. Record tenths as both fractions and decimals.
Reflection: How can we
For example,
describe numbers with
53.2 = 5 tens + 3 ones + 2 tenths
tenths using standard
53.2 = 53 ones + 2 tenths
and non-standard
53.2 = 532 tenths
place value?
53.2 = 3 tens + 12 ones + 12 tenths
Problem Solving
47.3 is equal to:
(a) 4 tens and 7 tenths and 3 ones
(b) 4 tens and 7 ones and 3 tenths
(c) 473 ones
Problem Solving
46.8 is equal to:
(a) 468 tens
(b) 468 ones
(c) 468 tenths
Problem Solving
47.3 is equal to:
(a) 43
7
10
3
10
(b) 47
(c) 473
Place Value 20
Fractions and Decimals 11
x 10
thousands
x 10
hundreds
x 10
x 10
hundreds
÷ 10
tens
x 10
tens
÷ 10
x 10
ones
÷ 10
÷ 10
÷ 10
thousands
x 10
0.8 x 10 = 8
tenths
÷ 10
x 10
ones
÷ 10
.
.
tenths
÷ 10
Place Value 20
Fractions and Decimals 11
x 10
thousands
x 10
hundreds
x 10
x 10
hundreds
÷ 10
tens
x 10
tens
÷ 10
x 10
ones
÷ 10
÷ 10
÷ 10
thousands
x 10
8 ÷ 10 = 0.8
tenths
÷ 10
x 10
ones
÷ 10
.
.
tenths
÷ 10
Place Value 20
Fractions and Decimals 11
Investigation:
1.
2.
3.
4.
5.
6.
Reflection: Why do digits
Draw a multiplicative place value chart to tenths.
move to the left when
Place cards in columns to make a number.
we multiply by 10 and to
Record the number.
the right when we divide
Move the digits one column to the left.
by 10?
Record the new number.
What happened to the value of the number when you moved the digits one column to
the left? Problem Solving
Alex placed a digit in the tenths column.
He multiplied it by 10.
Which column is the digit in now?
What is the value of the digit now?
Problem Solving
Alex placed a digit in the ones column.
He divided it by 10.
Which column is the digit in now?
What is the value of the digit now?
Place Value 20
Fractions and Decimals 11
Place Value 20
Fractions and Decimals 11
More Investigations:
1.
2.
3.
4.
5.
Sit with a friend.
Each select cards to make a number with tenths.
Place your numbers in order.
Explain your order using place value.
Each of you make a number with tenths that would come between your
numbers.
6. For example,
Reflection: How did you use place value to order your numbers?
Place Value 20
Fractions and Decimals 11
More Investigations:
1. Sit with a friend.
2. Take turns to take a card and place it in either the tenths
place or the ones place or the tens place.
3. Once placed it cannot be changed.
4. Read your number out loud.
5. The child who creates the highest / lowest number takes
all cards.
6. Explain your number using standard place value.
7. Each place your number on the same number line,
explaining your placement.
Reflection: How did you use place value to decide the values
of your numbers?
Place Value 20
Fractions and Decimals 11
More Investigations:
1.
2.
3.
4.
5.
Sit with a friend.
Take turns to flip 2 or 3 cards and each make a number with tenths.
Read your numbers out loud.
Each place your number on the same number line.
Each suggest a number that would come between the 2 numbers, using
place value to explain how you know.
Reflection: How did you use place value to find a number between your
numbers?
Place Value 20
Fractions and Decimals 11
More Investigations:
1. Sit with a friend.
2. 2 or 3 cards are selected to be a target number with tenths.
3. Each of you flip 2 or 3 cards to make a number with tenths.
4. The child who makes a number closest to the target number wins.
Reflection: How did you use place value to find make a number close to
the target number?
Place Value 20
Fractions and Decimals 11
More Investigations:
1. Measure lengths in millimetres.
2. Convert to centimetres and millimetres, then to centimetres and a
fraction of a centimetre, then to centimetres and a decimal fraction
of a centimetre.
For example,
45 mm = 4 cm + 5 mm = 41/2 cm = 4.5 cm.
Reflection: How are multiplicative place value and metric
measurement related?
Place Value 20
Fractions and Decimals 11
More Investigations:
1. Sit with a friend.
2. Make a place value slide:
3. Take a sheet of paper and cut slits into which you
thread a strip of paper, for example,
4. Record a number onto the strip, for example,
5. Record the number’s value.
6. Move it between place value columns.
7. Record the number’s new value.
8. What number did you multiply or divide by?
Reflection: Why are we multiplying by 10 when we
move digits to the left and dividing by 10 when we
move digits to the right?
Place Value 20
Fractions and Decimals 11