Decimals to Thousandths: a week of ready-to-teach maths

Five days of lessons for Year 5 Number. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out place-value and decimal cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the two card sheets once; the cards are reused all week.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: the places to the right of the point do not stop at hundredths. Cut a hundredth into ten equal parts and each part is a thousandth, 0.001. Every place is ten times smaller than the one to its left, so decimals are compared place by place from the left, never by how many digits they have: 2.35 is larger than 2.305.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

How we say decimals

This pack reads 2.375 as “two and three hundred and seventy-five thousandths” or “two point three seven five”. Both are fine once children can say what each digit is worth. Avoid “two point three hundred and seventy-five”: it hides the places and invites the slip that 2.375 is bigger than 2.4. A number less than one keeps its zero before the point: 0.375, not .375.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Day 1 makes the thousandth from the hundredth; Day 2 builds whole numbers and decimal parts into one number; Day 3 gives each number an exact place on the line by zooming in three times; Day 4 compares and orders by place; and Day 5 sorts the zeros that matter from the zeros that do not. It builds on the Year 4 tenths and hundredths, and it is the place value that measuring with decimals, percentages and operations with decimals lean on in Years 5 and 6.

Materials for the week (one trip)

• From the classroom: scissors, pencils, coloured pencils, 30 cm rulers marked in millimetres, one metre ruler, this pack printed.
• For Day 3: a strip of masking tape along the floor marked 1.4 and 1.5, and sticky notes (optional).
• For Day 5: a food label or a kitchen scale that shows kilograms to three places (optional).
• Cut out once, use all week: the place-value cards and the decimal cards in this pack. No maths equipment to buy.

Words for the word wall

whole, tenth, hundredth, thousandth, decimal point, place value, digit, number line, interval, zoom, compare, order, greater than, less than, equal to

Dear families

This week in maths, Year 5 takes decimals one place further, to thousandths. A thousandth is a hundredth cut into ten, so 2.375 is 2 ones, 3 tenths, 7 hundredths and 5 thousandths. We find decimals on a number line by zooming in, and we compare them place by place: 2.35 is larger than 2.305, even though it has fewer digits.

Try this at home

• Look for decimals with three places: a fuel price such as $1.899 a litre, or a kitchen scale showing 0.375 kg. Ask what each digit is worth.
• Ask which is larger, 2.35 or 2.305. Write 2.35 as 2.350 and compare the digits from the left.
• Count by thousandths across a hundredth: 1.418, 1.419, 1.420, 1.421.
• Ask what number sits halfway between 1.42 and 1.43.

My decimals this week

Fill one row a day. Find a decimal at home with two or three places and pull it apart.

Printed from the free seegongsik Decimals to Thousandths teaching pack · seegongsik.com/au/y5/number/AC9M5N01/pack

Ten times smaller again

Children meet the thousandth, a hundredth cut into ten equal parts. They carry the place-value ladder past the hundredths and write numbers of thousandths as decimals.

We are learning to

• explain that a thousandth is one of a thousand equal parts of one whole, a hundredth cut into ten,
• say how many thousandths make a hundredth, a tenth and one whole,
• write a number of thousandths as a decimal (45 thousandths is 0.045).

Success criteria

• I can say what each place after the point is worth, out to thousandths.
• I can write thousandths as a decimal, with zeros where they are needed.

You need

A metre ruler, and the class’s 30 cm rulers with millimetre marks. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B by revealing the ladder again.

Watch for these ideas

• Thinking a thousandth is bigger than a hundredth because a thousand is bigger than a hundred. The more equal parts, the smaller each part.
• Writing 7 thousandths as 0.7 or 0.07. The thousandths are the third place after the point: 0.007.
• Thinking decimals stop at two places, like money. A scale can show 1.375 kg.

Answers

• Part A: hundredths 1/100, thousandths 1/1000; tenths 0.1, thousandths 0.001. Part B: 10; 100; 1000; 4 parts shaded is 0.004.
• Part C: 0.007; 0.045; 0.302; 0.09 (or 0.090); 1.006. Part D: 0.003; 0.05, 0.005; 0.08, 0.008.

The thousandth

A. Fill the ladder

B. Zoom in, ten parts at a time

1 hundredth = ______ thousandths    1 tenth = ______ thousandths    1 whole = ______ thousandths

Shade 4 parts of the last bar. As a decimal of the whole: ________

C. Write the decimal

7 thousandths = __________

45 thousandths = __________

302 thousandths = __________

90 thousandths = __________

1 whole and 6 thousandths = __________

D. Ten times smaller each step

3,  0.3,  0.03,  ______

50,  5,  0.5,  ______,  ______

0.8,  ______,  ______

Build it from its places

Children build numbers greater than one out to thousandths from place-value cards, say what each digit is worth, and use a zero to hold a place that is empty.

We are learning to

• say what each digit of a number like 2.375 is worth,
• write a decimal as a sum of its places (2.375 = 2 + 0.3 + 0.07 + 0.005),
• use a zero to hold an empty place (3 ones, 4 hundredths and 6 thousandths is 3.046).

Success criteria

• I can build a number to thousandths with the cards and read it aloud.
• I can write a number from its parts, putting a zero in any empty place.

You need

The place-value cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the cards for 2.375; start Session B by building 3.046.

Watch for these ideas

• Reading 2.375 as “two point three hundred and seventy-five” and then thinking it is more than 2.4.
• Building 3 ones, 4 hundredths and 6 thousandths as 3.46. Without the zero, the 4 slides into the tenths place.
• Thinking the point is the middle of a number. It marks where the ones end: 12.406 has two places before it, three after.

Answers

• Part A: 6 thousandths (0.006); 2 tenths (0.2); 1 ten (10); 7 hundredths (0.07); 9 thousandths (0.009).
• Part B: 5.618 = 5 + 0.6 + 0.01 + 0.008; 3.046 = 3 + 0.04 + 0.006; 12.406 = 10 + 2 + 0.4 + 0.006; 7.09 = 7 + 0.09.
• Part C: 4.208; 6.053; 19.007; 2.415. Part D: two and three hundred and seventy-five thousandths; six hundred and four thousandths; three and nine hundredths.

Build it from its places

A. What is the digit worth?

B. Write it as a sum of its places

5.618 = ______________________________________

3.046 = ______________________________________

12.406 = ______________________________________

7.09 = ______________________________________

C. Write the number

4 ones, 2 tenths and 8 thousandths = __________

6 ones, 5 hundredths and 3 thousandths = __________

1 ten, 9 ones and 7 thousandths = __________

2 ones, 4 tenths, 1 hundredth and 5 thousandths = __________

D. Say it in words

2.375 = _____________________________________________

0.604 = _____________________________________________

3.09 = _____________________________________________

Check with a partner: read each number aloud so the last word tells the smallest place.

Zoom in on the line

Children place a number with three decimal places on a number line in three moves: the tenth it falls in, then the hundredth inside that tenth, then the thousandth. Each zoom shares one interval into ten equal jumps, the same move that made the next place.

We are learning to

• name the two tenths, and then the two hundredths, that a decimal sits between,
• zoom in on an interval and count thousandths to place a number exactly,
• read the number at a mark on a zoomed number line.

Success criteria

• I can place a number like 1.425 on a line by zooming in twice.
• I can read the number at an arrow on a line from 3.2 to 3.3 or from 0.57 to 0.58.

You need

A floor line of masking tape marked 1.4 at one end and 1.5 at the other, and sticky notes (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by zooming into 1.4 to 1.5 again.

Watch for these ideas

• Placing 1.425 between 1.4 and 1.42 because 425 sounds big. Find the tenth first, then the hundredth.
• Counting the marks instead of the jumps after a zoom. Start at the left label and count jumps.
• Thinking nothing fits between 1.42 and 1.43. Every hundredth holds ten thousandths.

Answers

• Part A: 1.425 is between 1.4 and 1.5; 3.082 is between 3.0 and 3.1; 0.958 is between 0.9 and 1.0; 2.604 is between 2.6 and 2.7. Part B: 1.42 and 1.47 are 2 and 7 jumps past 1.4; 1.425 and 1.428 are 5 and 8 jumps past 1.42.
• Part C: A = 3.26, B = 3.29; C = 0.573, D = 0.578. Part D: 1.425; 2.35; 0.605.

Zoom in on the line

A. Between which two tenths?

1.425 is between ______ and ______

3.082 is between ______ and ______

0.958 is between ______ and ______

2.604 is between ______ and ______

B. Zoom in and mark each number with an arrow

C. What number is at each arrow?

D. Halfway between

Halfway between 1.42 and 1.43 is __________

Halfway between 2.3 and 2.4 is __________

Halfway between 0.6 and 0.61 is __________

Compare by place, not by length

Children line decimals up by place and compare from the left, so 2.35 beats 2.305 even with fewer digits. Then they order sets of decimals, including numbers greater than ten.

We are learning to

• write decimals with the same number of places by adding zeros on the far right,
• compare two decimals from the left and use <, > and =,
• order a set of decimals, including numbers greater than one, smallest first.

Success criteria

• I can say which of two decimals is larger and point to the place that decides it.
• I can order five decimals, smallest first.

You need

The decimal cards (cut-out sheet 2), one set per group of four. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by comparing 4.06 and 4.6 on the board.

Watch for these ideas

• Thinking the decimal with more digits is larger, so 2.305 beats 2.35. Pad with zeros and compare from the left.
• The opposite slip: thinking the shorter decimal is larger because its digits sit in bigger places. 0.7 is smaller than 0.75.
• Reading the digits after the point as a whole number (305 is more than 35). The places decide.

Answers

• Part A: circle 2.4, 6.7, 9.909, 1.05. Part B: 0.45 > 0.405; 2.09 < 2.1; 1.3 = 1.300; 3.008 < 3.08; 5.62 > 5.618; 0.7 > 0.699.
• Part C: 3.04, 3.044, 3.4, 3.404, 3.44; 2.15, 2.5, 12.05, 12.5, 12.505. Part D: heaviest D (1.5 kg), lightest E (1.025 kg); lightest first E, C, B, A, D. The twelve cards, smallest first: 1.077, 1.607, 1.68, 1.7, 2.053, 2.3, 2.305, 2.35, 4.006, 4.06, 4.066, 4.6.

Which is larger?

A. Write both with three decimal places, then circle the larger

B. Write <, > or =

0.45 ____ 0.4052.09 ____ 2.11.3 ____ 1.3003.008 ____ 3.085.62 ____ 5.6180.7 ____ 0.699

C. Put them in order, smallest first

D. Five parcels at the post office

The heaviest parcel is ______    The lightest parcel is ______

Lightest first: ______, ______, ______, ______, ______

Zeros that count, zeros that do not

Children sort the two kinds of zero in a decimal. A zero on the far right adds no value, so 2.5, 2.50 and 2.500 are one number; a zero between the point and a digit holds a place, so 2.05 is much smaller than 2.5. They read measures written to thousandths, fix two slips, and finish the week with the unit quiz as a class game.

We are learning to

• explain why a zero on the far right adds no value (2.5 = 2.50 = 2.500),
• explain why a zero between the point and a digit holds a place (2.05 is not 2.5),
• read and compare measures written to thousandths, such as 1.050 kg.

Success criteria

• I can say whether a zero changes a decimal’s value, and why.
• I can find and fix a mistake in comparing or ordering decimals.

You need

The place-value cards (cut-out sheet 1). A food label or kitchen scale showing kilograms to three places (optional). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part B; start Session B with the food label.

Watch for these ideas

• Dropping a zero that holds a place, so 2.05 is written 2.5.
• Thinking 2.50 is larger than 2.5 because it has more digits.
• Crossing out any zero: 3.070 is 3.07, but it is not 3.7.

Answers

• Part A: same, different, different, same, different, same, same. Part B: 2.500, 0.700, 4.060, 3.000, 12.400.
• Part C: Mia: 2.375 < 2.4, because 2.4 is 2.400 and its 4 tenths beat 3 tenths. Sam put the shortest first; by place the order is 5.149, 5.18, 5.2.
• Part D: 1.05 kg; 2.08 kg is heavier; yes, the same amount; $1.899 a litre is cheaper.

Zeros that count

A. Same value or different? Circle one.

2.5 and 2.50same  /  different

2.05 and 2.5same  /  different

4.6 and 4.06same  /  different

1.40 and 1.4same  /  different

5.008 and 5.08same  /  different

3.070 and 3.07same  /  different

0.300 and 0.3same  /  different

B. Write each number with three decimal places

2.5 = ________0.7 = ________4.06 = ________3 = ________12.4 = ________

C. Spot the slip

Mia says 2.375 is larger than 2.4 because 375 is more than 4. What would you tell her?

___________________________________________________________

Sam put 5.18, 5.149, 5.2 in order, smallest first, like this: 5.2, 5.18, 5.149. Write the right order.

___________________________________________________________

D. Measures to thousandths

A bag of rice is labelled 1.050 kg. Write the mass without the zero on the far right: ________ kg

Two parcels weigh 2.08 kg and 2.075 kg. Which is heavier? ________

One jug holds 1.250 L and another holds 1.25 L. Do they hold the same amount? ________

Fuel costs $1.899 a litre at one station and $1.92 at another. Which is cheaper? ________

Place-value cards

Cut out the cards. To build a number, lay one card from each row side by side and read them as a sum: 2 and 0.3 and 0.07 and 0.005 make 2.375. Leave a row out when its place is empty: 3 and 0.04 and 0.006 make 3.046, and the empty tenths place is written as a zero.

Teacher note: one set per pair, kept in an envelope all week. A pair can build any number from 0.001 to 99.999 with at most five cards, one from each row.

Decimal cards and zoom strips

Decimal cards (Day 4)

Cut out the twelve cards. Order them, smallest first, by comparing place by place from the left.

Teacher note: the cards hold the board pairs from “Which is larger?” and their look-alikes. The order is on the Day 4 plan.

Zoom strips (Day 3)

Cut out the three strips and lay them one under the other. Each strip is one jump of the strip above, cut into ten. Mark 1.425 on all three.

Teacher note: 1.425 sits between the marks for 1.4 and 1.5 on the first strip, between 1.42 and 1.43 on the second, and on the fifth mark past 1.42 on the third.

What we know: Decimals to Thousandths

Work on your own. Show your thinking if you can.

1. In 6.284, the 8 is worth ______________ and the 4 is worth ______________.
2. Write as a decimal: 9 thousandths = __________    3 + 0.4 + 0.009 = __________
3. How many thousandths make one hundredth? ______   How many thousandths make one whole? ______
4. Write 5.106 as a sum of its places: ______________________________
5. 2.736 is between the tenths ______ and ______, and between the hundredths ______ and ______.
6. What number is at the arrow? __________
7. Write <, > or = : 0.62 ____ 0.6181.5 ____ 1.5003.09 ____ 3.1
8. Put these in order, smallest first: 7.3, 7.03, 7.303, 7.033.   ______________________________

Answers and marking guide

Answers

1. 8 hundredths (0.08) and 4 thousandths (0.004).
2. 0.009; 3.409.
3. 10 thousandths make one hundredth; 1000 thousandths make one whole.
4. 5 + 0.1 + 0.006 (no hundredths, so no hundredths part).
5. 2.7 and 2.8; 2.73 and 2.74.
6. 4.157 (7 thousandths past 4.15).
7. 0.62 > 0.618; 1.5 = 1.500; 3.09 < 3.1.
8. 7.03, 7.033, 7.3, 7.303.

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, naming the place of the digit that decides.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: the places, building numbers, the number line, comparing and ordering, and the zeros.