Stage 3 Outcome A student: › describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM › selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM › orders, reads and represents integers of any size and describes properties of whole numbers MA3-4NA [Pages 190-191]

Language: Students should be able to communicate using the following language: ascending order, descending order, zero, ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, digit, place value, expanded notation, round to, whole number, factor, highest common factor (HCF), multiple, lowest common multiple (LCM).

Teaching and Learning Activities Notes/ Future Directions/Evaluation Date/ LAC Icons

Ignition Activities Mental calculation. Begin with a number. Ask students to calculate a series of tasks in their head e.g. begin with 15, add 10, add 10, add 100, subtract 10, add 100, what is the number?

Maths Tipping. Students stand around the room. Make a set of five/six digit number cards. Ask questions such as: how many tens altogether in 50000? What number is 100 more than 60002? The student who answers correctly may take one step towards another student. If that student is tipped they sit down.

Bingo Students make up a bingo card (5 x 5) or (6 x 6) and fill it with five/six-digit numbers e.g. using the digits 6, 3, 2, 7, 5 and 0. The teacher reads a clue, e.g. the number 100 more than 25630. If the student has that number, they cross it out. First to five in a row, column or diagonal is the winner. Make a place value slider up to 6 digits. Demonstrate counting forwards and backwards.

~ 1 ~

Explicit Teaching

Place Value Rap http://www.rockinthestandards.com/site/pages/teacher-zone/teaching-tips/place-value-rap.php Listen

Here's some explanation for some of the lyrics:

Starting at the decimal, sandwiched in between

Zeroes hold the empty places, haven’t you seen?

When you consider the place values that come between significant digits and the decimal point, if a place contains no numbers, a zero is needed in order to hold that place. For example, in the number 2.04, the zero is sandwiched between the 4 and the decimal. Therefore the zero is important because it holds the tenths place.

Reading big numbers each comma’s a word

“Thousand, Million, Billion,” commas, haven’t you heard? Word!

This is helping kids with reading larger numbers. Did you realize that commas indicate a special word. For example, to read 30,008,400 we say 30 million, eight thousand, four hundred. The first comma we come to say, "Million," and the second comma we read, "Thousand." In the song, the students learn these words for the commas starting at the decimal point and working to the left.

Let’s take it to the right of the decimal point

We’ve got tenths, hundredths, thousandths, ten thousandths

Smaller than a 1 with a T H

The place values to the right of the decimal point all sound just like those to the left with one exception. The places on the right all include T H at the end of the word. Also, all these places represent values less than one whole.

Literacy

~ 2 ~

Explicit Mathematical Teaching

Partition numbers of any size in non-standard forms

eg. 163480 + 150000 = (150000 + 13480) + 150000

Students require multiple opportunities to partition numbers before you introduce partitioning to solve multiplication problems

C

ritical and creative thinking

Explicit Mathematical Teaching Developing knowledge of forwards and backwards counting skills will assist students in using mental calculations to solve two/three/four-digit addition and subtraction tasks. The “empty number line” could be used to record student’s thinking and to demonstrate building-on by tens, hundreds, thousands, millions and tens of millions and appropriate abbreviations (eg. 1,000 = K, or $1K) Demonstrate counting forwards and backwards on a thousands chart by 10,100. Discuss the sequence - what changes, what doesn’t change - which columns change? Show the pattern between the 2 digit, 3 digit, 4 digit numbers e.g. 150, 160, 170 …. and 2150, 2160, 2170 ….. Have students generate their own symbol system to replace the digits 0 to 9 e.g @ = 0, ! = 1, & = 2 etc, therefore 201 = &@!. When we increase this by ten it becomes &!! and ten more makes &&!. Discuss and compare the pattern formed - symbol to pattern. Introduce counting by hundreds. Demonstrate and discuss similarities with counting by tens - which columns change, which don’t? Increase the number of digits - 5 or 6 digit number. Add 10 to 999, 9 999, 99 999, 999 999. Discuss how the units digit remains the same.

Literacy

~ 3 ~

Explicit Teaching – Money Students solve money problems of any size, as well as other real-life situations. Explicitly demonstrate how to identify, count and represent any sum of money. Students will also recognise and use abbreviations of numbers such as $1000 +$1K .

Literacy

Explicit Teaching - Highest Common Factor Demonstrate using the factor trees below. Students write all factors of the number in their lowest form.

Select common factors and solve as a number sentence. Students complete the following factor trees to find the Highest Common Factor:

a) 72, 108 b) 90, 216 c) 48, 224 d) 120, 405 e) include numbers of your own

Material adapted from http://www.mathsonline.com.au

Literacy C

ritical and creative thinking

Highest Common Factor http://au.ixl.com/math/year-6/greatest-common-factor

Literacy C

ritical and creative thinking

~ 4 ~

Explicit Teaching - Lowest Common Multiple Demonstrate using the factor trees below. Students write all factors of the number in their lowest form.

Cross out the factors from smaller number that is visible within the factors of the larger number. Write the factors of the larger number followed by the number of the smaller number that have not been crossed out. Solve. Students complete the following factor trees to find the Lowest Common Multiple:

a) 60, 84 b) 72, 126 c) 300, 250 d) 240, 900 e) include numbers of your own

Material adapted from http://www.mathsonline.com.au Lowest Common Multiple http://au.ixl.com/math/year-6/least-common-multiple

Literacy C

ritical and creative thinking

~ 5 ~

Whole Class Teaching Activities-some suggestions Count –Off Activities Roll three ten-sided (decahedron) die. Have the students start counting from the number rolled, adding ten, hundred, thousand to the count each time. Then count backwards by tens, hundreds, thousands. Have one student select a number and call out the number. Once the student calls out the selected number, the rest of the class continue counting by adding ten or hundred, thousand each time. Pupils count forward or back within an appropriate number range. Ask them to stop straight away when they counted a certain number of steps. For instance they count back 5000 from 8750 in steps of 1000. What number did they end up with? Give pupils the starting and finishing numbers and size of steps. They count within these numbers then hold up fingers to show how many steps have been counted eg Count on from 256 to 286 in tens? How many tens? Count back from 2654 to 2054. How many hundreds?

Nudge ‘We are learning how a number containing nines “rolls” over to leave zeros when 1, 10, 100 ... is added to the number, and how zeros “roll” back to nines with subtraction by 1, 10 ,100 ... Activity The students use the numeral cards to recreate counting sequences in a way that’s similar to the action of a car odometer. They can wear hats marked with the place values involved, for example, ones, tens, hundreds, thousands ... 9 9 9 9 Have a student as the ones counter, counting in ones. Stop them at nine. Ask, “What will happen when one is added?” Discuss how adding one rolls nine over to 10 and that another counting place (tens) is needed. Count in ones from 95 until 99 rolls over to 100. Start with 93 and add 10 to it. Discuss how the nine rolls over. Repeat by adding 10 to 94, 99, 90 ... Add 1, 10, then 100 to 99. Add 1, 10, 100 to 899. Add 1, 10, 100 to 998. Activity Roll 1 000 back 1, 10, 100. Roll 3 000 back 1, 10, 100. Roll 309 back 1, 10, 100.

Totals Use the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and addition to make the largest possible total and the smallest possible total. Use addition signs and subtraction signs to total 100.

~ 6 ~

Complete the Table Numbers Between Sum Difference The numbers are 50 and 100 135 5 65, 70 10 and 100 90 60 100 and 200 205 55 100 and 200 262 42 500 and 1000 1 585 85

Guess and Check Give each student two identical subtraction squares. On the first square students record their estimates of the answers, in the second square students record the answers they obtained using a calculator. Estimate

- 2869 6431 7963 8064

1863

2000

2679

196

Guided group/Independent Activities-some suggestions How many tens/hundreds/thousands/millions/tens of millions? Write a start number on the board or say it aloud to the students eg 35 670.How many tens/hundreds thousands will we have to count to get past 40 000? Repeat for other numbers? State the place value of digits in numbers of any size.

Bingo Teacher or child reads out statements on small cards eg two hundred less than 45 600 and children check their bingo boards to see if they have that number eg 45 400 State the place value of digits in numbers of any size.

Tens/Hundreds/Thousands Jumps Draw open number line segments from various numbers with intervals of either tens/hundreds or thousands. Invite the class to count in tens /hundreds or

~ 7 ~

thousands along the segments forwards and backwards. Ask students questions about the number line eg ‘If I started at 10 000 how many jumps of 100 would it take to to get to 11 500? Sketch jumps suggested by students on the number line and discuss. State the place value of digits in numbers of any size. Arrange numbers of any size in ascending and descending order. Maths for Sustainability Website http://maths4sustainability.wordpress.com/2010/07/22/hello-world/ Use sustainability website to interpret and explore large numbers in real life situations.

Sustainability W

ork and enterprise

Computer Learning Objects Hopper Challenge : Whole Numbers TaLe Reference Number:L1087 Students select a jump size between 1 and 10 and the starting point is generated randomly on a grid of whole numbers between 0 and 999

Wishball Challenge ; Whole Numbers TaLe reference Number : L871 The Wishball series of learning objects encourages thinking about place value. It also provides opportunities for mental addition and subtraction. Students work with whole numbers up to thousands.

~ 8 ~

Identity Factors http://au.ixl.com/math/year-6/identify-factors

Critical and creative

thinking

Prime Factorisation http://au.ixl.com/math/year-6/prime-factorisation

Literacy C

ritical and creative thinking

~ 9 ~

Mystery Numbers http://www.starrmatica.com/standalone/starrMaticaplaveValueMysteryNumbers.swf

Literacy C

ritical and creative thinking

Sale Prices http://au.ixl.com/math/year-6/sale-prices

Literacy C

ritical and creative thinking

Which is the better coupon? http://au.ixl.com/math/year-6/which-is-the-better-coupon

Literacy C

ritical and creative thinking

~ 10 ~

The Factor Game http://illuminations.nctm.org/ActivityDetail.aspx?ID=12

C

ritical and creative thinking

Factorise http://illuminations.nctm.org/ActivityDetail.aspx?ID=64

Critical and creative thinking

Product Game http://illuminations.nctm.org/ActivityDetail.aspx?ID=29

~ 11 ~

Primary Krypto http://illuminations.nctm.org/ActivityDetail.aspx?ID=173

C

ritical and creative thinking

Place Value http://www.bbc.co.uk/bitesize/ks2/maths/number/place_value_headings/play/

~ 12 ~