STAGE 3 MATHEMATICS TEACHING AND LEARNING OVERVIEW 2016
TERM: 1 / WEEK: 2-3 / STRAND: Whole Number / SUB-STRAND: / WORKING MATHEMATICALLY:OUTCOMES: / · MA3-4NA orders, reads and represents integers of any size and describes properties of whole numbers
Links to Working Mathematically Outcomes:
· MA3-1WM describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions
· MA3-2WM selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations
· MA3-3WM gives a valid reason for supporting one possible solution over another
CONTENT: / Year 5-
· apply an understanding ofplace value and the role of zero to read and write numbers of any size
· state the place value of digits in numbers of any size
· arrange numbers of any size in ascending and descending order
· record numbers of any size using expanded notation
· partitionnumbers of any size in non-standard forms to aid mental calculation
Year 6-
· recognise the location of negativewhole numbers in relation to zero and place them on a number line
· use the term 'integers' to describe positive and negative whole numbers and zero
WALT: / WALT- Use place value to further extend understanding of how our number system works so that we can read, alter and understand the use of large numbers in our world. Locate and compare positive and negative numbers on a number line.
WILF: / WILF- numbers arranged in ascending or descending order, record numbers using expanded notation, understand how zero plays an important role in numbers , apply understanding to solve problems and think critically about what you have learned during each lesson.
ASSESSMENT FOR LEARNING: (Pre Assessment) / Pre Assessment
Fill in missing numbers in a sequence e.g. write the next three numbers counting forwards/backwards by 10/100 on and off the decade. (560, 8962)
Count by 10/100 forwards/backwards on a grid from given starting number.
On a blank grid students devise their own largest possible starting number and decide to count forwards/backwards by tens or hundreds, completing only the first row and column.
Have 3 or 4 random shaded boxes that students need to fill in with a missing number. Explain how you got your answer.
WARM UP/DRILL: / Mentals x10
Speed Test
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-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.
Newmans Prompts-
1. Paul buys a new Harley Davidson motorbike for $25 595. In the first year he owns it, it depreciates in value by $5 000 but in the second year it appreciates in value by $3 000. How much is his bike worth?
2. There were 25 students in a class. In a class competition, the average number of points scored per student was 150.
What was the total number of points scored by all the students in the class?QUALITY TEACHING ELEMENTS: / INTELLECTUAL QUALITY: / QUALITY LEARNING ENVIRONMENT: / SIGNIFICANCE:
£ Deep knowledge
£ Deep understanding
£ Problematic knowledge
£ Higher-order thinking
£ Metalanguage
£ Substantive Communication / £ Explicit quality criteria
£ Engagement
£ High expectations
£ Social support
£ Students’ self-regulation
£ Student direction / £ Background knowledge
£ Cultural knowledge
£ Knowledge integration
£ Inclusivity
£ Connectedness
£ Narrative
RESOURCES: / “Place Value Story” can be found at: https://www.youtube.com/watch?v=qOgWFBVdots
Counting on Teaching Activities: https://portalsrvs.det.nsw.edu.au/f5-w-68747470733a2f2f6465747777772e6465742e6e73772e6564752e6175$$/curr_support/maths/counting_on/Learning_Resources/pdf/co_pv.pdf
Selection of dice - six and ten sided, sets of numeral cards 0-9, set of numeral cards 1-1000
“Rockin' the Standards Place Value Rap” can be found at: https://www.youtube.com/watch?v=AuE46_-7L5c
“We Will Round You” can be found at https://www.youtube.com/watch?v=41QZvFIC8mk
Counting on Teaching Activities: https://portalsrvs.det.nsw.edu.au/f5-w-68747470733a2f2f6465747777772e6465742e6e73772e6564752e6175$$/curr_support/maths/counting_on/Learning_Resources/pdf/co_pv.pdf
Selection of expanded notation dice, sets of numeral cards 0-9
ABORIGINAL 8 WAYS OF LEARNING: / Story Sharing Community Links Deconstruct Non-Linear Land Links Symbols & Images Non-verbal Learning Maps
Reconstruct
Link to information about 8 Ways teaching and learning:
https://intranet.ecu.edu.au/__data/assets/pdf_file/0016/510073/8-Aboriginal-ways-of-learning-factsheet.pdf
WHOLE CLASS INSTRUCTION
MODELLED ACTIVITIES / GUIDED & INDEPENDENT ACTIVITIES
Explicit Mathematical Teaching
£ Students need to develop an understanding of place value relationships such as: 10 thousand = 100 hundreds = 1000 tens = 10 000 ones.
£ Watch YouTube clip of the “Place Value Story”. Explain that this is an American clip and that in Australia, we do not use commas when writing large numbers.
£ Explain that large numbers are written in groups of three starting from the ones using spaces not commas. Teach that groups of three belong to millions, thousands and ones and this determines the name of the number e.g. Two hundred and fifteen million four hundred and twenty six thousand eight hundred and ten. Identify groups beyond the millions.
£ Number People: Make number cards with the digits 0-9. Hand out, for example, five/six/seven cards to students. Without speaking, the students are asked to make the largest number, smallest number, the smallest odd number etc. Extend range of numbers.
Students predict the total, then investigate: How many four/five/six digit numbers can be made using the digits 8, 2, 0, 3, each once only? Extend to combining more digits.
£ Watch YouTube Clip of the “Rockin' the Standards Place Value Rap”
£ The convention for writing numbers of more than four digits requires that they have a space (and not a comma) to the left of each group of three digits, when counting from the Units column.
£ Students need to develop an understanding of place value relationships such as: 10 thousand = 100 hundreds = 1000 tens = 10 000 ones.
£ Explain to the students how each place-value house is broken into hundreds, tens, and ones.
£ Help the students to read the numbers in their house positions. In particular, assist the students to read numbers like 34 009 083 080, where the zero’s must be noticed but are not read out loud.
£ Notice the first house needs no name. (It is called “The Trend Setter House” because it starts the pattern of column names within every house.)
Give the students a number and get them to add the place-value houses then read aloud the number. Once the students’ knowledge is secure ask them to read numbers like 34 908 345 002 without houses. / LEARNING SEQUENCE
Remediation S2 / £ Ordering Numbers to 1000 on washing line (string)
Hand out several number cards to each child from a shuffled pack of 1-1000 cards. First ask the children, in
pairs, to order their cards. Then name a starting number and an end number and ask children to come out and
place their cards in order on the string(washing line). Repeat for different sections of the number line. For
example, start: number 350 and end number 500. Other children are asked to place their numbers in between
350 and 500 in turn.
Background Information
Students need to develop an understanding of place value relationships, such as 10 thousand = 100 hundreds = 1000 tens = 10 000 ones.
Support: peer tutor grouping strategies
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 ...
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.
Partition Method
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
LEARNING SEQUENCE
S3 / · Highest Number (Counting On pg. 105-106)
1. Students play in pairs, sharing one score sheet. Players take turns to roll a die to try to make the highest
number they can. Once a number has been placed in a column its position cannot be changed. The student
who makes the higher number wins that game.
2. Students play several games to determine an overall winner.
3. The teacher ties the lesson together by asking, What is the largest possible number you can score? (9999 if
you are using 0–9 dice and playing a 4-digit game.) Who scored closest to this? What was your highest number?
What was your lowest number?
4. Some of the results may be written on cards and pinned onto a “clothesline” to help students order 3-digit
and 4-digit numbers.
· The Nasty Game (Counting On pg. 107-108)
1. Students play in groups of 4 and 4 games must be played. Play is similar to highest number except that
players place numbers in their opponent’s score columns.
· Investigation: Ordering Numbers: Students could:
- Order countries according to area or population
- Student writes a number and tells the class what range it falls in eg between 400 000 and 500 000. Other
students guess and are told higher, lower until it is reached
- Find missing numbers from number patterns eg 999 999, 989 999, ------, 969 999, ------, ------, etc.
· Climb The Ladder (Counting On pg 104). Get three 0-9 dice. Players take turns to throw the three dice. The player decides which digit is the hundreds, which one is the tens and which is the ones. Each student draws a five square ladder. Students write the number they have made onto one “rung” of their ladder. The ladder must progress from smallest to largest numbers, from bottom to top. If you cannot put your number on the ladder in order, you must lose that turn. First one to complete their ladder wins.
· 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.
· How many tens/hundreds/thousands?
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?
· 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
· 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 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 get to 11 500?
Sketch jumps suggested by students on the number line and discuss.
Present similar number problems to students using money
Online Resources
· Interactive Maths
Fantastic online resource including notebook files for the smart board, iPad apps and online games to play.
http://interactivemaths.wikispaces.com/Whole+Number
Place Value Teaching Activities
· Expanded Notation Using: Place Value Houses
We Are Learning To ...identify multi-digit numbers up to trillions.
Explain to the students how each place-value house is broken into hundreds, tens, and ones.
Help the students to read the numbers in their house positions. In particular, assist the students to read numbers like 34 009 083 080, where the zeros must be noticed but are not read out loud.
Notice the first house needs no name. (It is called “The Trend Setter House” because it starts the pattern of column names within every house.)
Give the students a number and get them to add the place-value houses then read aloud the number. Once the students’ knowledge is secure ask them to read numbers like 34 908 345 002 without houses.