Dimension: / Number / Focus: / Patterns: place value, multiples, factors, primes, composites and simple powers.
VELS Learning Focus Statement:
2.75Use of place value (as the idea that ‘ten of these is one of those’) to determine the size and order of decimals to hundredths
3.0
Use place value (as the idea that ‘ten of these is one of those’) to determine the size and order of whole numbers to tens of thousands, and decimals to hundredths.
Round numbers up and down to the nearest unit, ten, hundred, or thousand.
3.25
Use of large number multiples of ten to approximate common quantities; for example, 100 000 people in a major sports venue
Representation of square numbers using a power of 2; for example, 9 = 32
Students demonstrate an understanding of whole numbers up to millions and decimals to hundredths using models, including number lines.
3.5
Listing of objects and their size, where size varies from thousandths to thousands of a unit
Addition, subtraction and multiplication of fractions and decimals (to one decimal place) using approximations such as whole number estimates and technology to confirm accuracy
Students can use physical models and number lines to compare, rename and identify decimals, such as 3.2 is 32 tenths.
Students can create and describe patterns using calculators, including sets of multiples and squares.
Model and identify integers, positives and negatives on a number line.
3.75
Multiplication by increasing and decreasing by a factor of two; for example, 24 × 16 = 48 × 8 = 96 × 4 = 192 × 2 = 384 × 1 = 384
Creation of sets of multiples of numbers and their representation in index form; for example, 3, 9, 27 written as31, 32, 33 respectively
Students can identify multiples and factors, using factor trees, powers, prime and composite numbers.
Students can count and skip count with both positive and negative integers.
4.0
Comprehend the size and order of small numbers (to thousandths) and large numbers (to millions)
Create sets of number multiples to find the lowest common multiple of the numbers
Interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4
Identify square, prime and composite numbers
Create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers
Calculate simple powers of whole numbers (for example, 24 = 16)
4.25
Identification of square numbers up to, and including, 100
Use of index notation to represent repeated multiplication
Multiply by powers of 10, link division by powers of 10 to multiplication by decimals and use these in estimation
Explain dividing by a number between one and zero, such as dividing by 0.1 is finding out how many tenths
Determine prime factors and use them to express any whole number as a product of powers of primes and to find its composite factors
Use knowledge of perfect squares to determine exact square roots
4.5
Location of the square roots from √(1) to √(100) by their approximate position on the real number line
Construction of factor trees for the expression of numbers in terms of powers of prime factors
Vocabulary Development:
Array, pattern, prime, factor, multiple, composite, squared numbers, triangular numbers, consecutive, digit, equation, expanded, hundred, largest, smallest, ascending, descending, million, square, thousand, ten, unit, decimal, tenth, hundredth, , powers, indices.Establishing Prior Knowledge
§ Write these numbersa. One hundred and sixty four b. Nine hundred and nine, c. Two thousand and sixteen d. Fifty three thousand two hundred
e. Six million four hundred and four thousand f. Six and eight tenths g. Six and four tenths h. Fourteen and fifty two hundredths
i. Fourteen and two thousandths j. Thirty eight thousand and five and seventy three thousandths
§ Write out the numbers 0 – 20. Circle the prime numbers, shade the factors of 6 green, shade the multiples of 6 red. Underline all the composite numbers.
§ Draw a factor tree / list for the number 24.
§ Write a sentence / illustration on how to use square numbers.
§ Create a pattern starting at 9 that someone else could continue.
It is important that students can describe their pattern to others. Get them to check each other’s patterns.
**Look for realistic and more elaborate rules.
Common Assessment Tasks
Assessment FOR Learning / Assessment AS Learning / Assessment OF Learning§ See above (Establishing Prior Knowledge) / § Annotated notes
§ Reflective journals
§ Learning tasks
§ Share and reflection / § Unit Post-test Lower & Upper: Start Right compilation test
§ Annotated notes
§ Work samples
§ Tiered lesson outcomes
§ Unit vocabulary assessment
§ Self assessment outline
Other Resources:
Maths on the Go Book 1 – Rob Vingerhoets Open Ended Maths Activities – Sullivan & Lilburn Maths on the Go Book 2 – Rob VingerhoetsFrameworks Mathematics 5 & 6 (FM5 / FM6) Excel Start Up Maths 5 & 6 VELS Assessment Maps
Maths made Easy 6 – Dorling Kindersley Aust. 40 Fabulous Math Mysteries Kid’s Can’t Resist Strategic Maths: Number - Baker
Internet access Dice Money Sets
Playing cards Sir Cumference and All the King’s Tens: A math adventure Uno’s Garden - Graeme Base
Teaching and Learning Sequence
Warm up
/Student Learning Activity (including introduction)
/Share / Reflection / Assessment
Session 1Prior Knowledge / To establish prior knowledge, determine entry points for learning. / Using only the numerals 0-8
/ Establishing Prior-knowledge tasks
§ Write these numbers
a. One hundred and sixty four,
b. Nine hundred and nine,
c. Two thousand and sixteen
d. Fifty three thousand two hundred
e. Six million four hundred and four thousand
f. Six and eight tenths
g. Fourteen and fifty two hundredths
h. Fourteen and two thousandths
i. Thirty eight thousand and five and seventy three thousandths
§ Write out the numbers 0 – 20. Circle the prime numbers, shade the factors of 6 green, shade the multiples of 6 red. Underline all the composite numbers.
§ Draw a factor tree / list for the number 24.
§ Write a sentence / illustration on how to use square numbers.
§ Create a pattern starting at 9 that someone else could continue.
It is important that students can describe their pattern to others. Get them to check each other’s patterns.
**Look for realistic and more elaborate rules. / Self reflection
1) I was most confident answering task number ______because______
2) I was not confident to answer task ______because ______
3) I was unable to answer and would like more practice with task / the skills of ______
Share.
Final 5
1. Write 5002 in digits
2. Which is the 100s digit in 5302
3. Which is bigger, seven zero zero two (7002) or seven zero two zero (7020)?
4. What no. is 10 times larger than 56?
5. 450 ÷ 10 = ?
Session 2
Place value names
Base 10 system
Increasing / Decreasing by base 10 / To use the place value names and understand the base ten number system / Picture book:
Sir Cumference & All The Kings Men
Discuss patterns / News at Ten Cartoon. (team folder)
There are 3 different suggestions shown, is there a right / wrong way? Why do each of these strategies work?
When you were in grade 2/3 you usually just added a zero to multiply by 10, but now we talk about moving the decimal point. How does this work? How do these strategies relate / differ?
Using a calculator investigate
8.2 x 10 =
8.2 x 100 =
8.2 x 1000 =
Predict, what will 8.2 x 1,000,000 = ?
52 ÷ 10 =
520 ÷ 100 =
5200 ÷ 1000 =
Predict, what will the missing number be: __ ÷ 1,000,000 = 52?
Game – Beat the calculator
/ Place value Y-Chart
Looks like
Feels like
Sounds like
Final Five
1. Write 16,007 in figures
2. Which is the 100s digit in six five three zero (6530)?
3. Which is bigger eight zero zero six (8006) or eight zero five zero (8050)?
4. 250 x 10 = ?
5. What is the value of the 4 in three two four zero (3240)?
Session 3
Ordering
-ascending
-descending / To order numbers up to thousands (or higher) and down to tenths / Mind-reader
Students work in small table groups, read out some clues and students to solve them mentally. Ask a group to report back at the end of the session.
Students can’t write down the clues, read them out twice.
Go over the clues: E.g.
I am 3 digit number.
I am on odd number.
The digit in the middle is even.
The numbers are consecutive.
If you add my 3 digits it adds up to 13.
A: 5, 6, 7 / The Human number line (Maths on the Go 2 – Vingerhoets, team folder)
Pp 44 (need sticky notes)
As you control the group activity you can hand out a variety of numbers on the sticky notes including;
Whole numbers, decimals, fractions, sums following patterns from session 2 i.e. 100 x 5, 450 ÷ 10.
You could possibly run this in a couple of groups simultaneously
Lower – whole numbers (1,000 – 0)
Middle – Whole numbers (10,000 – 1,000)
Upper – Decimals (0 – 1)
Upper – Decimals / fractions (1,000 – 1001)
Ask students to alternate between ascending & descending order
Game – Order order (Maths on the go 1 pp 23-26 (teacher folder) / See-saw
In partners, students take it in turns to state something they saw or learnt in today’s session.
Final Five
1. Which number is the largest? Eight five zero zero (8500), eight zero two zero (8020) or eight zero zero zero (8000)
2. Write 204 in words
3. What no. is 100 times larger than 12?
4. What is the value of the 2 in six two one four three (62143)?
5. 1500 ÷ 100 = ?
Session 4
To identify and expand a large number into its parts / To visually represent a whole number as the sum of its parts / The Age,
Give pairs mixed ability pairs a page of a newspaper. How many words do you think are on this page?
Justify your answer (array)
Record all the newspaper word estimates in a corner of the board.
What is a reasonable estimate? / § Students rehearse breaking these newspaper estimates (all) down into their parts using the template and example shown
§ Ensure that all students are using this table correctly before completing
§ Complete the riddle ‘What happens when skiers get old? (Teacher folder) / Written sentence starter
I think that it’s useful to see (visualise) large numbers in expanded (sum) form because…
Final 5
1. What is the smallest number you can make with a 6, 4, 2, 3?
2. Write six thousand and fourteen in figures.
3. Which is the largest six four zero zero (6400), six zero zero four (6004) or six zero four zero (6040)?
4. Subtract the sum of 6 and 5 from 20.
5. What number is 10 times smaller than 620?
Session 5
Decimal place value / Listing of objects and their size, where size varies from thousandths to thousands of a unit / My brother’s Aussie Rules team ‘The Bright Mountain Men’ played on the weekend and although he told me they won I have forgotten the exact score. He was bragging that he kicked 8 goals & 2 behinds himself but I’m not sure if I can believe him or not. His team’s total score was 84 points, what could the exact score line be? / Discuss the place value names below zero (to hundredths Grade 5, further – Grade 6)
Where have you seen these before? (tenths, hundredths, thousandths)
Illustrate what they look like. i.e.
FM 6 Chapter 1, Activity 7, Qn. 1-5 (teacher folder)
Complete these activities with students in pairs (able & less able) / Discussion
What did you find out about the decimal form of
1/10
1/100
1/1000?
Why do you think the first number after the decimal is called the tenths?
Final 5
1. What is the smallest number you can make with 9, 4, 5 & a decimal point?
2. What number is 1000 times bigger than 56?
3. What is the value of the 3 in sixteen point two three four (16.234)?
4. Expand the number 13,250 into its parts.
5. What is 9 x 4?
Session 6
Decimal place value / Listing of objects and their size, where size varies from thousandths to thousands of a unit / Choose any number between 1-9
Now skip count on from this in 2s,
3s,
4s,
5s,
6s,
7s,
8s,
9s,
10s. / Maths on the Go 1 – Just Gridding pp 17 – 20 (teacher folder)
After playing and completing individual grids in own books, students should be asked to identify objects that these numbers (horizontal rows) could reasonably represent i.e. 32 grapes in a bunch, 415 students at FPS, 2853 dollars for a plasma TV, 69,837 fans at the MCG etc.
As an extension, before playing again, students can design / alter their own grids by placing a decimal point along one of the vertical lines (of their choice or yours) to familiarise themselves with the vocabulary of decimals.
Show the diagram below for a constant reference point if needed (copy & paste into a new document to enlarge)
Puzzle 5s – I am a decimal. I have two digits before the point. I have two digits after the point. I read the same backwards as I do forwards. I have no zeros. My first digit is smaller than my second. The sum of my digits is 8. What number am I?
Puzzle 6s – I am a decimal. I have two digits before the point. I have two digits after the point. My first digit is smaller than my second. My second is the same as my third. My first digit is one less than my last digit. My digits all add up to 11. What number am I?