stage 3 maths program...mel reskic shell cove public school - 2018 stage 3 maths program term 2 week...

Mel Reskic Shell Cove Public School - 2018

Stage 3 Maths Program Term 2 Week 6

NSW K-10 Mathematics Syllabus Outcomes

Learning Goal – Whole Number (refer to outcome)

Whole Number (1) MA3-4NA – Orders, reads and represents integers of any size and describes properties of whole numbers - Read, write and order numbers of any size - State the place value of digits in numbers of any size - Record numbers of any size using expanded notation Data (1) MA3-18SP – Uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables - Construct data displays, including tables, column graphs, dot plots

and line graphs, appropriate for the data type - Describe and interpret data presented in tables, column graphs, dot

plots and line graphs Working Mathematically - 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

Success Criteria – Whole Number (refer to indicators) Learning Goal – Data (refer to outcome) Success Criteria –Data (refer to indicators)


Mathematics Weekly Plan

Term – 1 2 3 4 Week – 1 2 3 4 5 6 7 8 9 10 Strands – Whole Numbers (1)/ Data (1)

Monday Tuesday Wednesday Thursday Friday Key Ideas: Whole Number Data

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Additional warm up activities: TEN: Using your PLAN Data, students will work on TEN based activities for 10 minutes. Activities are differentiated based on group needs (view PLAN Data/Clusters).

Mark Pre-test as a whole class and provide immediate feedback.

TEN/ Ninja Numeracy/

Quick Revision Mentals

TEN/ Five Minute Frenzy/


TEN/ Five Minute Frenzy/


Mark Post-test as a whole class and provide immediate feedback.

Prob

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What is the place value of the numbers underlined? 673 983 92 703 27 283 9 270 32 442 620

Write the following numbers in words: 509 340 Write the following words in numbers: Two million, three hundred thousand and four.

Write the following number in expanded notation: 4 265 = 4 × 1 000 + 2 × 100 + 6 × 10 + 5 × 1.

Post-Test: Whole Number & Data.


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Place value: Begin by writing a number of the board, five digits or less. Access student’s prior knowledge by asking volunteers to read the number aloud. Repeat this with several numbers but do not ease them. Example numbers for students to read: 467; 435; 6 009; 6 090; 52 749; 52 974. Using a number from the above examples, ask students to read each of the digits in terms of its ‘place value’ to gain access to their prior knowledge. Display a Place Value chart on the board or provide a hard copy for students to glue in their books to refer to. Depending on your student’s levels, you may wish to stop at a certain number or extend them beyond hundred-billions.

Select two numbers from the above list e.g. 52 749 and 52 974 and ask students which is greater? How can you tell? A possible strategy to assist students is to write the two numbers, one under the other, so that the same-place digits are aligned and then to complete the values of the aligned pair of digits, start with the first pair (ones column) onto the left. For example:

The thousands digits are the same; their value is 2 000 each. The hundreds digits are not the same; 900 is greater than 700, so 52 974 is greater than 52 749. Additional revision: To demonstrate that is greater than, we write it as = 52 974 > 52 749 Remind students the meaning of > (is greater than) and Review meaning of < (is less than). Write a variety of umbers for students to classify as ‘greater’ or ‘less’ using the symbols above: 871 > 429 167 < 968 597 < 625 888 > 136 Explain to the students that what we have been viewing is the ‘place value’ of numbers. The place (location) of each digit is important. It determines the value of that digit. For example: the 3 in the number 342 indicates 300, since it is located in the hundreds place value column. The 4 in the number 342 indicates 40, as it is located in the tens place value column. Example: The digits of a number are written in columns which are divided into groups of hundreds, tens and ones (units). This is shown in the example below. Display on board.

The number 5 764 392 (shown in the example) is written as; five million, seven hundred and sixty-four thousand, three hundred and ninety-two. When writing numbers of more than four digits, it is usual to leave a space to the left of each group of three digits, when counting from the Units column. Guided examples: Encourage students to identify in each of these numbers, what value does the digit 5 have? 17 526 010 = 5 represents " five hundred thousand" 2 110 735 000 = 5 represents "five thousand" Additional Modelling: ordering of numbers: Ordering numbers:

Explicitly model how to place these numbers in order from smallest to largest (ascending order):

Revision Place Value: place value is the value of a number in a set position. Write the following numbers on the board and encourage students to find the value of the ‘3’ in each: 30 in 1 234 300 in 2 346.04 30 000 in 1 236 790 0.03 in 12.439 Quick revision on ‘greater than’ and ‘less than’: 247 > 135 1 914 < 5 224 24 945 > 14 484 934 443 > 807 275 Writing numbers into words and the rules: View how to write numbers into word form. Explicitly model by reading numbers and using rules to write numbers in words. Example: 179. Read; this number contains one hundred, seven tens and nine units. Keeping this in mind, we can write it as: One hundred seventy-nine. Hyphens (-): are used between the smallest two digits in a number; between tens and units (e.g. a hundred and twenty-seven), ten thousand and a thousand (six hundred and forty-seven thousand), ten million and a million (seven hundred and seventy-two million). The word ‘and’ must be used to break numbers up and toward the end before writing the units/ones. A trick to this is to read the word aloud and add in and in places you actually say it e.g. 3 452 = three thousand, four hundred and fifty-two. Explain that when a number involves more than 3 digits e.g. 12933, we break the number up in groups of 3 digits by leaving a gap in between the numbers = 12 933. commas. The trick is starting from the hundreds column and then counting the next three digits, if possible. Write various numbers on the board (include examples with zeros), read the numbers out loud and model writing them in words: 682 Six hundred and eighty-two 988 Nine hundred and eighty-eight 1 167 One thousand, one hundred and sixty-seven 5 341 five thousand, three hundred and forty-one 60 014 = sixty thousand and fourteen 43 095 = forty-three thousand and ninety-five 43 090 = forty-three thousand and ninety 7 936 211 Seven million, nine hundred and thirty-six thousand, two hundred and eleven Model examples how to write numbers from words. https://www.youtube.com/watch?v=XvJu1fDJxok Use the following clip to assist in modelling how to write numbers from words. Use a blank place value sheet to assist in writing number out correctly. Use whiteboards and encourage students to hold up answers when they are ready. Note any students who cannot get this will be part of your revision group. Examples to model: Seven thousand, two hundred and seventy-three = 7 273 One thousand, three hundred and sixteen = 1 316 Three thousand, eight hundred and twenty-nine = 3 829 Extension examples: One billion, sixty million, five hundred and twenty thousand. = 1 060 520 000 Four hundred and sixteen thousand, seven hundred and three. = 416 703 Additional examples for students to complete: • Seven thousand, three hundred and ninety-four • Seven thousand, seven hundred and twenty-five • Ninety-four thousand, two hundred forty-seven • Forty-nine thousand, seven hundred and twenty-two

Writing numbers revision: We can write numbers in several ways. Example: The number, 4365 can be written in: • numeric form/ standard form: 4 365 • words: four thousand, three hundred and sixty-five • expanded form: 4 000 (4 x 1 000) + 300 (3 x 100) + 60 (6 x

10) + 5 (5 x 1). Explain that this will be the focus of today’s lesson.

Expanded Notation: Numbers written in expanded notation are broken up into their place values. To work this out, you simple multiply the number by the place value of its position.

It is simply writing a number to show the value of each digit. It is shown as a sum of each digit multiplied by its matching place value (ones, tens, hundreds, etc.) Standard Notation is just the number as we normally write it e.g. above 293. The best way to attempt these problems is to look at them digit by digit. Example: 704 806 The largest unit is 100 000 write the number 7. After 100 000s comes the 10 000s, how many are there? None, so write a zero. How many thousands: write the number 4. How many hundreds? Write the 8 How many tens? None so write a zero How many units (ones)? Write the number 6 = 704 806. Expanded Notation = 7 x 100 000 + 4 x 1000 + 8 x 100 + 6 Additional examples to model: 234 567 The number two hundred and thirty-four thousand, five hundred and sixty-seven can be written in expanded notation as: = 200 000 + 30 000 + 4 000 + 500 + 60 + 7 which is the same as: (2 x 100 000) + (3 x 10 000) + (4 x 1 000) + (5 x 100) + (6 x 10) + (7 x 1) 102 700 = (1×100 000) + (2×1 000) + (7×100) Additional Modelling: Another way to write numbers is using exponential notation (also called power). A number is often multiplied by itself several times. Instead of writing 10 x 10 x 10 x 10 we can write 104 or 10 to the power of 4. Using place value columns, each column has a place value ten times the value of the one to its right.

Ones = no tens, just ones = 100

Ten = 10 ones (units) = 10 x 1 = 101 Hundred = 10 tens = 10 x 101 = 102 Thousand = 10 hundreds = 10 x 102 = 103 Ten Thousand = 10 thousands = 10 x 103 = 104 Hundred Thousand = 10 ten thousand =10 x 104 = 105 One Million = 10 hundred thousand = 10 x 105 = 106

Basically, rather than writing a number e.g. 4 x 10 000, you would count how many zeros there are in ten thousand and simple write: 4 x 104 because 10 000 has 4 zeros in it. Model examples using the powers method: The number 1 234 567 is written in exponential notation as: = (1 x 106) + (2 x 105) + (3 x 104) + (4 x 103) + (5 x 102) + (6 x

101) + (7 x 1). Standard Form: 5 325 (Extension) Expanded Exponential Form: (5 × 103) + (3 × 102) + (2 × 101) + (5 × 100) Standard Form: 233 958 Expanded Exponential Form: (2 × 105) + (3 × 104) + (3 × 103) + (9 × 102) + (5 × 101) + (8 × 100)

Dot Plots: Dot plots are a graphical way of showing how often a particular choice was made or how many times an event occurred. They are best used for small to medium size data sets. It is a graphical display of data using dots.

Use the following example to model how to interpret the data of a dot plot. Just by looking at a dot plot we can see:

• the most frequent (common) choice/ event. • the highest and lowest scores • how spread out the scores are • whether there are any outliers (scores that are

very different from the rest) Worked Example QUESTION 1: Mrs. Thompson took a survey of the type of pets owned by her students and displayed her results in the dot plot below.

a) Which pet is most common?

Think: The most common pet will have the most dots, so the column will be the tallest.

Answer: Birds were the most common type of pets.

b) There is the fewest of which type of pet?

Think: "Fewest" means "least" so we are looking for the column with the least number of dots.

Answer: There is the fewest "other" pets.

c) How many students had cats?

Think: One dot represents one cat, so we need to count the number of dots.

Answer: 6 students had cats. d) Which pets could belong to the other category?

A) Birds B) Dogs C) Mice D) Cats

Think: We need to find the animal that was not mentioned in the dot plot.

Answer: Birds, dogs and cats were all columns in the dot plot, so C) mice could belong to the other category.

Additional Example to model: Minutes to eat breakfast

A survey of "How long does it take you to eat breakfast?" has these results:

Which means that 6 people take 0 minutes to eat breakfast (they probably had no breakfast!), 2 people say they only spend 1 minute having breakfast, etc. And here is the dot plot:

Review how to interpret dot plots using the following example with the whole class: The students in one social studies class were asked how many brothers and sisters (siblings) they each have. The dot plot here shows the results.

a. How many of the students have six siblings? b. How many of the students have no siblings? c. How many of the students have three or more siblings? Encourage students to sggest other questions that they could answer using this data. Model how to create a survey and complete a dot plot graph as a whole class: Example: What is my students favourite school subject? First, to get the data, create a tally chart and students will select their favourite subject:

Subject Tally Score English Maths History Science CAPA Sport

Interpret the tally marks and record as numbers. Draw a numberline and create spaces for each subject (x5) with the equal width apart. Create a title for your dot plot below the numberline, e.g. My students most favourite subject. Write each of the subjects below the line. Look at your table, add a dot above the line to represent each number of students who like that subject. Example: if 9 students like maths, then there should be 9 dots above maths. Note: the dots should be align with each other: Example of dots not align with each other:

Example of how dot plots should be placed and align with the other data:

For additional assistance, view the following clip on creating a dot plot graph: https://mathspace.co/study/#!curriculum/213/topic/3598/subtopic/76082/adaptiveworkout/12/76082/chapter/2567/ Model how to interpret data by establishing questions you wanted answered. Examples: What is the most favurite subject? What is the least favourite subject? How many students like CAPA? What is the difference between history and science? Was there a subject no student liked? Were there any two subjects the same number of students liked?


10 002, 102, 1002, 12 Answer = 12, 102, 1002, 10 002 Explicitly model how to place these numbers in order from largest to smallest (descending order): Three thousand and thirty, 30 500, three hundred and fifty, 33 Answer = 30 500, three thousand and thirty, three hundred and fifty, 33 Additional examples to model (ascending and descending orders): 2 362, 3 950, 2 328 4 003, 2 272, 7 228 32 567, 332 359, 52 396

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Revision Group - Names Work with these students and use a deck of cards or create simple maths task cards with a series of numbers on them. Underline a number and students will need to identify what the value of that number is. Create as well, task cards with two numbers on them and students will need to identify the number that is ‘greater’ or ‘less’ than. Using a range of the simple number cards, assist students in placing them in order (ascending in descending).

Using either decks of cards or use the following link to write some task cards with the numbers on them. Encourage students to continue practicing the reading of the numbers aloud. Monitor students understanding of this. Provide support to students to write simple numbers in words and gradually extend them to larger ones if they are ready. http://www.mathemania.com/pdf/write-ones-thousands-as-a-number.pdf - ones to thousands Extension: http://www.mathemania.com/pdf/write-ones-millions-as-a-number.pdf - ones to millions.

Work with these students. Write simple task cards or use deck of cards to create numbers and provide support for students to write the expanded notation form.

5/6M Town Groups Based on Continuum

Clusters

Students create their own survey on any chosen topic and will create a dot plot graph to display their data. Students will survey their class and or other classes (if possible). Students will come up with at least 5 questions that they want answered from their survey. Students who need support can work with the teacher in a small group and create a survey and plot together.

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Middle Group- Names Write a range of number cards with a number underlined. Students will write the number and identify the place value of that number. Within these cards, add questions that will test the students which number is ‘greater’ or ‘less’ than. Students will answer these in their maths books using the greater/less than symbols. Using the number cards or deck of cards, students place a range of numbers in order (ascending in descending).

Students practice reading their numbers aloud to a friend. Use the following words to write task cards involving numbers and students will need to write the words for them in their books. http://www.mathemania.com/pdf/write-ones-millions-as-a-number.pdf - ones to millions

Extension: If students are ready for an extension, students can be provided with task cards with numbers and/or words and write the opposite that involves decimals e.g. cards may say: one million and twenty-six hundredths, students will need to write: 1 000 000.26: http://www.mathemania.com/pdf/write-hundredths-millions-as-a-number.pdf

Create task cards or students can create them by rolling dice or using decks of cards. Once a number is created, students will write the expanded form of that number. These students should be completing in the range to ones – millions and higher if able to extend. If students are ready to be extended, students can write the exponential form of their numbers.


Clusters

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Main Group – Names Create numbers with larger numbers or students can create using deck of cards or dice and select a number they want to write the value of. These should include decimal numbers. Within these cards, add questions that will test the students which number is ‘greater’ or ‘less’ than. Students will answer these in their maths books using the greater/less than symbols. These should include numbers with decimals. Using the number cards or deck of cards, students place a range of numbers in order with decimals (ascending in descending).

Students practice reading their numbers aloud to a friend. Use the link to write number cards and students will need to write the number in words. https://drive.google.com/file/d/0B_wlnPzXZBUZUGlUUGNTZUVzZ2c/view Extension: Use the link to create number cards. These could include a mix of word cards and number cards where students will need to write the opposite to. These include decimals: http://www.mathemania.com/pdf/write-millionths-thousands-as-a-number.pdf - thousands to millionths http://www.mathemania.com/pdf/write-billionths-trillions-as-a-number.pdf -trillions to billionths

Using only the number cards, students will write the exponential form of that number. https://drive.google.com/file/d/0B_wlnPzXZBUZUGlUUGNTZUVzZ2c/view Extension: Create number cards that involve decimal numbers. Model to students how to write the expanded form with decimals. Use the following link to provide teacher support: http://www.coolmath.com/prealgebra/02-decimals/03-decimals-expanded-notation-02


Cluster

Extend students. Analyse plot graphs and model how to find the mode, mean and medium of the graph.


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Feedback – Use the thumb method after explicit modelling to determine students understanding and where they will be placed for group activities. Marking Exit Slips – Next to each students Exit Slip, the teacher will check students answers and will either write an: A = Achieved N/Y = Not Yet N/Y students will become your target group.

Revision: 6 376 83 823 Middle: 389 383 8 309 389 Main: 2893.3982 903 892 029

Which one is greater? Revision: 5 398, 4 983 Middle: 387 443, 383 484 Main: 1 983 726, 1 524 983 762

Expanded Notation: Revision: 7 394 Middle: 3 983 268 Main Exponential Form: 20 370 403 290

Students answer the following problem on their exit slips: The Norwood Ski Resort asked its guests how many times they went sledding last winter.

Sledging last winter

Number of times How many guests went sledding fewer

than 2 times? ______ guests

Students will write something that they have learnt and something that they still need more revision on in regards to dot plot graphs.

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• Complete iMaths worksheets related to topic. • Play dice place value game, students in two teams roll a dice and place that number somewhere on their place value chart. The chart can go beyond a million or

less depending on student’s needs. Extend students by adding decimals in; tenths, hundredths and thousandths etc. • Matching game: students match words to numbers. These can be extended by including decimals and going beyond a million. • Students challenge each other by creating numbers and seeing who has the ‘greater’ or ‘lesser’ value. These can be used on whiteboards and created with deck of

cards or rolling dice. If students use deck of cards, they need to each have the same number of cards and either try to make the largest or smallest number to win e.g. 7 cards each will equal a number in the millions column. The student who wins will collect their partners cards.

• Students create a variety of numbers with a partner and practice reading them aloud. They can write the numbers in words and check with a friend and practice the expanded form.

• Complete iMaths worksheets related to topic. • Students can work with a partner to create a jointed data survey on a

similar interest they like.

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stage 3 maths program...mel reskic shell cove public school - 2018 stage 3 maths program term 2 week...

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