stage 3 maths program · 8.3892 use the same or different decimals and point to a specific number...

Mel Reskic Shell Cove Public School - 2018

Stage 3 Maths Program Term 2 Week 4

NSW K-10 Mathematics Syllabus Outcomes

Learning Goal – Fractions & Decimals (refer to outcome)

Fractions & Decimals (1) MA3-7NA - Compares, orders and calculates with fractions, decimals and percentages - Apply the place value system to represent thousandths as decimals - Compare, order and represent decimals with up to three decimal

places Length (1) MA3-9MG - Selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length - Find perimeters of common two-dimensional shapes and record the

strategy - Record lengths and distances using decimal notation to three

decimal places 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 – Fractions & Decimals (refer to indicators) TIB – Learning Goal – Length (refer to outcome) Success Criteria –Length (refer to indicators) TIB –


Mathematics Weekly Plan

Term – 1 2 3 4 Week – 1 2 3 4 5 6 7 8 9 10 11 Strands – Fractions & Decimals (1)/ Length (1)

Monday Tuesday Wednesday Thursday Friday Key Ideas: Fractions & Decimals Length

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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.

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Pre-Test: Fractions & Decimals & Length

In 260.54, in which place is the 4? Hundredths

Which decimal is largest? 782.34 or 782.43

Place the following decimals in descending order: 4.78, 4.1, 2.5, 3.32

Post-Test: Fractions & Decimals & Length


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Main Focus + Language

• What is a decimal? A decimal is a number which contains a decimal point. Decimal numbers may be less than or greater than 0.

• The decimal point is used to separate the whole numbers (the units, tens and hundreds) from the fractions (the tenths, hundredths and thousandths). For this reason, it is always placed between the units column and the tenths column.

• If there are any whole numbers in the decimal, these belong on the left-hand side of the decimal place. Any fractions, or parts of a whole, belong on the right-hand side of the decimal place. Examples:

• Model an example: 6.28

The first column on the right-hand side of the decimal point is the tenths column = 2 tenths or 2/10. The tenths column is ten times smaller than the units column.

• The second column on the right-hand side of the decimal point is the hundredths column = 8 hundredths or 8/100. The hundredths column is ten times smaller than the tenths column. More examples: 0.273 = 2 tenths, 7 hundredths and 3 thousandths.

• Decimal place value: Model to students the names of digits after the decimal point. Students write them down in their books:

• The first digit after the decimal

represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.

Revision: write a range of decimals on the board and encourage students to read them: 0.003 87.65 37.03 28.293 8.3892

Use the same or different decimals and point to a specific number within the digit. Ask students to identify the place value column of that digit. Example: 93.983= 8 hundredths/ 8/100 7.3= 3 tenths/ 3/10 248.027 = 7 thousandths/ 7/1000 Additional activity: This can become a whole class activity. Place a similar table on the board with bold examples for students to identify the place value of the number:

Which decimal is bigger? We can compare decimals just like we compare whole numbers. Decimals are written to the right hand side of the decimal point on the place value table. Just like whole numbers, this pattern continues through tenths, hundredths, thousandths and many more!

The tenths column is the biggest in value after the decimal point. So if we're comparing decimals, the larger one will be the one with the largest number in the tenths column, regardless of what numbers are after it. If there is no number written, then just imagine that there is a zero there instead (e.g. 0.7 is the same as 0.70). Examples to model: Question 1:

Continue modelling how to determine the biggest decimal: Question 3: Evaluate: Which number is smaller 0.13 or 0.121? Think: The tenths columns both have ones so we need to look at the hundredths columns- one has a 3 and one has a 2 so the decimal with the 2 is smaller. We can still do this question by making them have the same name, 130 thousandths vs 121 thousandths. Here we can see that the 121 thousandths is smaller. Question 4: Evaluate: Which number is bigger 0.55 or 0.552 Think: The numbers in the tenths and hundredths columns are the same in both numbers, so now we will look at the thousandths- 0 and 2. And also, we could do this one this way, 550 thousandths vs 552 thousandths. So here the 552 thousandths is bigger. Explicitly model now how to place a range of decimals to at least 3 decimal places in order using the skills just modelled: If you want ascending order you always pick the smallest first. If you want descending order you always pick the largest first. Example: Put the following decimals in ascending order: 1.506, 1.56, 0.8 Two of them begin with "1"s and the other is a "0". Ascending order needs smallest first, and so "0" is the smallest. O.8 will be our first number. Now there are two numbers with the same "Tenths" value of 5, so move along to the "Hundredths”. One of those has a 6 in the hundredths, and the other has a 0, so the 0 is smaller and therefore comes next (remember we are looking for the smallest each time). In other words, 1.506 is less than 1.56: Only one number left, it must be the largest. Answer: 0.8, 1.506, 1.56 Additional examples: 0.423, 0.028, 0.403 Answer: 0.028, 0.403, 0.423 67.284; 72.153, 14.487, 67.648 Answer: 14.487, 67.284, 67.648, 72.153

• What is Perimeter? Ask students to provide a definition to access prior knowledge: Perimeter is the distance around a two-dimensional shape.

• Explain the formula for perimeter and model examples on the board: P = L + L + W + W

• the perimeter of this rectangle is 7+3+7+3 = 20

• the perimeter of this regular pentagon is: 3+3+3+3+3 = 5×3 = 15. In this example, if all edges are the same size, student just need to multiply the measurement by the number of sides to quickly solve the perimeter.

• Model how to solve the perimeter of 2D shapes that include decimals:

Use the algorithm for addition to model how to add decimals together. 32.2 + 32.2 + 62.1 + 62.1 = P =188.6km

40.5 + 40.5 + 36.5 + 36.5 = P =154.0m

• Revise basic conversion between Metric Units of measurement:

• 1 centimetre = 10 millimetres • 1 metre = 100 centimetres • 1 kilometre = 1000 metres

Model examples of simple conversions with the students using the image from above: • 800 cm = _____ m • 90 mm = _____ cm • 4 m = ______ cm • 9 m = ______ cm • 2 km = _________ m • 700 cm = _____ m • 9 km = _________ m • 5 km = _________ m Model conversions of length up to 3 decimal places: To convert from metres to kilometres, divide by 1000 (since there are 1000 metres in each kilometre). To divide a whole number by 1000, put a decimal point at the end of the number and the move it three places to the left. Examples to model: convert each of the following distances to kilometres: 300m 25m Step 1: To convert kilometres to metres, we need to divide by 1000. Step 2: Put a decimal point after the number (as 300.0 is the same as 300) and move it 3 places to the left. Step 3: Get rid of any unnecessary zeros. 300/1000=0.300 = 0.3 Answer: 300 m = 0.3 km Step 1: To divide by 1000, put a decimal point after 25 and move it three places to the left. Step 2: Since there are not enough digits, add zeros as you move the point. 25/1000 = 0.025 Answer: 25 m = 0.025 km Model additional examples of length to 3 decimal places. Encourage students to model how to answer: Convert to kilometres: 50 m 100 m 5 m 1300m Additional activity: In pairs/small groups, students complete the following word problems to 3 decimal places:


• Model how to read the whole set of up to three decimal digits as a number.

• Example: 0.4 is read as 4 tenths. As a fraction it is 4/10.

• 0.43 is read as 43 hundredths. As a fraction it is 43/100.

• 0.391 is read as 391 thousandths. As a fraction it is 391/1000.

• 0.047 is read as 47 thousandths. As a fraction it is 47/1000.

Additional Notes:

• Tenths have one digit after the decimal point. The decimal 0.8 is pronounced "eight tenths" or "zero point eight". It is equal to the fraction 8/10.

• Hundredths have two digits after the decimal point. The decimal 0.36 is pronounced "thirty-six hundredths" or "zero point thirty-six". It is equal to the fraction 36/100.

• Thousandths follow a similar pattern. They have three digits after the decimal point. The decimal 0.749 is pronounced "seven hundred forty-nine thousandths" or "zero point seven forty-nine".

• There may be zeros after the decimal point. The decimal 0.064 is pronounced "sixty-four thousandths" or "zero point zero sixty-four".

• A decimal number may be larger than 1. The word and may be used to indicate the decimal point so it should not be used in other parts of the name of the decimal. The decimal 234.987 could be pronounced Two hundred thirty-four AND nine hundred eighty-seven thousandths

Evaluate: Which decimal is bigger 0.87 or 0.23? Think: We can think of 0.87 as 87/100 and 0.23 as 23/100. If we say the number out loud, sometimes the bigger one becomes obvious. Lets try it,87hundredths and 23 hundredths. Because they have the same name (hundredths) its easy to see the 87 hundredths is bigger. Question 2: Evaluate: Which decimal is bigger 0.3 or 0.15677? Think: In this case, saying the number aloud doesn't help us yet, (3 tenths and 15677 hundred thousandths) This is because the names are not the same. If we just look at the value in the columns and compare them from left to right we can find the bigger (or smallest number). One number has a 3 in the tenths column and the other has a 1, so the one with the 3 is bigger. But what about when they have the same number in the tenths column? Well that's when we look to the next column (the hundredths column) and compare which number is bigger/ smaller in just the same way.

Model placing decimals in descending order: 0.402, 0.42, 0.375, 1.2, 0.85 There is a 1, all the rest are 0. Descending order needs largest first, so 1.2 must be the highest. Next view the “Tenths” column. The 8 is highest, so 0.85 is next in value. Now there are two numbers with the same "Tenths" value of 4, so move along to the "Hundredths". One number has a 2 in the hundredths, and the other has a 0, so the 2 is larger. So, 0.42 is bigger than 0.402: Only 0.375 left, so the answer is: Answer: 1.2, 0.85, 0.42, 0.402, 0.375 Additional examples: 0.034, 1.032, 0.133, 1.13 25.29, 29.25, 25.9, 29.5 6.06, 0.66, 6.6, 6.0

Mila ran 2500 m. How many kilometres did Mila run? __________ A track is 3.5 m long. How many meters in two laps? __________ The cyclists completed four laps of a 5 m track. How many kilometres did they ride? __________ James completed 10 laps of a 400 m running track. How many kilometres did James run? __________

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Revision Group - Names Using a deck of cards, students turn a variety of cards to create decimal numbers. Begin with 2 decimal places. Selecting a number, students identify which place value column the number represents e.g. 87.34 = the 3 = 3 tenths.

Write a variety of decimals on task cards. Work with this group to determine which decimal out of 2 task cards are bigger.

Using the following worksheet, work with these students to place the decimals in ascending and descending order. Model using whiteboards. Display place value chart for decimals for students to refer back to. Continue modelling and scaffolding using place value chart: Decimals Worksheet - Comparing and Ordering- Teach Starter.

5/6M Town Groups Based on Continuum

Clusters

In mixed ability groups, students can select and measure the perimeter of a range of items within the classroom. Students should record their measurements of length in their workbooks and complete measurements in decimal notation (if possible). Extension: convert recorded lengths to 3 decimal places e.g. 3.4 mm = 0.0034 m


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Middle Group- Names Using the following sheet as an example, create task cards for students to identify the place value of digits in decimal number problems: http://www.math-aids.com/cgi/pdf_viewer_8.cgi?script_name=place_and_value_decimal.pl&ldigits=6&rdigits=4&language=0&memo=&answer=1&x=115&y=43

Students play a decimal place value game: Which decimal is the largest: https://games4gains.com/blogs/teaching-ideas/decimal-place-value-card-game

Students use the following task cards to calculate which decimals are in the correct order for ascending and descending patterns: https://www.teacherspayteachers.com/Product/Ordering-Decimals-Task-Cards-252408 Alternatively, create your own task cards for students to place in order; minimum of 3 decimals places.


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Students write a variety of decimal numbers in expanded notations; fractions. Use following websites for additional information: https://www.homeschoolmath.net/teaching/d/tenths-place-value.php https://www.homeschoolmath.net/teaching/d/hundredths-b.php

Students complete a range of (decimal) riddle card challenges. Students will identify the value of each digit in numbers given to three decimal places, multiply, and divide numbers by 10, 100 and 1000 giving answers up to three decimal places. Students can work in pairs in their small groups and glue in activity sheets and answer in their books. https://www.twinkl.com.au/resource/t2-m-1571-decimal-place-value-riddle-challenge-cards https://www.twinkl.com.au/resource/t2-m-4417-year-6-decimal-place-value-maths-mastery-challenge-cards

Students complete a range of ascending and descending decimal problems involving negative numbers. Create task cards out of the following examples: https://www.dadsworksheets.com/worksheets/ordering-numbers-positive-and-negative-ordering-with-decimals.html


Clusters

Student complete word problem using larger numbers e.g. Extension: Jenny is walking from Fish Ville to Cowtown, a distance of 6.75km. She still has 1320m left to walk. How far has she walked already? Give your answer in km.

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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.

Identify the place value of the highlighted number: Revision: 23.43 45.234 Middle: 34.566 3.0034 Main: 344.224 3.56306

Which is the biggest? Revision: 73.45, 63.88 Middle: 284.245, 284.289 Main: 3234.4892, 3234.4829

Largest to smallest: Revision: 0.24; 0.95; 0.71; 0.16 Middle: 2.98; 2.06; 2.85; 2.651 Main: 4.143; 4.0343; 4.3455; 4.640

Students draw a 2D shape and label the measurements of each edge. Students calculate the perimeter of their shape.

Revision: 7 m = 7000 km 10 m = 1 cm Middle: 8000m = 8km 20mm = 2 cm Main: 478m = 3.478km 678mm = 0.678m

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• Play dice place value game, students in two teams roll a dice and place that number somewhere on their place value chart. The chart only has one whole number, tenths, hundredths and thousandths. The team with the largest number wins; to extend the game students can place the number they have rolled into the other teams place value chart.

• Complete iMaths worksheets. • Students challenge each other and create a range of decimals and using whiteboards, quickly place them in order from smallest to largest and vice

versa.

Students draw and cut out a variety of 2D shapes (regular/ irregular) and find the perimeter of each shape. Complete activity sheets/ word problems. Example (extension): https://static.studyladder.com.au/cdn/course/e9/7df6cadfa344/Studyladder+-+Recording+Length+using+Decimal+Notation.pdf Complete iMaths worksheets.


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stage 3 maths program · 8.3892 use the same or different decimals and point to a specific number...

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