Fractions+and+Decimals+Term+4

//__Students learn to - __// *model, compare and represent fractions with different denominators. * model, compare and represent decimals to 2 decimal places * add and subtract decimals with the same number of decimal places ( to 2 decimal places) * perform calculations with money ||
 * **Outcome: ** **Outcome:** NS2.4 – Models, compares and represents commonly used fractions and decimals, adds and subtracts decimals to two decimal places, and interprets everyday percentages.
 * Indicators: **

Revise with students the place of numbers. Then insert a decimal point between a group of numbers, like above, and explain the place value now that a decimal point has been added. Explain that numbers on the left of a decimal are whole numbers, and numbers on the right of the decimal are parts of a whole.
 * **Lesson 1 - Place Value of Decimals ** || =Register = ||
 * ** Place value with decimal numbers **
 * __ See appendix for activity sheets: __**
 * __ * ‘Decimal Place Value – unit 21’ on place value with decimal numbers. __**
 * __ * ‘Decimal notation (tenths)’ __**
 * __ * ‘Decimal notation (hundredths)’ __** ||  ||


 * **Lesson 2 - Rounding Decimals ** || =Register = ||
 * === Rounding Decimals to whole numbers: === ||  ||

If the number in the tenths column is **5 or above**, for example 1.6, the number would be **rounded up** to 2. If the tenths is **4 or less**, for example 5.3, the number would be **rounded down** to 5. Do some examples on the board to ensure student understanding. Then take a look at rounding hundredths to the nearest whole number. For example: 0.51 – closer to 1 ( as over 0.50) 0.64 – closer to 1 ( as over 0.50) 0.22 – closer to 0 ( as below 0.50) 0.99 – closer to 1 ( as over 0.50) 3.54 – closer to 4 ( as over 3.50) 6.77 – closer to 7 ( as over 6.50) 8.21 – closer to 8 ( as below 8.50) Rounding decimals is very similar to rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they are dropped and the tenths place does not change. For example, rounding 0.843 to the nearest tenth would give 0.8. If the hundredths and thousandths places are fifty or more, the tenths place is increased by one. The decimal 0.866 rounded to the nearest tenth is 0.9 Rounding decimals is very similar to rounding other numbers. If the thousandths place of a decimal is four or less, it is dropped and the hundredths place does not change. For example, rounding 0.843 to the nearest hundredth would give 0.84. If the thousandths place is five through nine, the hundredths place is increased by one. The decimal 0.846 rounded to the nearest hundredth is 0.85. ||
 * Explain to students that to be able to round decimals to whole numbers we need to take into account a few things. First we need to look at the tenths and see if the number in the tenths column is 5 or higher or less than 5.
 * Rounding Decimals to the Nearest Tenth **
 * Rounding Decimals to the Nearest Hundredth **
 * __ See appendix for activity sheets: __**
 * __ * ‘Ordering and rounding decimals – Unit 26’ __**
 * __ * ‘Rounding Money’ __**

Students design a menu for a local take-away food shop. Students investigate different selections from the menu that total different amounts eg $10, $20, $50. Possible questions include: . How much would it cost to feed yourself; yourself and a friend; or yourself and your family? . What is the change from $10/$20/$50 after the purchases? Students pose their own questions based on their own menu. This activity should be repeated using a restaurant menu. // (NB. Teacher to accommodate for class needs, depending on group of students teacher may want to create one menu for the class to use – see appendix for generic menu proforma) // The teacher provides cards each naming a different fraction with the same denominator. Students choose a card and peg it on a string number line in the appropriate place. The teacher provides cards, each naming a different decimal to 2 decimal places. Students choose a card and peg it on a string number line in the appropriate place. // Variation: // Students make their own cards and arrange them on their desk or a sheet of paper. Each student is given a set of cards with decimal numbers on them and is asked to order them on a number line between 0 and 1. Each student is then given a mixed set of cards with decimals and fractions on them eg, 0.15, 0.45. Students place them on a number line, discussing and justifying their placements. Students then select two of the numbers eg 0.15 and record six decimals or fractions between the numbers, eg 0.15, 0.2, , 0.37, , , , Students work in groups of four to create a set of 40 playing cards representing hundredths, using as many names as possible eg 73 hundredths, 73 out of one hundred,, 0.73. Students use the cards to play games such as Old Maid, Fish or Concentration. The teacher demonstrates how to use the calculator to produce decimal fractions from common fractions by dividing the numerator by the denominator eg 1÷ 2 = 0.5. Students find a number of fractions equivalent to 0.5, 0.25 and 0.125. Percent-to-fraction conversions. Explain to students that this is where you use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction. For instance: Convert 0.8 to a fraction.0.8 has only one decimal place, therefore the denominator of the fraction should be ten. Let's convert 0.34 to a fraction.0.34 has two decimal places, therefore the denominator of the fraction should be hundred. Let's convert 0.083 to a fraction.0.083 has three decimal places, therefore the denominator of the fraction should be a thousand.
 * **Lesson 3 - Addition and Subtraction of Money ** || =Register = ||
 * ** Design a Menu **
 * See appendix for an example of a Proforma to use with your class. **
 * Included are additional work sheets on adding and subtracting decimals. **
 * __ See appendix for activity sheets: __**
 * __ * ‘Design your own Pizza Menu!’ __**
 * __ * ’Adding and subtracting decimals – Unit 30’ __**
 * __ * ‘Money and decimals’ __** ||  ||
 * **Lesson 4 - Investigating Fractions (1/5, 1/10, 1/100) on number lines between 0 and 1 ** || =Register = ||
 * ** Clothes Line **
 * Part A **
 * Part B **
 * Ordering Fractions and Decimals (focus on fifths, tenths, and hundredths) **
 * //__ Additional game activity: __//****__ Representations – Card Game __**
 * __ See appendix for activity sheets: __**
 * __ * ‘Clothes line Activity cards’ __**
 * __ * ‘Revising fifths and tenths – Unit 8’ __**
 * __ * ‘Counting with fractions – Unit 13’ __** ||  ||
 * **<span style="font-family: 'Century Gothic','sans-serif';">Lesson 5 – Relating Percentages, Fractions and Decimals ** || =<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 12px; text-decoration: none;">Register = ||
 * ** Fractions to Decimals **
 * Percent to Fraction **
 * Decimals to fractions **

Percent to Decimal
||  ||   || Percent means "per 100", so 50% means 50 per 100, or simply 50/100. If you divide 50 by 100 you get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the "%" sign. ||

= = ** Fractions to Percents ** Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.

The simplest method is to use a calculator:
|| || Steps:
 * Divide the top of the fraction by the bottom,
 * Then multiply the result by 100 and read off the answer !

Example: What is 5 / 8 as a percent?
Get your calculator and type in "5 / 8 =", the calculator should show 0.625, then multiply by 100 and your answer is: 62.5% (remember to put the "%" so people know it is "per 100") Of course you can do the division in your head or on paper if you don't have a calculator!

//__ Another Method __//
Because percent means "per 100", you can try to convert the fraction to ? / 100 form.

Follow these steps:
|| Step 1: Find a number you can multiply the bottom of the fraction by to get 100. //__Example 1: Express 3/4 as a Percent__// Step 1: We can multiply 4 by 25 to become 100 Step 2: Multiply top and bottom by 25: Step 3: Write down 75 with the percent sign: **Answer = 75%**
 * Step 2: Multiply both top and bottom of the fraction by that number. ||
 * Step 3. Then write down just the top number with the "%" sign. ||
 * Step 3. Then write down just the top number with the "%" sign. ||


 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">×25 ||
 * || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">= || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">75  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">4 ||^   || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">100  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">×25 ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">4 ||^   || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">100  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">×25 ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">×25 ||

** Decimals to Percents ** Just move the decimal point 2 places to the right and add a "%" sign! Convert From Decimal to Percent || || In this box 50 of the 100 squares are green, so 50 / 100, or 0.5 of the box is green. Now, Percentage means "per 100", so 50% of the box is green. So 0.5 (a decimal number) = 50% (the "%" tells you that there is a hidden "/100" there) So, to convert from decimal to percentage, just multiply the decimal by 100, but remember to put the "%" sign so people know it is per 100.

//__ The Easy Way __// The easy way to multiply by 100 is to move the decimal point 2 places to the right. so: //__ Example: Convert 0.65 to percent __// <span style="color: black; font-family: 'Verdana','sans-serif'; font-size: 13px;">Move the decimal point two places to the right: 0.65 -> 6.5 -> 65. <span style="color: black; font-family: 'Verdana','sans-serif'; font-size: 13px;">Answer **0.65 = 65%**
 * **//__ From Decimal __//** || **//__ To Percent __//**  ||
 * || move the decimal point 2 places to the right, and add the "%" sign. ||


 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">Percent || Decimal || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">Fraction  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1% || 0.01 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/100  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">5% || 0.05 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/20  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">10% || 0.1 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/10  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">12½% || 0.125 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/8  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">20% || 0.2 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/5  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">25% || 0.25 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/4  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">331/3% || 0.333... || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/3  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">50% || 0.5 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">1/2  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">75% || 0.75 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">3/4  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">80% || 0.8 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">4/5  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">90% || 0.9 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">9/10  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">99% || 0.99 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">99/100  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">100% || 1 ||   ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">125% || 1.25 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">5/4  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">150% || 1.5 || <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">3/2  ||
 * <span style="color: black; display: block; font-family: 'comic sans ms'; font-size: 13px; text-align: center;">200% || 2 ||   ||

The teacher provides two sets of cards, the first with tenths expressed in fraction notation, and the second with tenths expressed in decimal notation. The teacher distributes the cards randomly to the students who then find the student/students with the same fraction represented. Possible questions include: . How many of the same fractions/decimals did you find? . How can you check if there are any more? . Is there another way to write that fraction/decimal? Variations: This activity should be repeated using cards with hundredths and a mixture of tenths and hundredths.
 * Match Up (See appendix for proforma) **


 * __ See appendix for activity sheets: __**
 * __ * ‘Revising decimals – Unit 15’ __**
 * __ * ‘Equivalent tenths and hundredth – Unit 23’ __**
 * __ * ‘Percentages – Unit 29’ __**
 * __ * ‘Match up’ __**

Students choose a fraction and create a poster, writing everything they know about that fraction. Students report back to the group their findings about their fraction. || 9/10  || <span style="display: block; font-family: 'arial black','sans-serif'; font-size: 24px; text-align: center;">Task: Design you own Pizza Menu Pizzas: Prices: Entrees: Prices: Deserts: Prices: * * * * * *  * * *  * * *  * * *  *  *  Beverages: Prices: * *  *  *  *  * ||
 * **<span style="font-family: 'Century Gothic','sans-serif';">Lesson 6 – Revision – Relating Fractions, Decimals & Percentages ** || =<span style="color: black; font-family: 'Century Gothic','sans-serif'; font-size: 12px; text-decoration: none;">Register = ||
 * ** Fraction Posters **
 * Restaurant Name: _

What change would you receive? What other combination of food could you buy for $15.00? What change would you receive? ||
 * You have $15.00 to spend. What could you buy for dinner for this amount?