The positioning system of numbers in decimal form. The binary number system and number systems used in some cultures through history, such as the Babylonian.
Main methods of calculating using natural numbers and simple numbers in decimal form when calculating approximations, mental arithmetic, and calcu lations using written methods and calculators. Using the methods in different situations.
Plausibility assessments when estimating and making calculations in everyday situations.
Lesson Objective: Students will be able to simplify fractions by finding the highest common factor (HCF)
Starter: Simplify the following fractions: a. 4/6 b. 6/9 c. 9/12 d. 13/169 e. 12/132 f. 42/63 g. 24/32 h. 25/75 Lesson: Key Words: equivalent, numerator, denominator, mixed number, improper fraction, least common multiple Review fraction vocabulary: equivalent fraction, numerator, denominator, mixed numbers, improper fractions (have students write down these words and then turn and talk to try and come up with definitions and number examples of each) Use this worksheet to review fractions with visuals (look at the images and determine the fraction for each image) → you can just project it on the whiteboard but can make copies if you feel your class needs support Introduce adding fractions: Show sample problem: 2/4 + 1/4 = Explain to students that when adding fractions we only add the numerators and the denominators stay the same Give students an example that adds up to an improper fraction: 3/5 + 4/5 = Ask students to solve this problem and see if they know how to change the improper fraction into a mixed number Introduce subtracting fractions: Show sample problem: 6/8 - 2/8 = When subtracting we only subtract the numerators Work in Class: 1. 5 + 1 = 6. 4 – 1 = 8 8 8 8 8 8 2. 3 + 3 = 7. 3 – 1 = 10 10 10 12 12 12 3. 2 + 4 = 8. 7 – 4 = 9 9 9 9 4. 3 + 5 = 9. 11 – 5 = 16 16 16 16 5. 7 + 2 = 10. 7 – 2 = 10 10 10 10 Textbook pg. 231 and 232 (work in partners and discuss answers) Support: Adding fractions: adding improper and change to simplest form Extension: Extension: pg. 232, Q. 11 - 14. Challenge: Have students complete these word problems with fractions (you can also use these throughout the week to give students an additional challenge) Conclusion: Conclusion: Ask students to write down 3 examples of where they can see and find fractions in their everyday lives. Have them share these with a partner and then with the whole class. Some examples could include: in recipes, money, splitting bills, pizza, etc.
Learning Objective: Students will be able to convert mixed numbers into improper fractions, multiply simple fractions, and most of them will be able to multiply mixed numbers. Review how to convert a improper fraction to a mixed number. Example: 24 5 = 1 and 4/5 Step 1: Divide the numerator by the denominator using the bus stop method. Step 2: The answer on top of the bar becomes the whole number. The remainder becomes the new numerator. The denominator stays the same. Review how to turn a mixed number into an improper fraction. 2 and 6/2 Step 1: Multiply the denominator by the whole number. Step 2. Add the numerator. (What you found will be the numerator) Step 3. The denominator stays the same. Step 4. Simplify! 6 x 2 + 2 = 14 = 7 6 6 3 Introduce Multiplying Fractions: To Multiply Fractions: Step 1. Multiply the numerators. Step 2. Multiply the denominators. Step 3. Simplify. Example: 3 x 6 = 18 = 1 4 9 36 2 Work in Class: a. 3 x 2 4 3 b. 2 x 3 5 9 c. 6 x 7 7 6 d. 12 x 4 15 10 e. 5 x 8 9 Extension: Multiplying Mixed Numbers / using operations / negative mixed numbers. Extra Practice Multiplying Proper and Improper Fractions: http://www.mathworksheets4kids.com/fractions/multiplication/proper-improper-1.pdf Extra Practice Multiplying Mixed Numbers: http://www.mathworksheets4kids.com/fractions/multiplication/mixed-1.pdf
Lesson Objective: Students will be able to divide fractions. Some will be able to divide fractions and mixed numbers.
Learning Objective: Students will be able to use the knowledge gained from learning about different operations with fractions to solve problems.
Calculate: 1/7 + 2/7 = ¼ + ¼ + ¼ = 4/9 - 2/9 = ⅞ - 2/8 - ⅛ = ¾ - ⅓ = 1/7 + ⅖ = ⅖ x 4/8 = 2/6 x 11/12 = ½ divided by ¾ = 3/7 divided by 5/9 = Find an Equivalent Fractions: ½ = ⅓ = 3/7 = Simplify: 3/9 = 5/25 = 3/12 = 56/64 = 34/204 = Compare Fractions: ½ or 5/11 ⅗ or 6/10 ⅕ or ⅙ 2/7 or 3/9 ⅔, ⅘, ⅖ 2/9 or 4/11 or 1/7 Use this Jeopardy Link here as an interactive way to review the different operations. Worksheets: Fractions Worksheets: Depending on what you think you need, tons of worksheets available
We will be reviewing all the content from before the break
Calculate:
13,4 x 2,6 =
2673 / 3 =
13 + 46 x 3 - (3 x 11) =
- 5 + 9 =
- 14 - 7 =
12 x -19 =
- 132 - 12 =
4/8 + 6/7 =
2/5 x 3/9 =
8(2/7) x 5(1/6) =
1/3 divided by 1/9 =
1/2 divided by 4/6=
Worksheets:
Objective (Teaching Point): to know that percentage is the number of parts per 100 to recognize equivalent percentages, fractions and decimals to convert between fractions and decimals Explain that “percent” means “out of 100”. Translated to Swedish is procent You can write any percent as a fraction with a denominator of 100. With the class convert 19% to a fraction. 19% = 19/100 Try a few examples of converting both percents to fractions and fractions to percents together with the class. Practice: In pairs have the class work on problems: KS3: Pg. 234 - 235
Objective (Teaching Point): Introduction to ratios Equivalent Ratios Lesson: Discuss with the students why we use ratios in real life. To begin, students must have a basic understanding of ratios. The lesson allows students to interact and to create visuals which match ratios, see the three formats for writing a ratio, and an introduction to equivalent ratios and unit rate. See the PDF files below. Equivalent ratios: Find equivalent ratios: 2 : 7 10 : 4 4 : 14 1 : 3 20 : 8 10 : 30 1 : 3,5 4 : 12 7 : 2 Simplifying Ratios: The process of finding the simplest form of a ratio is the same as the process of finding the simplest form of a fraction. Example 5 : 10 5 can be divided into both numbers (numerator & denominator) 1:2 This is the simplified ratio in the prefered format. Simplify the following ratios: 4 : 8 5 : 20 9 : 45 25 : 40 8 : 36 6 : 21 11 : 44 Equivalent ratios: Complete the following ratios: 1 : 3 = 4 : x 1 : 5 = 5 : x 1 : 4 = x : 20 2 : 5 = 8 : x 5 : 4 = x : 24 4 : 6 = 6 : x ( Can you suggest another way of dealing with this ratio?) Support: To support students remind them how to simplify fractions and find equivalent fractions. Extension:
Objective (Teaching Point): Using ratios with map scales. Starter: Solve the following problems and reduce answers to simplest terms without units: (a) 3 feet : 6 inches (b) 25 / 80 (b) 25 lb cement : 50 lb sand : 75 lb crushed rock LESSON Give me some scales that we use in maps. 1 : 50 000 Every cm represents 50 000 cm = 500 m = 0,5 km 1 : 100 000 Every cm represents 100 000 cm = 1000m = 1 km 1cm : 5km Every cm represents 5km 1cm : 10m Every 1cm represents 10m. Exercise in Class Calculate the actual distances that are represented by the following lengths on the map. A map has an actual scale of 1cm : 500m 3cm 8cm 13cm 0,5cm or 5mm 0,1cm or 1mm Introducing Direct Proportion: Example 1:- If a can of cola costs 20kr; how much is the cost of: 2 cans 5 cans 10 cans 11 cans Question 1:- 1 Litre of Petrol costs 8,3kr; How much will you pay for: 2 litres 5 litres 10 litres 20 litres Example 2:- If 120 calculators cost 1700 kr. How much will you pay for:- 1 calculator 5 calculators 7 calculators Question 2:- If 5 cinema tickets cost 400kr. How much will you pay for:- 1 cinema ticket 4 cinema tickets 9 cinema tickets Question 3:- If 3 glasses can fill up to 600ml of water. How much water can you fill in:- 7 glasses 9 glasses
Objective (Teaching Point): Introduction to proportional division Starter: 1. If a bar of chocolate costs 5kr; how much is the cost of: 2 bars 5 bars 10 bars 11 bars 2. My 3 friends and I decide to go and watch a basketball game. The four tickets would cost 600kr. After a week, 5 other friends of us decided to come with us to the game. By that time the prices increased by 5% per ticket. How much will they pay altogether? Lesson: Introduction to Proportional Division Steps: 1. Add the numbers in the ratio to find the total number of parts (ex. 2:5 = 7) 2. Divide the amount by the total number of parts to find the size of each part 3. Multiply the size of one part by the number of parts as given in the ratio 4. Check that the resulting amounts add up to the given total. Ex. 64 girls and boys have planned for a movie. They are in a ratio of 6 girls to 2 boys. How many girls are there? Explain the method: 1. Add the parts: 6 + 2 = 8 2. Divide amount by total parts: 64 : 8 = 8 3. Multiply: 8 x 6 = 48 boys, 8 x 2 = 16 girls 4. 48 boys + 16 girls = 64 (CHECK) Work in Class:
We will be reviewing all the content from this week.
The students will complete a checkpoint review for the unit Relationships and Change.