7th Grade Math Chapter Applying Rational Numbers Name: Period: Common Core State Standards CC.7.NS. - Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. CC.7.NS. - Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. CC.7.EE. - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Scope and Sequence Day Lesson - Day Lesson -6 Day Lesson - Day Lesson -6 Day Lesson - Day Lesson -7 Day Lesson - Day Lesson -7 Day Lesson - Day Lesson -8 Day 6 Lesson - Day 6 Lesson -8 Day 7 Lesson - Day 7 Review Day Day 8 Quiz Day 8 Review Day Day 9 Lesson - Day 9 Test Day 0 Lesson -
IXL Modules SMART Score of 80 is required Due the day of the exam Lesson 7.E. Add and subtract decimals 7.E. Add and subtract decimals: word problems Lesson 7.E. Multiply decimals 7.E. Multiply decimals and whole numbers: word problems Lesson 7.E. Divide decimals 7.E.6 Divide decimals and whole numbers: word problems Lesson 7.E.7 Estimate sums, differences and products of decimals 7.E.8 Add, subtract, multiply and divide decimals: word problems 7.E.0 Maps with decimal distances 7.E. Evaluate numerical expressions involving decimals Lesson 7.G. Add and subtract fractions 7.G. Add and subtract fractions: word problems 7.G. Add and subtract mixed numbers 7.G. Add and subtract mixed numbers: word problems 7.G. Estimate sums and differences of mixed numbers Lesson 6 7.G.7 Multiply fractions and whole numbers 7.G.9 Multiply fractions 7.G.0 Multiply mixed numbers 7.G. Multiply fractions and mixed numbers: word problems Lesson 7 7.G. Divide fractions 7.G. Divide mixed numbers 7.G. Divide fractions and mixed numbers: word problems
Lesson 8 7.G. Estimate products and quotients of fractions and mixed numbers 7.G.6 Add, subtract, multiply and divide fractions and mixed numbers: word problems 7.G.7 Maps with fractional distances 7.G.8 Evaluate numerical expressions involving fractions
Lesson - Adding and Subtracting Decimals Warm-Up
Examples: Adding Decimals Add. Estimate to check whether each answer is reasonable. +. 6. + 6-8. + (-0.97) 6.78 +.. + -7.89 + (-.8) Examples: Subtracting Decimals Subtract.. -.08 8 -.9.7 -.6 -.6
Examples: Application During one month in the United States, 9. million commuter trips were taken on buses, and 6. million commuter trips were taken on light rail. What was the total number of trips taken on buses and light rail? Estimate to check whether your answer is reasonable. In 999,.66 million bushels of corn were grown in the United States. In 000, the harvest yielded 69.8 million bushels. What was the total production for those two years? Estimate to check whether your answer is reasonable. 6
Lesson - Multiplying Decimals Warm-Up 7
Examples: Multiplying Integers by Decimals Multiply. 7 x 0. - x 0.0. x 8 x 0. - x 0.0.6 x Examples: Multiplying Decimals by Decimals Multiply. Estimate to check whether each answer is reasonable.. x.8 -.8 x 0.9. x.6 -.96 x 0.7 8
Examples: Application To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is 0.8. What would a person who weighs 8 pounds on Earth weigh on Mars. Jet fuel weighs approximately 6. pounds per gallon. If a plane was serviced with,0 gallons of fuel, how many pounds of fuel were used? 9
Lesson - Dividing Decimals Warm-Up When you divide two numbers, you can multiply by the same power of ten changing the final answer. By multiplying both numbers by the same power of ten, you can make the divisor an. Dividing by an integer is much than dividing by a decimal. Examples: Dividing Decimals by Decimals Divide. 8.8.6 8.8 (-.7) 6. 0. 6.8 (-.06) 0
Examples: Dividing Integers by Decimals Divide. Estimate to check whether each answer is reasonable.. - (-.) 6. - (-.) Examples: Transportation Application Eric paid $9. to rent a car. The fee to rent the car was $.7 per day. For how long did Eric rent the car? Jace took a trip in which he drove 0 miles. During the trip his truck used. gallons of gas. What was his truck s gas mileage.
Lesson - Solving Equations Containing Decimals Warm-Up Examples: Solving Equations by Adding and Subtracting Solve. n -.7 = 8. a +.66 = n -.6 =.7 a + 7. = 6
Examples: Solving Equations by Multiplying and Dividing Solve. x.8 =. 9 =.6d x. =. 9 =.d Examples: Problem Solving Application A board-game box is. inches tall. A toy store has shelving measuring inches vertically in which to store the boxes. How many boxes can be stacked in the space? A canned good is. inches tall. A grocery store has shelving measuring 8 inches vertically in which to store the cans. How many cans can be stacked in the space?
Lesson - Adding and Subtracting Fractions Warm-Up Examples: Adding or Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. 8 + 9 8-6 + 7 6 0-0 To add or subtract fractions with, you must rewrite the fractions with a denominator.
Two Ways to Find a Common Denominator Find the LCM (least common multiple) of the denominators. Multiply the denominators. Examples: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form. 6 + 7 8 - : - 7 + + : 6 - - +
Examples: Astronomy Application In one Earth year, Jupiter completes about completes about of its orbit around the Sun, while Mars of its orbit. How much more of its orbit does Mars complete than Jupiter? It takes Michelle hour to drive to work. It takes Luke hour to drive to work. How much longer does it take Luke to drive to work? 6
Lesson -6 Multiplying Fractions and Mixed Numbers Warm-Up To multiply fractions, multiply the to find the product s. Then multiply the to find the product s. Examples: Multiplying Fractions Multiply. Write the answer in simplest form. - x x 8 x (- ) - 6 x 6 x 9 6 (- ) x 7 7
Examples: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. x x 7 6 x x 6 x 6 x Examples: Transportation Application In 00, the car toll on the George Washington Bridge was $6.00. In 99 the toll was that toll. What was the toll in 99? of In 00, the fee to park in a parking garage was $.00. In 000 the fee was 00. What was the fee in 000? of the fee in 8
Lesson -7 Dividing Fractions and Mixed Numbers Warm-Up Two numbers are reciprocals or multiplicative inverses if their is. Dividing a number is the same as multiplying by its. Examples: Dividing Fractions Divide. Write each answer in simplest form. 6 6 9 8 9
Examples: Dividing Mixed Numbers Divide. Write each answer in simplest form. 8 7 8 7 0
Examples: Social Studies Application The life span of a golden dollar coin is 0 years, while paper currency lasts and average of years. How many times longer will the golden dollar stay in circulation? The average life of a queen ant is approximately years. The life span of a worker ant is 7 year. How many times longer will the queen ant live?
Lesson -8 Solving Equations Containing Fractions Warm-Up The goal when solving equations that contain fractions is the as when working with other kinds of numbers - to isolate the variable on one side of the equation. Examples: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. x - 7 = 7 9 + r = - x - 8 = 7 8 + t = - 7 Examples: Solving Equations by Multiplying
Solve. Write each answer in simplest form. 8 x = x = 9 8 x = x = 7 6 Examples: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains ounces of copper, what is the total weight of the sample? The amount of copper in zinc is of the total weight. If a sample contains ounces of copper, what is the total weight of the sample?