The Distributive Property


 Preston Harmon
 8 years ago
 Views:
Transcription
1 The Distributive Property Objectives To recognize the general patterns used to write the distributive property; and to mentally compute products using distributive strategies. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Apply equivalent names for sums and differences. [Number and Numeration Goal 4] Recognize patterns in number sentences of partial products. [Patterns, Functions, and Algebra Goal 1] Write special cases for basic arithmetic operations. [Patterns, Functions, and Algebra Goal 1] Recognize order of operations in using and applying distributive strategies. [Patterns, Functions, and Algebra Goal 3] Use distributive strategies to mentally compute products. [Patterns, Functions, and Algebra Goal 4] Key Activities Students apply the distributive property to simplify algebraic expressions and mentally calculate products. They also use the distributive property to factor expressions Playing Getting to One Student Reference Book, p. 31 Math Masters, p. 448 per partnership: calculator; overhead calculator (optional) Students practice comparing decimal numbers and apply proportional reasoning skills. Math Boxes 9 Math Journal, p. 39 straightedge Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Number and Numeration Goal ] Study Link 9 Math Masters, p. 86 Students practice and maintain skills through Study Link activities. ENRICHMENT Writing Number Stories Math Journal, p. 38 Students write number stories that can be solved using the distributive property. EXTRA PRACTICE Applying the Distributive Property Math Masters, p. 8 Students use the distributive property to solve problems. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 130 Students add the term distributive property to their Math Word Banks. Ongoing Assessment: Informing Instruction See page 9. Key Vocabulary distributive property Materials Math Journal, pp B Student Reference Book, pp. 48 and 49 Study Link 9 1 slate Advance Preparation Teacher s Reference Manual, Grades 4 6 pp Unit 9 More about Variables, Formulas, and Graphs
2 Getting Started Mathematical Practices SMP1, SMP, SMP3, SMP, SMP6, SMP, SMP8 Content Standards 6.NS.4, 6.EE., 6.EE.b, 6.EE.3 Mental Math and Reflexes Students find the total number of objects in a set when a fractional part of the set is given. Suggestions: 1_ of the people in the room is _ of the books on a shelf is _ of the marbles in a bag is _ of the crayons in a box is _ of the pages in a book is _ of the questions on a test is Discuss students strategies. Some students may prefer solving the problems by first translating them to equations. For example, 4_ 1 of the pages in a book is 40 can be translated as 4_ 1 x = 40. Math Message Be ready to explain how to mentally find the following products: 4 36 =? 99 8 =? $11.0 =? Study Link 9 1 FollowUp Briefly review the answers. 1 Teaching the Lesson Math Message FollowUp WHOLECLASS DISCUSSION Students share solution strategies. Help them record their strategies as number sentences. Be sure to include distributive strategies as you record solutions. Examples: 4 36 = 4 (30 + 6) = (4 30) + (4 6) = = 144, or 4 36 = 4 (404) = (4 40)  (4 4) = = = (1001) 8 = (100 8)  (1 8) = = 9, or 99 8 = (90 + 9) 8 = (90 8) + (9 8) = 0 + = 9 $11.0 = ($ $0.0) = ($1.00 )  ($0.0 ) = $ $.0 = $.0, or $11.0 = ($ $0.0) = ($11.00 ) + ($0.0 ) = $.00 + $.0 = $.0 ELL Lesson 9 93
3 Algebra The Distributive Property You have been using the distributive property for years, probably without knowing it. For example, when you solve 40 * with partial products, you think of as 0 and multiply each part by 40. The distributive property says: 40 * (0 ) (40 * 0) (40 * ). The distributive property can be illustrated by finding the area of a rectangle. * * * * 80 Adjusting the Activity To extend the activity and review order of operations, write the expressions without parentheses. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Show how the distributive property works by finding the area of the rectangle in two different ways. Method 1 Find the total width of the rectangle and multiply that by the height. A 3 cm * (4 cm cm) 3 cm * 6 cm 18 cm Method Find the area of each smaller rectangle, and then add these areas. A (3 cm * 4 cm) (3 cm * cm) 1 cm 6 cm 18 cm Both methods show that the area of the rectangle is 18 cm. 3 * (4 ) (3 * 4) (3 * ). This is an example of the distributive property of multiplication over addition. The distributive property of multiplication over addition can be stated in two ways: a * (x y) (a * x) (a * y) (x y) * a (x * a) (y * a) Student Reference Book, p. 48 Ask students to look for patterns in the number sentences. Include the following points in your discussion: One of the factors is rewritten as a sum (or difference) of two numbers, each of which can be easily multiplied by the other factor. Parentheses are useful for keeping track of this sum (or difference) when it is rewritten. The original product becomes the sum (or difference) of two simple products. This strategy for making mental calculations is based on the distributive property. This property gets its name because the factor outside the parentheses is distributed to each of the terms within the parentheses. To support English language learners, model the meaning of the word distribute. (See margin.) The papers are distributed to each student. Summarizing the Distributive Property (Student Reference Book, pp. 48 and 49) WHOLECLASS DISCUSSION The factor is distributed to each term. The distributive property of multiplication over subtraction can also be stated in two ways: a * (x y) (a * x) (a * y) (x y) * a (x * a) (y * a) Show how the distributive property of multiplication over subtraction works by finding the area of the shaded part of the rectangle in two different ways. Method 1 Multiply the width of the shaded rectangle by its height. A 3 cm * (6 cm cm) 3 cm * 4 cm 1 cm Algebra Method Subtract the area of the unshaded rectangle from the entire area of the whole rectangle. A (3 cm * 6 cm) (3 cm * cm) 18 cm 6 cm 1 cm Both methods show that the area of the shaded part of the rectangle is 1 cm. 3 * (6 ) (3 * 6) (3 * ) This is an example of the distributive property of multiplication over subtraction. Algebraic Thinking Use the two examples on pages 48 and 49 of the Student Reference Book to discuss how the distributive property summarizes students work in Lesson 91. Then review the four different general patterns for the distributive property. Remind students that, as with other equations, they can interchange the left and right sides. Distributive Property of Multiplication over Addition a (x + y) = (a x) + (a y) (x + y) a = (x a) + (y a) Distributive Property of Multiplication over Subtraction a (x  y) = (a x)  (a y) (x  y) a = (x a)  (y a) Use the distributive property to solve the problems * (100 40). (3 1) * * (80 ) 4. Use a calculator to verify that 1.3 * (46 89) (1.3 * 46) (1.3 * 89). Check your answers on page 43. Student Reference Book, p Unit 9 More about Variables, Formulas, and Graphs
4 Make sure students understand that these general statements do not show four different properties but are different ways of stating the same general property. Demonstrate this by writing special cases. Examples: a (x + y) = (a x) + (a y) (30 + ) = ( 30) + ( ) = 4 (x + y) a = (x a) + (y a) (30 + ) = (30 ) + ( ) = 4 a (x  y) = (a x)  (a y) (40  ) = ( 40)  ( ) = 4 (x  y) a = (x a)  (y a) (40  ) = (40 )  ( ) = 4 Ongoing Assessment: Informing Instruction Students may recognize that they can use the Commutative Property of Multiplication to write the second general pattern and special case in each example. Although they can also change the order of numbers or expressions being added, watch for students who try to change the order in which numbers or expressions are subtracted. Date 9 Time The Distributive Property The distributive property is a number property that combines multiplication with addition or multiplication with subtraction. The distributive property can be stated in 4 different ways. Multiplication over Addition For any numbers a, x, and y: a º (x y) (a º x) (a º y) (x y) º a (x º a) (y º a) Use the distributive property to fill in the blanks r 4 6 n 13 n f x (6 º d) (6 º ) ( º 1) ( º h) 1. 4 º (0 8) (4 º ) (4 º ). 6 º 34 ( º 30) ( º 4) 3. (6 º 0) (6 º 4) º (0 ) 4. ( ) º 8 (40 º 8) (6 º ). 8 º (90 3) ( º 90) (8 º 3) 6. (0 º ) (8 º ) ( ) º. 9 º (0 ) (9 º ) ( º ) 8. 4 º ( 6) ( º ) ( º ) 9. (41 19) º ( º ) ( º ) 10. (18 4) º r (18 º ) ( º r ) 11. º (w ) ( º w) ( º 6) 1. n º (13 ) ( º ) ( º ) 13. (f 8) º 1 ( º ) ( º ) 14. (9 º x) (1 º x) ( ) º 1. 6 º (d ) 16. º (1 h) Math Journal, p. 38 Multiplication over Subtraction For any numbers a, x, and y: a º(x y) (a º x) (a º y) (x y) º a (x º a) (y º a) Pose problems that students can solve mentally by applying the distributive property. Suggestions: , _ , ,98 Using the Distributive Property (Math Journal, p. 38) PARTNER Algebraic Thinking The problems on journal page 38 provide practice with four different ways of stating the distributive property. For most of the problems, there are many ways to fill in the blanks to obtain true sentences. Each problem, however, has a unique solution in the form of the distributive property. For example, in Problem 1, 4 (0 + 8) = (4 0) + (4 8) is a true sentence, but 4 (0 + 8) = (4 0) + (4 8) is the only solution in the form of the distributive property. When students have finished, go over their answers. Game Master Name Date Time 1 Getting to One Record Sheets Player s Name Player s Name Draw a line to separate each round. Draw a line to separate each round. Guess Display Result Guess Display Result on calculator Write: on calculator Write: (to nearest 0.01) L if too large (to nearest 0.01) L if too large S if too small if exact S if too small if exact Adjusting the Activity Divide journal page 38 into two sections problems without variables (Problems 1 9) and problems with variables (Problems 10 16). Have students use a blank sheet of paper to cover the second section while they work on the first section. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Math Masters, p. 448 Lesson 9 9
5 Factoring with the Distributive Property (Math Journal, pp B) WHOLECLASS Have students look at Problem on journal page 38. Remind them that this problem illustrates how the distributive property can be used to mentally solve the multiplication problem Tell students that when they apply the distributive property to solve multiplication problems mentally, they are distributing a number across a sum. In Problem, the 8 is distributed across the sum This process is called expanding the expression 8 (90 + 3). Now have students look at Problem 6. Ask them how Problem 6 is different from Problem. Sample answer: The left side of the equation in Problem 6 shows the expression expanded. Tell students that in this problem, the is undistributed from the expression (0 ) + (8 ). Applying the distributive property in this way is called factoring the expression (0 ) + (8 ). Because is a factor of both 0 and 8, it is a factor of the whole expression. In all the examples of factored expressions students have seen so far, the two addends have been written as products. Tell students that they can use their knowledge of greatest common factors to factor an expression even if the two addends are written as whole numbers. Write on the board. Walk students through the following steps to help them use the distributive property to factor this expression: Step 1: Find the greatest common factor of 33 and 1. List the factors of 33: 1, 3, 11, and 33. List the factors of 1: 1,, 3, 4, 6, and 1. From the lists, you can see that the greatest common factor of 33 and 1 is 3. Step : Write 33 and 1 as products, with their GCF as one of the factors. 33 = = 3 4 Step 3: Rewrite the original sum, substituting the products from Step for the addends = Step 4: Use the distributive property to factor the expression on the right side of the equal sign, or undistribute the = 3 (11 + 4) 9A Unit 9 More about Variables, Formulas, and Graphs
6 Point out that because you factored out the greatest common factor, the addends 11 and 4 have no common factor other than 1. Help students use mathematical language to express the meaning of the final number sentence. You might use language such as the following: 3 is a factor of the expression The sum is a multiple of the sum Factoring 3 out of the expression produces the expression 3 (11 + 4). Write other sums on the board. Ask students to identify the greatest common factor of the addends and use the GCF to factor the expression. Encourage students to check that the final two addends have no common factor other than 1. Suggestions: ; (9 + 13) ; 1 ( + 3) + 0 ; ( + 4) + 1 3; 3 (9 + ) ; (3 + ) ; ( ) 4 When students seem comfortable with the procedure, read journal page 38A as a class. Then have students work with a partner to complete the problems on journal page 38B. Date 9 Factoring Sums Time The Distributive Property of Multiplication over Addition a (x + y ) = a x + a y (a x ) + (a y ) = a (x + y ) (x + y ) a = x a + y a (x a) + (y a) = (x + y ) a The equation = 3 ( + ) is a special case of the distributive property in which the addends on the left side are written as whole numbers instead of products. This equation tells you a lot about these numbers. Here are some true statements about the relationships among the numbers and expressions in this equation: 3 is a factor of both 1 and 1. 3 is a factor of the expression The expression is a multiple of the expression +. When you use the distributive property to write as 3 ( + ), we say you factor 3 out of the sum You can use the distributive property to factor a sum of any two whole numbers. In this activity, you will factor out the greatest common factor of two addends. You will be rewriting the original sum as a multiple of another sum whose addends have no common factors other than 1. Complete the following steps for each sum. a. Find the greatest common factor of the two addends. b. Use the distributive property to factor the GCF out of the sum. Complete the number sentence to show the result. c. Fill in the blanks to give an example of what your number sentence shows. Example: a. Greatest common factor: b. Number sentence: = ( ) c. Fill in the blanks: The expression is a multiple of the expression. 38A_38B_EMCS_S_G6_MJ_U09_644.indd 38A Math Journal, p. 38A 3/9/11 11:13 AM Date 9 Time Factoring Sums continued Follow the directions on journal page 38A a. Greatest common factor: b. Number sentence: = ( + ) c. Fill in the blanks: is a factor of the sum a. Greatest common factor: b. Number sentence: 30 + = ( + ) c. Fill in the blank: The expression 30 + is a of the expression a. Greatest common factor: 4 b. Number sentence: ) = ( + c. Fill in the blanks: 4 is the greatest common factor of the numbers 48 and a. Greatest common factor: 9 b. Number sentence: c. Fill in the blanks: When the number 9 is factored out of the sum + 63, the result is the expression 9 (3 + ) a. Greatest common factor: b. Number sentence: c. Write your own sentence multiple Sample answer: + 63 = 9 (3 + ) 1 Sample answer: = 1 (3 + ) Sample answer: The sum is a multiple of the sum 3 +. Math Journal, p. 38B 38A_38B_EMCS_S_G6_MJ_U09_644.indd 38B 3/9/11 11:13 AM Lesson 9 9B
7 Getting to One Materials 1 calculator Players Skill Estimation Object of the game To correctly guess a mystery number in as few tries as possible. Directions 1. Player 1 chooses a mystery number that is between 1 and Player guesses the mystery number. 3. Player 1 uses a calculator to divide Player s guess by the mystery number. Player 1 then reads the answer in the calculator display. If the answer has more than decimal places, only the first decimal places are read. 4. Player continues to guess until the calculator result is 1. Player keeps track of the number of guesses.. When Player has guessed the mystery number, players trade roles and follow Steps 1 4 again. The player who guesses their mystery number in the fewest number of guesses wins the round. The first player to win 3 rounds wins the game. Player 1 chooses the mystery number 6. Player guesses: 4. Player 1 keys in: 4 6. Answer: 0.69 Too small. Player guesses: 3. Player 1 keys in: 3 6. Answer: 1.1 Too big. Player guesses: 6. Player A keys in: 6 6. Answer: 1. Just right! Advanced Version Allow mystery numbers up to 1,000. Student Reference Book, p. 31 Games For a decimal number, the places to the right of the decimal point with digits in them are called decimal places. For example, 4.06 has decimal places, 13.4 has 1 decimal place, and 0.80 has 3 decimal places. Links to the Future Students will apply their knowledge of the distributive property when they factor and multiply polynomials in future algebra courses. Ongoing Learning & Practice Playing Getting to One (Student Reference Book, p. 31; Math Masters, p. 448) PARTNER Divide the class into pairs. Distribute a calculator and a game record sheet (Math Masters, p. 448) to each partnership. Students read the directions on page 31 in their Student Reference Book. If an overhead calculator is available, ask a volunteer to demonstrate how to play the game. Encourage students to play a practice game. Math Boxes 9 (Math Journal, p. 39) INDEPENDENT Date 9 1 a. 1 Math Boxes 1. Use the distributive property to fill in the blanks. a. 8 º (30 4) ( 8 º 30 ) ( 8 º 4 ) 9 b. ( º) ( º6) 9º( 6) c. (0 6) º 10 (0 º 10) (6 º ) 9 d. (9 1) ()(9) ()(1) 3. Find the number. of what number is 1? 0 b. 3 of what number is? c. of what number is 14? 3 d. of what number is 9? 0 e of what number is 84? Time. Circle the expressions that represent the area of the rectangle. 4 a. 4m 8 b. 4 º m c. 8m d. (m ) º 4 e. 4( m) f. 8 m 4. Write,, or. a. 8 (1) 36 () m b. 1 (3 4 ) 3 º 8 c. 400 º 3 0 d. 1 / 3 º 10 1 e Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 94. The skill in Problem previews Unit 10 content. Writing/Reasoning Have students write a response to the following: Explain how you found the coordinates of the midpoint of AB in Problem d. Sample answer: For the x value of the midpoint, I found the mean of the xcoordinates. For the y value of the midpoint, I found the mean of the ycoordinates. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 3 Use Math Boxes, Problem 3 to assess students ability to find the total number of objects in a set when a fractional part of the set is given. Students are making adequate progress if they complete parts a e. Some students might be able to mentally solve these problems. [Number and Numeration Goal ] Study Link 9 (Math Masters, p. 86) INDEPENDENT Plot and label points on the coordinate grid as directed. a. Plot (4,). Label it A. b. Plot (4,). Label it B. c. Draw line segment AB. B y x Home Connection Students practice using the distributive property. d. Name the coordinates of the midpoint of AB. ( 0, 0 ) A 34 Math Journal, p Unit 9 More about Variables, Formulas, and Graphs
8 3 Differentiation Options Name Date Time STUDY LINK 9 Study Link Master Using the Distributive Property Reminder: a º (x y) (a º x) (a º y) a º (x y) (a º x) (a º y) ENRICHMENT INDEPENDENT Writing Number Stories (Math Journal, p. 38) 1 30 Min To further explore applications of the distributive property, students choose expressions on journal page 38 and make up number stories that fit those expressions. Example: 4 (0 + 8) Four friends shared a pile of coins. Each person received dimes and 8 pennies. How much money was originally in the pile? Have students share their stories with other students. 1. Use the distributive property to rewrite each expression. a. (3 4) ( º ) ( ) b. (3 π) ( º ) ( ) c. (3 y) ( º ) ( ) d. (3 ( 4)) ( ) ( ( 4)) e. (3 ( π)) ( ) ( ( )) f. (3 ( y)) ( ) ( ( )). Use the distributive property to solve each problem. Study the first one. a. (110 ) ( 110)+( ) b. 0 (4 19) c. (3 0) 40 d. (90 8) 11 e. 9 (1 ) 4 y (0 4) (0 19) (3 40) (0 40) 1,80,000 3,80 (90 11) (8 11) (9 1) (9 ) Circle the statements that are examples of the distributive property. a. (80 ) (10 ) (80 10) b. 6 (3 0.) (6 3) 0. c. 1(d t) 1d 1t d. (a c) n a n c n e. (16 4m) f. (9 º 1 ) (1 3 º 1 ) (9 1 3 ) (4m 9.) º 1 Practice y EXTRA PRACTICE INDEPENDENT Applying the Distributive Property (Math Masters, p. 8) 1 Min Write each quotient in lowest terms Math Masters, p To provide extra practice applying the distributive property, have students write number models to show how they solved number stories. ELL SUPPORT SMALLGROUP Building a Math Word Bank (Differentiation Handbook, p. 130) 1 Min To provide language support for vocabulary terms, have students use the Word Bank template found on Differentiation Handbook, page 130. Ask students to write distributive property and represent the term with a picture and other words that describe it. See the Differentiation Handbook for more information. Name Date Time 9 Teaching Master Applying the Distributive Property 1. Cheng and of his friends are buying lunch. Each person gets a hamburger and a soda. How much money will they spend in all? Write a number model to show how you solved the problem. Answer Sample answer: $ ( ) c $1.00 $.90 Explain how the distributive property can help you solve Problem 1. Sample answer: Using the distributive property, you can first add the two values 1.10 and 0.90 and then multiply the sum by 6.. Minowa signed her new book at a local bookstore. In the morning she signed 36 books, and in the afternoon she signed 1 books. It took her minutes to sign each. How much time did she spend signing books? Sample answer: Write a number model to show how you solved the problem. (36 1) t Answer hours and 1 minutes 3. Ms. Hays bought fabric for the school musical chorus. She bought 4 yards each of one kind for 30 group costumes and 4 yards each of another kind for 6 soloists. How many yards did she buy in all? Sample answer: Write a number model to show how you solved the problem. Answer (30 4) (6 4) y 144 yards 4. Mr. Katz gave a party because all the students got 100% on their math test. He had budgeted $1.1 per student. It turned out that he saved $0. per student. If there are 30 students, how much did he spend? Sample answer: Write a number model to show how you solved the problem. (30 1.1) (30 0.) n Answer $.00 Fill in the missing numbers according to the distributive property ( 0 8 ) 6 6. ( 0 6) ( 8 6) (0 8) 6 Math Masters, p. 8 Lesson 9 9
Objective To guide the development and use of a rule for generating equivalent fractions. Family Letters. Assessment Management
Equivalent Fractions Objective To guide the development and use of a rule for generating equivalent fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationFactor Trees. Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers.
Factor Trees Objective To provide experiences with finding the greatest common factor and the least common multiple of two numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice
More informationParentheses in Number Sentences
Parentheses in Number Sentences Objective To review the use of parentheses. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management
More informationObjective To introduce the concept of square roots and the use of the squareroot key on a calculator. Assessment Management
Unsquaring Numbers Objective To introduce the concept of square roots and the use of the squareroot key on a calculator. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More informationBaseball Multiplication Objective To practice multiplication facts.
Baseball Multiplication Objective To practice multiplication facts. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common
More informationSunriseSunset Line Graphs
SunriseSunset Line Graphs Objectives To guide children as they analyze data from the sunrisesunset routine; and to demonstrate how to make and read a line graph. www.everydaymathonline.com epresentations
More informationBuying at the StockUp Sale
Buying at the StockUp Sale Objective To guide children as they multiply using mental math and the partialproducts algorithm. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM
More informationComparing Fractions Objective To provide practice ordering sets of fractions.
Comparing Fractions Objective To provide practice ordering sets of fractions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management
More informationChange Number Stories Objective To guide children as they use change diagrams to help solve change number stories.
Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationReview: Comparing Fractions Objectives To review the use of equivalent fractions
Review: Comparing Fractions Objectives To review the use of equivalent fractions in comparisons. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
More informationVolume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.
Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game
More informationAddition of Multidigit Numbers
Addition of Multidigit Numbers Objectives To review the partialsums algorithm used to solve multidigit addition problems; and to introduce a columnaddition method similar to the traditional addition
More informationMultiplication and Division of Positive and Negative Numbers
Multiplication and Division of Positive Objective o develop and apply rules for multiplying and dividing positive and www.everydaymathonline.com epresentations eoolkit Algorithms Practice EM Facts Workshop
More informationCalculator Practice: Computation with Fractions
Calculator Practice: Computation with Fractions Objectives To provide practice adding fractions with unlike denominators and using a calculator to solve fraction problems. www.everydaymathonline.com epresentations
More informationComparing and Ordering Fractions
Comparing and Ordering Fractions Objectives To review equivalent fractions; and to provide experience with comparing and ordering fractions. www.everydaymathonline.com epresentations etoolkit Algorithms
More informationSubtracting Mixed Numbers
Subtracting Mixed Numbers Objective To develop subtraction concepts related to mixed numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
More informationThe Lattice Method of Multiplication
The Lattice Method of Multiplication Objective To review and provide practice with the lattice method for multiplication of whole numbers and decimals. www.everydaymathonline.com epresentations etoolkit
More informationReading and Writing Large Numbers
Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and numberandword notations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice
More informationVolume of Pyramids and Cones
Volume of Pyramids and Cones Objective To provide experiences with investigating the relationships between the volumes of geometric solids. www.everydaymathonline.com epresentations etoolkit Algorithms
More informationReading and Writing Small Numbers
Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationHidden Treasure: A Coordinate Game. Assessment Management. Matching Number Stories to Graphs
Hidden Treasure: A Coordinate Game Objective To reinforce students understanding of coordinate grid structures and vocabulary. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM
More informationMeasuring with a Ruler
Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations
More informationObjectives To review making ballpark estimates; and to review the countingup and tradefirst subtraction algorithms. materials. materials.
Objectives To review making ballpark estimates; and to review the countingup and tradefirst subtraction algorithms. Teaching the Lesson materials Key Activities Children make ballpark estimates for digit
More informationMultiplying Fractions by Whole Numbers
Multiplying Fractions by Whole Numbers Objective To apply and extend previous understandings of multiplication to multiply a fraction by a whole number. www.everydaymathonline.com epresentations etoolkit
More informationObjective To introduce a formula to calculate the area. Family Letters. Assessment Management
Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationObjective To guide exploration of the connection between reflections and line symmetry. Assessment Management
Line Symmetry Objective To guide exploration of the connection between reflections and line symmetry. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationFrames and Arrows Having Two Rules
Frames and Arrows Having Two s Objective To guide children as they solve FramesandArrows problems having two rules. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop
More informationMiddle Value (Median) of a Set of Data
Middle Value (Median) of a Set of Data Objectives To guide children as they sort numerical data and arrange data in ascending or descending order, and as they find the middle value (median) for a set of
More informationReview of Basic Fraction Concepts
Review of asic Fraction Concepts Objective To review fractions as parts of a whole (ONE), fractions on number lines, and uses of fractions. www.everydaymathonline.com epresentations etoolkit lgorithms
More informationCapacity. Assessment Management
Capacity Objective To review units of capacity. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards
More informationThe HalfCircle Protractor
The Halfircle Protractor Objectives To guide students as they classify angles as acute, right, obtuse, straight, and reflex; and to provide practice using a halfcircle protractor to measure and draw
More informationAssessment Management
Facts Using Doubles Objective To provide opportunities for children to explore and practice doublesplus1 and doublesplus2 facts, as well as review strategies for solving other addition facts. www.everydaymathonline.com
More informationLine Plots. Objective To provide experience creating and interpreting line plots with fractional units. Assessment Management
Line Plots Objective To provide experience creating and interpreting line plots with fractional units. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family
More informationBox Plots. Objectives To create, read, and interpret box plots; and to find the interquartile range of a data set. Family Letters
Bo Plots Objectives To create, read, and interpret bo plots; and to find the interquartile range of a data set. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L34) is a summary BLM for the material
More informationUsing Proportions to Solve Percent Problems I
RP71 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving
More informationObjectives To review and provide practice with the lattice method for multiplication.
Objectives To review and provide practice with the lattice method for multiplication. Teaching the Lesson materials Key Activities Students review the lattice method for multiplication with  and digit
More informationSolving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions.
Solving Proportions by Cross Multiplication Objective To introduce and use cross multiplication to solve proportions. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop
More informationMath 25 Activity 6: Factoring Advanced
Instructor! Math 25 Activity 6: Factoring Advanced Last week we looked at greatest common factors and the basics of factoring out the GCF. In this second activity, we will discuss factoring more difficult
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationU.S. Traditional Long Division, Part 1 Objective To introduce U.S. traditional long division.
Algorithm Project U.S. Traditional Long Division, Part 1 Objective To introduce U.S. traditional long division. www.everydaymathonline.com etoolkit Algorithms Practice EM Facts Workshop Game Family Letters
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationConsultant: Lynn T. Havens. Director of Project CRISS Kalispell, Montana
Teacher Annotated Edition Study Notebook Consultant: Lynn T. Havens SM Director of Project CRISS Kalispell, Montana i_sn_c1fmtwe_893629.indd i 3/16/09 9:17:03 PM Copyright by The McGrawHill Companies,
More informationHow To Factor Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles
More informationContents. Sample worksheet from www.mathmammoth.com
Contents Introduction... 4 Warmup: Mental Math 1... 8 Warmup: Mental Math 2... 10 Review: Addition and Subtraction... 12 Review: Multiplication and Division... 15 Balance Problems and Equations... 19 More
More informationThird Grade Math Games
Third Grade Math Games Unit 1 Lesson Less than You! 1.3 Addition TopIt 1.4 Name That Number 1.6 Beat the Calculator (Addition) 1.8 Buyer & Vendor Game 1.9 TicTacToe Addition 1.11 Unit 2 What s My Rule?
More informationHow To Factor By Gcf In Algebra 1.5
72 Factoring by GCF Warm Up Lesson Presentation Lesson Quiz Algebra 1 Warm Up Simplify. 1. 2(w + 1) 2. 3x(x 2 4) 2w + 2 3x 3 12x Find the GCF of each pair of monomials. 3. 4h 2 and 6h 2h 4. 13p and 26p
More information1) (3) + (6) = 2) (2) + (5) = 3) (7) + (1) = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = 7) (5)(4) = 8) (3)(6) = 9) (1)(2) =
Extra Practice for Lesson Add or subtract. ) (3) + (6) = 2) (2) + (5) = 3) (7) + () = 4) (3)  (6) = 5) (+2)  (+5) = 6) (7)  (4) = Multiply. 7) (5)(4) = 8) (3)(6) = 9) ()(2) = Division is
More informationClifton High School Mathematics Summer Workbook Algebra 1
1 Clifton High School Mathematics Summer Workbook Algebra 1 Completion of this summer work is required on the first day of the school year. Date Received: Date Completed: Student Signature: Parent Signature:
More informationPocantico Hills School District Grade 1 Math Curriculum Draft
Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next
More informationAssessment Management
Weight Objectives To review grams and ounces as units of mass and weight; and to guide the estimation and measurement of weight in grams and ounces. www.everydaymathonline.com epresentations etoolkit Algorithms
More informationFactoring Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor x x 3 10. Answer: x 5 x Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials. Part 1 of the lesson consists
More informationProgress Check 6. Objective To assess students progress on mathematical content through the end of Unit 6. Looking Back: Cumulative Assessment
Progress Check 6 Objective To assess students progress on mathematical content through the end of Unit 6. Looking Back: Cumulative Assessment The MidYear Assessment in the Assessment Handbook is a written
More informationNCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5
NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationIntroduction to Fractions, Equivalent and Simplifying (12 days)
Introduction to Fractions, Equivalent and Simplifying (12 days) 1. Fraction 2. Numerator 3. Denominator 4. Equivalent 5. Simplest form Real World Examples: 1. Fractions in general, why and where we use
More informationEveryday Mathematics GOALS
Copyright Wright Group/McGrawHill GOALS The following tables list the GradeLevel Goals organized by Content Strand and Program Goal. Content Strand: NUMBER AND NUMERATION Program Goal: Understand the
More informationFACTORING QUADRATICS 8.1.1 and 8.1.2
FACTORING QUADRATICS 8.1.1 and 8.1.2 Chapter 8 introduces students to quadratic equations. These equations can be written in the form of y = ax 2 + bx + c and, when graphed, produce a curve called a parabola.
More informationGRADE 5 SKILL VOCABULARY MATHEMATICAL PRACTICES Evaluate numerical expressions with parentheses, brackets, and/or braces.
Common Core Math Curriculum Grade 5 ESSENTIAL DOMAINS AND QUESTIONS CLUSTERS Operations and Algebraic Thinking 5.0A What can affect the relationship between numbers? round decimals? compare decimals? What
More informationRational Number Project
Rational Number Project Fraction Operations and Initial Decimal Ideas Lesson 12: Overview Students review ordering and equivalence and practice adding and subtracting decimals in problem solving contexts.
More informationNF512 Flexibility with Equivalent Fractions and Pages 110 112
NF5 Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
More informationFree PreAlgebra Lesson 55! page 1
Free PreAlgebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can
More informationVocabulary Cards and Word Walls Revised: June 29, 2011
Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More informationUnit 7 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationIn this section, you will develop a method to change a quadratic equation written as a sum into its product form (also called its factored form).
CHAPTER 8 In Chapter 4, you used a web to organize the connections you found between each of the different representations of lines. These connections enabled you to use any representation (such as a graph,
More informationRounding Decimals S E S S I O N 1. 5 A. Rounding Decimals
S E S S I O N 1. 5 A Math Focus Points Rounding decimals to the nearest one, tenth, and hundredth Today s Plan ACTIVITY DISCUSSION Rounding a 9 Up SESSION FOLLOWUP 45 MIN CLASS PAIRS INDIVIDUALS 15 MIN
More informationPossible Stage Two Mathematics Test Topics
Possible Stage Two Mathematics Test Topics The Stage Two Mathematics Test questions are designed to be answerable by a good problemsolver with a strong mathematics background. It is based mainly on material
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationLesson Plan Assembly Line Grade 6 Ratios
CCSSM: Grade 6 DOMAIN: Ratios and Proportional Relationships Cluster: Understand ratio concepts and use ratio reasoning to solve problems. Standard: 6.RP. Understand the concept of a ratio and use ratio
More informationMinnesota Comprehensive AssessmentsSeries III
Name Minnesota Comprehensive AssessmentsSeries III Mathematics Item Sampler Grade 3 ITEM SAMPLERS ARE NOT SECURE TEST MATERIALS. THIS ITEM SAMPLER TEST BOOK MAY BE COPIED OR DUPLICATE State of Minnesota
More information1 ENGAGE. 2 TEACH and TALK GO. Round to the Nearest Ten or Hundred
Lesson 1.2 c Round to the Nearest Ten or Hundred Common Core Standard CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Lesson Objective Round 2 and 3digit numbers
More informationGrade 5 Mathematics Curriculum Guideline Scott Foresman  Addison Wesley 2008. Chapter 1: Place, Value, Adding, and Subtracting
Grade 5 Math Pacing Guide Page 1 of 9 Grade 5 Mathematics Curriculum Guideline Scott Foresman  Addison Wesley 2008 Test Preparation Timeline Recommendation: September  November Chapters 15 December
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationFSCJ PERT. Florida State College at Jacksonville. assessment. and Certification Centers
FSCJ Florida State College at Jacksonville Assessment and Certification Centers PERT Postsecondary Education Readiness Test Study Guide for Mathematics Note: Pages through are a basic review. Pages forward
More informationMTH 086 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 20, 2006
MTH 06 College Algebra Essex County College Division of Mathematics Sample Review Questions 1 Created January 0, 006 Math 06, Introductory Algebra, covers the mathematical content listed below. In order
More informationMinnesota Academic Standards
A Correlation of to the Minnesota Academic Standards Grades K6 G/M204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley
More information1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH
1 ST GRADE COMMON CORE STANDARDS FOR SAXON MATH Calendar The following tables show the CCSS focus of The Meeting activities, which appear at the beginning of each numbered lesson and are taught daily,
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationSQUARES AND SQUARE ROOTS
1. Squares and Square Roots SQUARES AND SQUARE ROOTS In this lesson, students link the geometric concepts of side length and area of a square to the algebra concepts of squares and square roots of numbers.
More informationFactoring and Applications
Factoring and Applications What is a factor? The Greatest Common Factor (GCF) To factor a number means to write it as a product (multiplication). Therefore, in the problem 48 3, 4 and 8 are called the
More informationMathematics Scope and Sequence, K8
Standard 1: Number and Operation Goal 1.1: Understands and uses numbers (number sense) Mathematics Scope and Sequence, K8 Grade Counting Read, Write, Order, Compare Place Value Money Number Theory K Count
More informationVoyager Sopris Learning Vmath, Levels CI, correlated to the South Carolina College and CareerReady Standards for Mathematics, Grades 28
Page 1 of 35 VMath, Level C Grade 2 Mathematical Process Standards 1. Make sense of problems and persevere in solving them. Module 3: Lesson 4: 156159 Module 4: Lesson 7: 220223 2. Reason both contextually
More informationSimplifying Improper Fractions Poster
Simplifying Improper Fractions Poster Congratulations on your purchase of this Really Good Stuff Simplifying Improper Fractions Poster a reference tool showing students how to change improper fractions
More informationEveryday Mathematics CCSS EDITION CCSS EDITION. Content Strand: Number and Numeration
CCSS EDITION Overview of 6 GradeLevel Goals CCSS EDITION Content Strand: Number and Numeration Program Goal: Understand the Meanings, Uses, and Representations of Numbers Content Thread: Rote Counting
More informationPrinciples of Mathematics MPM1D
Principles of Mathematics MPM1D Grade 9 Academic Mathematics Version A MPM1D Principles of Mathematics Introduction Grade 9 Mathematics (Academic) Welcome to the Grade 9 Principals of Mathematics, MPM
More informationFactoring Polynomials
UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can
More informationMATH Student Book. 5th Grade Unit 7
MATH Student Book th Grade Unit Unit FRACTION OPERATIONS MATH 0 FRACTION OPERATIONS Introduction. Like Denominators... Adding and Subtracting Fractions Adding and Subtracting Mixed Numbers 0 Estimating
More informationCurrent California Math Standards Balanced Equations
Balanced Equations Current California Math Standards Balanced Equations Grade Three Number Sense 1.0 Students understand the place value of whole numbers: 1.1 Count, read, and write whole numbers to 10,000.
More informationFactors and Products
CHAPTER 3 Factors and Products What You ll Learn use different strategies to find factors and multiples of whole numbers identify prime factors and write the prime factorization of a number find square
More informationFlorida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies  Upper
Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies  Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic
More informationAlgebra 1. Practice Workbook with Examples. McDougal Littell. Concepts and Skills
McDougal Littell Algebra 1 Concepts and Skills Larson Boswell Kanold Stiff Practice Workbook with Examples The Practice Workbook provides additional practice with workedout examples for every lesson.
More informationTransition To College Mathematics
Transition To College Mathematics In Support of Kentucky s College and Career Readiness Program Northern Kentucky University Kentucky Online Testing (KYOTE) Group Steve Newman Mike Waters Janis Broering
More informationThe majority of college students hold credit cards. According to the Nellie May
CHAPTER 6 Factoring Polynomials 6.1 The Greatest Common Factor and Factoring by Grouping 6. Factoring Trinomials of the Form b c 6.3 Factoring Trinomials of the Form a b c and Perfect Square Trinomials
More informationAlgebra Word Problems
WORKPLACE LINK: Nancy works at a clothing store. A customer wants to know the original price of a pair of slacks that are now on sale for 40% off. The sale price is $6.50. Nancy knows that 40% of the original
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationProperties of Real Numbers
16 Chapter P Prerequisites P.2 Properties of Real Numbers What you should learn: Identify and use the basic properties of real numbers Develop and use additional properties of real numbers Why you should
More informationCOMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS
COMMON CORE STATE STANDARDS FOR MATHEMATICS 35 DOMAIN PROGRESSIONS Compiled by Dewey Gottlieb, Hawaii Department of Education June 2010 Operations and Algebraic Thinking Represent and solve problems involving
More informationNS650 Dividing Whole Numbers by Unit Fractions Pages 16 17
NS60 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE
More information