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Math Expressions and Utah State Core Standards Alignment
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Third Grade – Math Expressions
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Unit 1: Content and Pacing GuideBig IdeasLessonsCore Standards: Major work, Supporting, AdditionalComments VocabularyLesson Focus: I canSelect an appropriate Check for Understanding -- Modify as neededInstructional Routines and Math Language Routines
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Multiplication and Division with 0 - 5, 9, and 10: Pre-Assessment (SLO) 1 day; 19 lessons (Lessons 6, 9, 14, and 18 may take 2 days); Quick quizzes and Strategy/Fluency Checks -- 4 days; Unit Assessments 2 days; Total days -- 30.Meanings of Multiplication and Division: 5's and 2's1.1 Multiply with 5OA. 1, OA.4, OA.7, OA.9There are quite a few routines and materials that need to be managed in these first two units. Read about them in the Math Background pages. Consider how you want to manage the materials and where you would like to store the materials to complete the recommended dashes and signature sheets. There are several strategy cards to keep track. Additionally, students use the white boards and number paths to keep track of their count bys., read description on page 1W in the teacher text book. Please read the "Teaching Note" on page 3 about the convention of group size. count-by, equation, multiplication, factor, product, multiplier, multiplesI can dentify and use patterns to multiply with 5.Describe ways to find 8 x 5. Hector has some nickels in his pocket. He has no other coins. Could he have exactly 28¢? Explain.
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1.2 Multiplication as Equal GroupsOA.1, OA.3, OA.7Have small paper plates and counters available for students who may need a more concrete experience creating equal groups before they are able t represent the equal groups drawings.equal groups, in each, in every, per, equal shares drawing, function tableI can use multiplication and drawings to represent equal groups situations.Draw an equal shares drawing to find the number of markers in 8 packages of markers with 5 markers in each package; you know that 2 x 4 = 8 and that 40 is the same as 4 tens. Explain how you could use this infomration to find 2 x 40.
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1.3 Multiplication and ArraysOA.1, OA.3, OA.5, OA.7Important: Quick Practice for fluency. Fluency folder made from pages 15-18 student activity book. Linking cubes can be used as a concrete representation of arrays.array, row, column, Commutative Property of MultiplicationI can use arrays and the Commutative Property in multiplication.Draw arrays to show why 2 x 5 equals 5 x 2. How can you use 7 x 9 = 63 to find the unknown factor in the equation 9 x __ = 63?
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1.4 The Meaning of DivisionOA.1, OA.3, OA.4, OA.5, OA.7Activity 2 is a STRONG concept builder. Students are asked to relate multliplication to division and determine the meaning of the factors and the product to see how they relate to the divisor, dividend, and quotient. Be sure to give students ample opportunities to discuss and make meaning of the numbers in the situations. division, dividend, divisor, quotientI can relate division to multiplication with an unknown factor.What multiplication equation with an unknown number can you write to find 20 ÷ 5 = ___? Explain how you can use a multiplication equation to find the quotient 40 ÷ 5.
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1.5 Multiply and Divide with 2OA.1, OA.2, OA.3, OA.4, OA.6, OA.7, OA.9The number line can be a helpful tool to keep track of student count bys. If students are having a hard time keeping track of the count bys and the total number of items, have them count stacks of linking cubes so they can clearly see the number of groups. The Check Sheets are a way for students to record their practice. The Check Sheet Answer strips are found on page M7 of the Teacher Resource Book (TRB)multiplier, pictograph, even number, odd numberI can identify patterns in 2s count-bys and multiplications and relate multiplication and division.Explain how patterns in the 2s count-bys and mutiplications can help you when multiplying; How is finding the number of earrings in 6 pairs diffrent from finding how many pairs you can make with 6 earrings?
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1.6 Build Fluency with 2s and 5sOA.1, OA.2, OA.3, OA.4, OA.6, OA.7, OA.9(Recommended 2 days). The Class Multiplication Table is available through the Math Expressions manipulative kit. It is also available in the teacher resource book and in the Number Charts iTools. The Targets are found on M11 of the TRB and will need to be prepared in advance. (These are included in the Math Expressions manipulative kit.)column, row, factor, productI can build fluency with 2s and 5s multiplications and divisions.If you know that 7 x 2 = 14, what other multiplications and divisions do you know?; Explain how you can find and write two multiplication and two division equations that are related. Give an example.
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Patterns and Strategies: 9s and 10s1.7 Multiply and Divide with 10OA.1, OA.4, OA.6, OA.7, OA.9Base ten blocks can be used to represent groups of ten. These can also be easily displayed as an array/area model. This is the first time students will see a letter as a variable in an equation.equation, variableI can explore patterns in 10s count-bys, multiplications, and division and solve problems.Give an example of a number that is a 10s count-by and explain how you know; Explain how multiplying with 10 is related to multiplying with 2 and multiplying with 5.
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1.8 Multiply and Divide with 9OA.1, OA.2, OA.3, OA.4, OA.6, OA.7, OA.9There are several strategies for solving nine. Students can relate 9 facts to known ten facts and then subtract out the 9 fact. They can use the finger trick to help remember the facts. They can decompose the 9 into 5 and 4 and combine know facts of five and four. Students may select the strategies they connect to the most. Quick 9's, multiplier fingerI can identify patterns and learn a strategy for quickly multiplying and dividing with 9s.What method would you use to find 6 x 9?
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1.9 Build Fluency with 2s, 5s, 9s, and 10sOA.1, OA.2, OA.3, OA.4, OA.6, OA.7, OA.9(2 days)fast array drawingI can build fluency with 2s, 5s, 9s, and 10s multiplications and divisions.Which problem has an unknown total? How is multipllication related to addition? How is multiplication related to division? Give examples to explain your answers.
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Strategies for Factors and Products: 3s and 4s1.10 Multiply and Divide with 3OA.5, OA.6, OA.7, MD.5, MD.7product, multiplier, commutative, divisorI can look for patterns with 3s and learn a new strategy for finding products for multipliers greater than 5. Draw a picture to show how you can use the 5s shortcut method to solve Problem 8. Explain how the 5s shortcut can help when you don't know the answer to a multiplication.
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1.11 Multiplication and AreaOA.1, OA.2, OA.4, OA.5, OA.6, OA.7, OA.9, MD.7Area is revisited in depth in Unit 5. Strategy practice cards are located on pages 55A and 55Z of the Student Activity Book. Students can cut the cards out and use for practice and review. The cards are also available in the TRB and the Math Expressions Manipulative Kits. area, array, Distributive property, square unitsI can use the area model for multiplications.Describe ways to find the area of a given rectangle (shown in square units); Explain how to find the area of a rectangle-shaped garden.
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1.12 Multiply and Divide with 4OA.1, OA.2, OA.4, OA.5, OA.6, OA.7, OA.9, MD.7Relating multliplying by four to multiplying by 2 (double and double) is a strategy that will be explored in greater detail in a future lesson, but if students are prepared you may want to focus on this strategy during this lesson.repeated addition, multiplication, equal shares drawing, product, multiplierI can look for patterns and learn a strategy for solving problems involving 4s.Draw a picture to show how you can use the answers to 5 x 4 and 3 x 4 to find 8 x 4.; Create a function table that shows the relationship bettween a number of squares and the number of sides in the squares. The table should have at least 5 rows.
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1.13 Use the Strategy CardsOA.1, OA.2, OA.3, OA.4, OA.6, OA.7Be sure to have a routine for managing the strategy cards.count-bys, fast array, 5s shortcutI can develop and use multiplication and division strategies to solve problems.What four equations can you write for this fast array drawing?;Les said that anyone who knows 3s multiplications also knows 3s divisions. Do you agree with Les? Explain.
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1.14 Build Fluency with 2s, 3s, 4s, 5s, 9s, and 10sOA.1, OA.2, OA.3, OA.4, OA.5, OA.6, OA.7(2 days). Student will work on Independent activities to work toward fluency. They can select which works best for them or you can direct students to practice a certain activity: Go Ahead, Go for Speed, Invent a Game or Play a Game, Write a Word Problem, Invent Rhymes or Songs. Review strategies for multlipying and dividing. Creating an anchor chart for students to reference is helpful.I can build fluency with 2s, 3s, 4s, 5s, 9s, and 10s multiplications and divisions.What strategy did you use to solve Problem ____?; Write a word problem that can be solved using multiplication. Solve the problem. Then change the problem so it can be solved using division.
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Multiply with 1 and 01.15 Multiply and Divide with 1 and 0OA.5, OA.6, OA.7, OA.9Third grade students may, but need not use formal terms for these properties (OA.5). It is important that they understand the concept of the properties but do not need to recall from memory the formal term.Commutative Property of Multiplication, Associative Property of Multiplication, Identity Property of Multiplication, Zero Property of Multiplication.I can use multiplication properties and division rules as strategies to multiply and divide with 1 and 0.Explain what you know about multiplying or dividing a number by 1 and multiplying or dividing a number by 0; Draw pictures or arrays to show why 6 x 1 = 1 x 6 = 6. Use labels to explain your drawing.
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1.16 Solve and Create Word ProblemsOA.1, OA.2, OA.3, OA.4, OA.6, OA.7Student Pairs who have signatures for both Study Sheet A and B and Chek Sheets 1-4 may choose or continue an Independent Activity from lesson 14 (see TE 128) or they can be a Helping Partner for students who still need practice.equal groups, arrayI can identify, solve, and create multiplication and division word problems.Which of the problems on this page are array problems? Write an equal groups division word problem in which the unknown is the group size.
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1.17 Practice Multiplication and DivisionOA.6, OA.7Multiplication Three-In-a-Row and Division Race can be found in the student activity book pages 81 and 82. Students will also need access to the strategy cards. A variety of multiplication and division games can be found in the district fluency folder located on the JSD website. I can apply what I have learned to solve word problems and practice multiplications and divisions.Write two multiplication equations and two division equations using the numbers 8, 4, and 2 in each; Without dividing, how can you tell that 72 ÷ 8 is greater than 64 ÷ 8? Explain your thinking.
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1.18 Build Fluency with 0s, 1s, 2s, 3s, 4s, 5s, 9s, and 10sOA.1, OA.2, OA.3, OA.4, OA.6, OA.7(2 days)Multiples, Quotients, divisorI can apply the skills I have learned to build fluency in multiplications and divisions.Write a related multiplication or division equation for the equation you wrote for Problem ___; How can you tell if 10 ÷ 2 or 16 ÷ 2 has the greater quotient without dividing?
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1.19 Focus on Mathematical PracticesOA.1, OA.2, OA.3, OA.4, OA.5, OA.7, OA.9, MD.3There is an additional in-depth inquiry task entitled "Array Game" that would be a nice companion to this lesson. This can be found on-line in the personal math trainer.I can use Mathematical Practices to solve a variety of real world problems. Create clever or humorous rhymes to match multiplications or divisions. For example I know 3 times 2 is 6 so is 2 plus 2 plus 2 sticks.
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Assessments
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Multiplication and Division with 0 -5, 9, and 10LessonsCheck for Understandings: Select from suggested check for understandings found on the last activity for the lesson in the student book, or on the math writing prompt. Select the best method for checking for understanding; e.g. whole group response on a math board, turning a paper in to be reviewed, digital response on the personal math trainer.
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Big IdeasOA.1, OA.4, OA.5, OA.7Quick Quiz and Strategy Check: Recommended after lesson 6 (Pages 33 and 34)
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OA.4Quick Quiz and Strategy Check: Recommended after lesson 9 (Pages 47 and 48)
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OA.3, MD.5Quick Quiz and Strategy Check: Recommended after lesson 14 (Pages 69 and 70)
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OA.3, OA.5, OA.9Quick Quiz and Fluency Check: Recommended after lesson 19 (Pages 95 and 96)
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UnitOA.1, OA.3, OA.5, OA.6, OA.7, OA.9, MD.7Required: JSD Modified Unit Test -- Administer directly on MasteryConnect or print and enter scores on MasteryConnect using the Performance Grader. Optional: Review Test, Performance Task (Make Travel Plans)1, 2, 3, 4, 5, 6, 8, (9 or 10), 12, 13,
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Intervention and Digital ResourcesSee page 172 for reteaching suggestions and resources.
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