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Mathematics Pacing Guide

Time Frame: 6 Weeks – September/October Fourth Grade

Unit 1: Number and Operations in Base Ten

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RI.4.3 Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, |

| |including what happened and why, based on specific information in the text. |

|5. Use appropriate tools strategically | |

| |RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in a text relevant to |

|7. Look for and make use of structure |a grade 4 topic or subject area. |

| | |

|8. Look for and express regularity in repeated reasoning | |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

Mathematics Pacing Guide

Time Frame: 5 Weeks – October/November Fourth Grade

Unit 2: Operations and Algebraic Thinking

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RI.4.1 Refer to details and examples in a text when explaining what the text says explicitly and when |

| |drawing inferences from the text. |

|2. Reason abstractly and quantitatively | |

| |RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in a text relevant to |

|3. Construct viable arguments and critique the reasoning of others |a grade 4 topic or subject area. |

| | |

| |SL.4.5 Add audio recordings and visual displays to presentations when appropriate to enhance the development|

| |of main ideas or themes. |

|Common Core |Essential |Assessment |Vocabulary |Resources |

| |Questions | | | |

|Use the four operations with whole numbers to solve |How do factors and |Before |area model |MAISA curriculum units and resources: |

|problems. |multiples help us make |Pretest |array | |

|4.OA.1 Interpret a multiplication equation as a comparison, |connections between |Discussion about what students already |composite |Atlas/Browse/View/UnitCalendar?Source |

|e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times|multiplication and |know |division |SiteID=&CurriculumMapID=800&Year |

|as many as 7 and 7 times as many as 5. Represent verbal |division? | |equation |ID=2013 |

|statements of multiplicative comparisons as multiplication |How do models help |During |factor pairs | |

|equations. |us better understand |Quiz |factors |Literature Connection: |

| |multiplication and | |inverse operations |Anno, Masaichiro and Mitsumasa. Anno’s Mysterious Multiplying |

|4.OA.2 Multiply or divide to solve word problems involving |division and why their |Daily Assignments |multiples |Jar. New York: Putnam Publishing, 1999. |

|multiplicative comparison, e.g., by using drawings and |respective algorithms | |multiplication |Giganti, Paul Jr. Each Orange Had 8 Slices. New York: |

|equations with a symbol for the unknown number to represent |work?  |Observations |multiplicative |Greenwillow, 1992. |

|the problem, distinguishing multiplicative comparison from |How does the knowledge of | |comparison |Hong, Lily Toy. Two of Everything. Morton Grove, IL: Albert |

|additive comparison. |fact families assist with |Centers- flashcards, |patterns |Whitman, 1993. |

| |solving multiplication/ |multiplication/division games |prime | |

|4.OA.3 Solve multistep word problems posed with whole |division problems? | |properties of |lessonplans/pdf/msmp/factor.pdf |

|numbers and having whole-number answers using four |In what ways does |Journals |multiplication |The Factor Game is available on this site for students to play |

|operations, including problems in which remainders must be |multiplicative comparison | |(commutative and |and work with factors of numbers. |

|interpreted. Represent these problems using equations with a|(3 X 4 or 3+3+3+3) assist |Teacher created worksheets |associative) | |

|letter standing for the unknown quantity. Assess the |with developing fluency of| |remainder | |

|reasonableness of answers using mental computation and |multiplication of whole |After |square |This site provides an opportunity to work with prime and |

|estimation strategies including rounding. |numbers? |Post test |variable |composite numbers. |

| | | | | |

|Gain familiarity with factors and multiples. | |Project- Solve real-world problems. Use| | |

|4.OA.4 Find all factor pairs for the whole number in the | |arrays to show multiplication problems | |Detail.aspx?ID=U100 |

|range 1-100. Recognize that a whole number is a multiple of | | | |This site features the Product Game which helps students |

|each of its factors. Determine whether a given whole number | | | |understand the relationship between factors and multiples. |

|in the range 1-100 is a multiple of a given one-digit | | | | |

|number. Determine whether a given whole number in the range | | | | |

|of 1-100 is prime or composite. | | | | |

| | | | | |

|Generate and analyze patterns. | | | | |

|4.OA.5 Generate a number or shape pattern that follows a | | | | |

|given rule. Identify apparent features of the pattern that | | | | |

|were nor explicit in the rule itself. For example given the | | | | |

|rule “Add 3” and the starting number 1, generate terms in | | | | |

|the resulting sequence and observe that the terms appear to | | | | |

|alternate between odd and even numbers. Explain informally | | | | |

|why numbers will continue to alternate in this way. | | | | |

Mathematics Pacing Guide

Time Frame: 8 Weeks December/January Fourth Grade

Unit 3: Numbers and Operations – Fractions

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RI.4.3 Explain events, procedures, ideas, or concepts in historical, scientific, or technical text, |

| |including what happened and why, based on specific information in the text. |

|2. Reason abstractly and quantitatively | |

| |RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in a text relevant to |

|3. Construct viable arguments and critique the reasoning of others |a grade 4 topic or subject area. |

| | |

|4. Model with mathematics |RI.4.7 Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, |

| |diagrams, time lines, animations, or interactive elements on the web pages) and explain how the information |

|5. Use appropriate tools strategically |contributes to an understanding of the text in which it appears. |

| | |

|6. Attend to precision |W.4.2.Write informative/explanatory texts to examine topic and convey ideas and information clearly. |

| |(d) Use precise language and domain-specific vocabulary to inform about or explain the topic. |

|7. Look for and make use of structure | |

| | |

|8. Look for and express regularity in repeated reasoning | |

|Common Core |Essential |Assessment |Vocabulary |Resources |

| |Questions | | | |

|CRITICAL AREA: |How are fractions used in |Before |Decimal |Fraction vocabulary words: |

|Developing an understanding of addition and subtraction of |everyday life? |Pretest |decimals |

|fractions with like denominators, multiplication of | | |decimals: tenths |ml |

|fractions by whole numbers, and division of whole numbers |How can understanding unit|District test data analysis |equivalent decimals | |

|with fractional answers |fractions help us make | |greatest |MAISA curriculum units and resources: |

| |sense of, build, and use |During |least | |

|Extend understanding of fraction equivalence and ordering |other fractions? |Quiz |multiple |Atlas/Browse/View/UnitCalendar?Source |

|4.NF.1 Explain why a fraction a/b is equivalent to a | | | |SiteID=&CurriculumMapID=800&Year |

|fraction (n × a)/(n × b) by using visual fraction models, |How and when are |Daily Assignments |Fractions |ID=2013 |

|with attention to how the number and size of the parts |equivalent fractions | |common denominator | |

|differ even though the two fractions themselves are the same|helpful in solving |Observations |common factor | |

|size. Use this principle to recognize and generate |problems? | |common multiple |lessonplans/pdf/msmp/factor.pdf |

|equivalent fractions. | |Centers- decimal games |decimals |The Factor Game is available on this site for students to play |

| |How is estimating useful | |decimals: tenths, |and work with factors of numbers. |

|4. NF.2 Compare two fractions with different numerators and |when performing operations|Journals |hundredths | |

|different denominators, e.g., by creating common |with fractions? | |denominator |Literature Connection: |

|denominators or numerators, or by comparing to a benchmark | |Fraction strip practice |divisor |Adler, David A. Fraction Fun. New York: Holiday House, 1996. |

|fraction such as 1/2. Recognize that comparisons are valid |What models help | |equivalent |Leedy, Loreen. Fraction Action. New York: Holiday House, 1994. |

|only when the two fractions refer to the same whole. Record |visualize, reason about, |Teacher created worksheets |equivalent decimals |McMillan, Bruce. Eating Fractions. New York: Scholastic, 1991. |

|the results of comparisons with symbols >, =, or 1 as a sum of | | |least |Pattern blocks |

|fractions 1/b. | |Visual representation of Fraction |lowest term fraction |Rulers marked in tenths (both centimeter and inch) |

|a. Understand addition and subtraction of fractions as | |Strips |mixed number |Tenths and hundredths grid paper |

|joining and separating parts referring to the same whole. | | |multiple | |

|b. Decompose a fraction into a sum of fractions with the | |Diagram of equal fractions |numerator | |

|same denominator in more than one way, recording each | | |percent | |

|decomposition by an equation. Justify decompositions, e.g., | | |pictograph | |

|by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 | | |round | |

|+ 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + | | |simplest form | |

|1/8. | | |simplify | |

|c. Add and subtract mixed numbers with like denominators, | | |whole number | |

|e.g., by replacing each mixed number with an equivalent | | | | |

|fraction, and/or by using properties of operations and the | | | | |

|relationship between addition and subtraction. | | | | |

|d. Solve word problems involving addition and subtraction | | | | |

|of fractions referring to the same whole and having like | | | | |

|denominators, e.g., by using visual fraction models and | | | | |

|equations to represent the problem. | | | | |

| | | | | |

|4. NF.4 Apply and extend previous understandings of | | | | |

|multiplication to multiply a fraction by a whole number. | | | | |

|a. Understand a fraction a/b as a multiple of 1/b. For | | | | |

|example, use a visual fraction model to represent 5/4 as the| | | | |

|product 5 × (1/4), recording the conclusion by the equation | | | | |

|5/4 = 5 × (1/4). | | | | |

|b. Understand a multiple of a/b as a multiple of 1/b, and | | | | |

|use this understanding to multiply a fraction by a whole | | | | |

|number. For example, use a visual fraction model to express | | | | |

|3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In| | | | |

|general, n × (a/b) = (n × a)/b.) | | | | |

|c. Solve word problems involving multiplication of a | | | | |

|fraction by a whole number, e.g., by using visual fraction | | | | |

|models and equations to represent the problem. For example, | | | | |

|if each person at a party will eat 3/8 of a pound of roast | | | | |

|beef, and there will be 5 people at the party, how many | | | | |

|pounds of roast beef will be needed? Between what two whole | | | | |

|numbers does your answer lie? | | | | |

| | | | | |

|Understand decimal notation for fractions, and compare | | | | |

|decimal fractions | | | | |

|4. NF.5 Express a fraction with denominator 10 as an | | | | |

|equivalent fraction with denominator 100, and use this | | | | |

|technique to add two fractions with respective denominators | | | | |

|10 and 100. For example, express 3/10 as 30/100 and add | | | | |

|3/10 + 4/100 = 34/100. (Students who can generate equivalent| | | | |

|fractions can develop strategies for adding fractions with | | | | |

|unlike denominators in general. But addition and subtraction| | | | |

|with unlike denominators in general is not a requirement at | | | | |

|this grade.) | | | | |

| | | | | |

|4. NF.6 Use decimal notation for fractions with denominators| | | | |

|10 or 100. For example, rewrite 0.62 as 62/100; describe a | | | | |

|length as 0.62 meters; locate 0.62 on a number line diagram.| | | | |

| | | | | |

| | | | | |

|4. NF.7 Compare two decimals to hundredths by reasoning | | | | |

|about their size. Recognize that comparisons are valid only | | | | |

|when two decimals refer to the same whole. Record the | | | | |

|results of comparisons with the symbols >, =, or ................
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