bloomfield public schools · bloomfield grade 4 (2016-2017) 4 title of unit operations &...

Bloomfield Grade 4 (2016-2017)

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BLOOMFIELD PUBLIC SCHOOLS

Bloomfield, New Jersey 07003

Curriculum Guide

Mathematics Grade 4

Prepared by:

Nancy Schultz

Salvatore Goncalves, Superintendent of Schools Sandra Searing, Assistant Superintendent of Curriculum and Instruction

Roger Marchegiano, Supervisor of Mathematics

Conforms to the New Jersey Student Learning Standards

Board Approved: August 23, 2016


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Title of Unit Operations & Algebraic Thinking Grade Level 4 Curriculum Area Mathematics Time Frame 21-24 days

Desired Results (Stage 1)Established Goals/Standards

4.OA.A.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1 4.OA.A.3 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Paint an array HEALTH: Plan a walking program and get moving-use a chart to record results MUSIC: Estimate how many songs you will download in one week SOCIAL STUDIES: Draw your own version of a Senate Chamber using different arrays and factors of 32 (for 32 senators) 21st Century Interdisciplinary Themes:

_X Global Awareness _X Financial, economic, business, and entrepreneurial literacy __ Civic Literacy __ Health Literacy

TransferStudents will be able to independently use their learning to use the four operations with whole numbers to solve problems.

MeaningUnderstandings Students will understand that…

Essential QuestionsStudents will keep considering…

U1 - multiplication involving whole numbers (greater than 1) makes the answer become larger than either number. U2 - when solving word problems, remainders must be interpreted.

Q1 - What types of problems involve multiplication and division in the answer?


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Knowledge Students will know…

SkillsStudents will be able to…

K1 - sometimes one needs to multiply or divide numbers to find an answer.

S1 - Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. S2 - Represent verbal statements of multiplicative comparisons as multiplication equations. S3 - Multiply to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. S4 - Divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. S5 - Distinguish multiplicative comparison from additive comparison. S6 - Solve multi-step word problems posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. S7 - Represent word problems using equations with a letter standing for the unknown quantity. S8 - Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Evidence (Stage 2) Checks for Alignment Evaluation Criteria

Performance is judged in terms of… Assessment Evidence

U1 – U2 Q1 K1

Formative question-answer in class homework portfolio

Summative periodic assessment tasks/checklists

Transfer Task(s)

Use the four operations with whole numbers to solve problems

S1 – S8

Learning Plan (Stage 3) Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals. Required Activities Required Resources

Ten-Minute Math (TMM) Activity Discussion Math Workshop Assessment Session Follow-Up Games

Investigations3 Unit 1: 1.5, 1.6, 1.8 Unit 3: 1.1, 1.4, 2.5, 3.6 Unit 4: 1.4, 1.5 Unit 5: 2.6, 2.7, 3.3, 3.4, 3.5, 3.6 Unit 7: 1.2, 2.4, 2.5, 3.4, 3.5, 3.6 Unit 8: Investigation 1

Grade 4 Mathematics Curriculum Binder Suggested Activities Suggested Resources Illuminations lessons

http://illuminations.nctm.org http://nlvm.usu.edu


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Title of Unit Operations & Algebraic Thinking Grade Level 4 Curriculum Area Mathematics Time Frame 3-6 days


4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books SCIENCE: Factor sifter for numbers 1-100 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to gain familiarity with factors and multiples.



U1 - factors of a number are less than or equal to the number. U2 - multiples of a number are greater than or equal to the number. U3 - the determination of prime or composite is unrelated to the size of the number.

Q1 - Why do we need factors and multiples? Q2 - Why do we need to distinguish a number as being prime or composite? Q3 - How does finding factors or multiples of a number help us to solve problems?



K1 - a factor is one of 2 or more numbers that form a product when multiplied together. K2 - a multiple is a number which is a product of some specified number and another number. K3 - a prime number is a number that has only two factors, 1 and itself. K4 - a composite number is a number that has more than 2 factors. K5 - a whole number is a multiple of each of its factors.

S1 - Find all factor pairs for a whole number in the range 1 – 100. S2 - Determine whether a given whole number in the range 1 – 100 is a multiple of a given one-digit number. S3 - Determine whether a given whole number in the range 1 – 100 is prime or composite.


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U1 – U3 Q1 – Q3 K1 – K5



Transfer Task(s)

Gain familiarity with factors and multiples

S1-S3

Learning Plan (Stage 3) Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals. Required Activities Required Resources Ten-Minute Math (TMM)

Activity Discussion Math Workshop Assessment Session Follow-Up Games

Investigations3 Unit 1: 1.1, 1.2, 1.3, 1.6, 1.7, 1.8, Investigation 2 Unit 3: TMM 1.4, TMM 2.1, TMM 2.2, 3.1, TMM 3.1, 3.2, TMM 3.2, TMM 3.3

Grade 4 Mathematics Curriculum Binder

Suggested Activities Suggested Resources Illuminations lessons http://illuminations.nctm.org

http://nlvm.usu.edu


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Title of Unit Operations & Algebraic Thinking Grade Level 4

Curriculum Area Mathematics Time Frame 7-10 days


4.OA.C.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not 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 the numbers will continue to alternate in this way.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books HEALTH: Exercise equations SCIENCE: Balancing act-experiment weighing different objects and balancing them on a pan-balance MUSIC: Balanced tunes SOCIAL STUDIES: Money In, Money Out 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to generate and analyze patterns.



U1 - patterns have units that repeat over and over. U2 - the unit in a pattern must be identified.

Q1 - How does recognizing a pattern help one to solve problems? Q2 - Why does one need to look for patterns?



K1 - pattern types, e.g., ABABAB… K2 - patterns can be made from numbers, shapes, letters, etc.

S1 - Generate a pattern that follows a given rule. S2 - Identify apparent features of the pattern that were not explicit in the rule itself.


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U1 – U2 Q1 – Q2 K1 –K2



Transfer Task(s)

Generate patterns Analyze patterns

S1 – S2

Learning Plan (Stage 3) Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals.

Required Activities Required Resources


Investigations3 Unit 8: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10



http://nlvm.usu.edu


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Title of Unit Numbers & Operations in Base Ten1 Grade Level 4



4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.A.3 Use place value understanding to round multi-digit whole numbers to any place. _______________

1Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Computer colors-use the number 16,777,216 (number of colors on a palette for a computer) MUSIC: Music countdown-choose an album and use the number sold to explore place value SCIENCE: Elephant Lineup-make an elephant card and line up your elephants using weight, age, etc… HEALTH: Make calorie cards and compare the numbers SOCIAL STUDIES: Make a card for the population of different cities and compare the populations using place value 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to generalize place value understanding for multi-digit whole numbers.


Essential Questions Students will keep considering…

U1 - place value is used to round numbers. U2 - place value can be used to compare and order numbers.

Q1 - What does knowing place value help us to do?



K1 - how a base-ten numeral is related to the numeral name and the expanded form. K2 - that in a multi-digit whole number, a digit in one place represents ten times what it represents to its right.

S1 - read multi-digit whole numbers using base-ten numerals, numeral names, and expanded form. S2 - write multi-digit whole numbers using base-ten numerals, numeral names, and expanded form. S3 - compare two multi-digit numbers based on meanings of the digits in each place, using <, =, and > symbols. S4 - use place-value understanding to round multi-digit whole numbers to any place.


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U1 – U2 Q1 K1 – K2



Transfer Task(s)

Generalize place value understanding for multi-digit whole numbers

S1 – S4



Investigations3 Unit 5: 1.1, 2.4, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 Unit 6: 1.4, TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5, TMM 1.6, TMM 3.1, TMM 3.2, TMM 3.3, TMM 3.4, TMM 3.5, TMM 3.6 Unit 8: TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5



http://nlvm.usu.edu


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Title of Unit Number & Operations in Base Ten1 Grade Level 4



4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. 4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. _________________

1Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Add up your impressions using Pointillism SCIENCE: Measure the difference of heights for students in the class HEALTH: Add up sit-ups SOCIAL STUDIES: Make a card for different mountains-use subtraction to compare different heights of mountains 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to use place value understanding and properties of operations to perform multi-digit arithmetic.



U1 - the standard algorithm is one way to get the answer to an addition or subtraction problem. U2 - one should use an alternate algorithm to check the answer to a problem. U3 - place value helps to understand the appropriate size of an answer.

Q1 - How are strategies useful in solving computation problems? Q2 - Why does it help to know inverse relationships?


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K1 - addition and subtraction are inverse operations. K2 - multiplication and division are inverse operations.

S1 - fluently add multi-digit whole numbers using the standard algorithm. S2 - fluently subtract multi-digit whole numbers using the standard algorithm. S3 - multiply a whole number of up to four digits by a one-digit whole number. S4 - multiply two two-digit numbers. S5 - find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. S6 - illustrate and explain calculations by using equations, rectangular arrays, and/or area models.



U1 – U3 Q1 – Q2 K1 – K2



Transfer Task(s)

Use place value understanding to perform multi-digit arithmetic Use properties of operations to perform multi-digit arithmetic

S1 – S6



Investigations3 Unit 1: 1.1, 1.4, 1.6 Unit 3: Investigation 1, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, Investigation 3 Unit 4: 1.2, 4.5, 4.6, TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5, TMM 3.1, TMM 3.2, TMM 3.3, TMM 3.4 Unit 5: 1.4, 1.5, 1.6, 2.4, 2.5, 2.6, 2.7, 3.4, 3.5, 3.6, TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5, TMM 1.6, TMM 2.5, TMM 2.6, TMM 2.7, TMM 3.4, TMM 3.5, TMM 3.6 Unit 6: TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5, TMM 1.6, TMM 3.1, TMM 3.2, TMM 3.3, TMM 3.4, TMM 3.5, TMM 3.6 Unit 7: Investigation 1, Investigation 2, Investigation 3 Unit 8: TMM 1.1, TMM 1.2, TMM 1.3, TMM 1.4, TMM 1.5

Grade 4 Mathematics Curriculum Binder Suggested Activities Suggested Resources

Illuminations lessons http://illuminations.nctm.org http://nlvm.usu.edu


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Title of Unit Number & Operations – Fractions1 Grade Level 4 Curriculum Area Mathematics Time Frame 8-12 days


4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Create a fraction puzzle using different artwork SOCIAL STUDIES: Design an opinion poll and record results as fractions SCIENCE: Measure several plants and express their heights in fractions MUSIC: Make a spinner with 2, 4, 6, 8, 10, 12, 14, and 16 to give you a numerator, or number of notes. Toss a coin to give you the denominator, or type of note HEALTH: Use fractions to create portions of healthy snacks 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to extend understanding of fraction equivalence and ordering.



U1 - equivalent fractions represent the same amount of a whole. U2 - fraction comparisons are only valid when they refer to the same whole. U3 - in order to find the fraction equivalent to one half, the numerator must be the denominator divided by 2; or the denominator must be 2 times the numerator.

Q1 - Why does one need to use fractions? Q2 - Why does one need to find equivalent fractions?


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K1 - the same number must multiply the numerator and denominator in order for fractions to be equivalent. K2 - 1/2 can be used as a benchmark to compare fractions. K3 - “<” means less than; “>” means greater than; and “=” means equal to.

S1 - identify equivalent fractions. S2 - generate equivalent fractions. S3 - explain fractions that are equivalent through visual models. S4 - compare two fractions using a benchmark fraction. S5 - compare two fractions using common numerators or denominators.



U1 – U3 Q1 – Q2 K1 – K3



Transfer Task(s)

Extend understanding of fraction equivalence Extend understanding of ordering fractions

S1 – S5



Investigations3 Unit 6: 1.1, 1.2, 1.3, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.8


Suggested Activities Suggested Resources



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Title of Unit Number & Operations – Fractions1 Grade Level 4



4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify

decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, 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.B.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?

1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books such as Sir Cumference and The First Round Table and model a round table by using fractions and decimals ART: Using a hundredths grid, challenge a partner to figure out how much of each color is used to make a picture SCIENCE: Write a fraction label for your plant, then fertilize it. Express the amounts of each main ingredient in fraction and decimal form HEALTH: Make your own healthy store circular, where the prices are all in fractions 21st Century Interdisciplinary Themes:


Transfer Students will be able to independently use their learning to build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.


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U1 - a fraction (with a numerator greater than 1) is made up of unit fractions, e.g. 3/7 = 1/7 + 1/7 + 1/7. U2 - addition and subtraction of fractions is joining and separating parts referring to the same whole. U3 - a fraction a/b is a multiple of 1/b. U4 - a multiple of a/b is a multiple of 1/b.

Q1 - How operations are allowed with fractions? Q2 - When would one need to add, subtract, multiply, or divide a fraction?



K1 - fractions must have common denominators in order to be added or subtracted. K2 - when adding or subtracting fractions with like denominators, one must add or subtract the numerators and keep the denominator the same. K3 - mixed numbers are multiples of fractions.

S1 - decompose a fraction into the sum of fractions in more than one way. S2 - justify decompositions. S3 - add mixed numbers with like denominators. S4 - subtract mixed numbers with like denominators. S5 - solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators. S6 - multiply a fraction by a whole number. S7 - solve word problems involving multiplication of a fraction by a whole number.



U1 – U4 Q1 – Q2 K1 – K3



Transfer Task(s)

Build fractions from unit fractions by applying previous understandings of operations on whole numbers

Build fractions from unit fractions by extending previous understandings of operations on whole numbers

S1 – S7


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Learning Plan (Stage 3)

Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals.

Required Activities Required Resources


Investigations3 Unit 6: 1.1, 1.2, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4 Grade 4

Mathematics Curriculum Binder

Suggested Activities Suggested Resources



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Title of Unit Number & Operations – Fractions1 Grade Level 4 Curriculum Area Mathematics Time Frame 8-11 days

Desired Results (Stage 1) Established Goals/Standards

4.NF.C.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 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 4.NF.C.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.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. _________________

1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 2 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.

Primary Interdisciplinary Connections LAL: Connect math and literacy through reading books ART: Make a picture on the back of a hundreds grid, take away some, and see if your partner can guess how much is missing HEALTH: See how fast you can jump 10 jumping jacks SCIENCE: A bird that weighs 0.43 kg will eat up to 0.09 kg of food per day. Who is going to reach a kg of food first? MUSIC: Make concert tickets out of index cards. Estimate to see how low you can get your total price to be for your group SOCIAL STUDIES: Use decimal form to write different stamp amounts on stickers-incorporate weight into different prices21st Century Interdisciplinary Themes:


Transfer Students will be able to independently use their learning to understand decimal notation for fractions, and compare decimal fractions.

Meaning Understandings Students will understand that…

Essential Questions Students will keep considering…

U1 - decimals and fractions are related. U2 - fractions with a denominator of 10 or 100 can be written in decimal form. U3 - comparisons of decimals are valid only when the two decimals refer to the same whole.

Q1 - Why does one need to change a fraction to a decimal? Q2 - When is it easier to use the decimal form of a fraction? Q3 - Why would decimal forms of a fraction need to be compared?


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Skills Students will be able to…

K1 - the decimal point location is related to the size of the denominator when the denominator is a multiple of 10. K2 - decimal forms of numbers are easiest to find when the denominator is a multiple of 10.

S1 - find a fraction with a denominator of 100 for a fraction with a denominator of 10. S2 - add two fractions with respective denominators 10 and 100. S3 - write fractions with denominators 10 or 100 in decimal form. S4 - compare two decimals to hundredths by reasoning about their size. S5 - compare two decimals using the symbols >, =, or <, and justify the conclusions.



U1 – U3 Q1 – Q3 K1 – K2



Transfer Task(s)

Understand decimal notation for fractions Compare decimal fractions

S1 – S5

Learning Plan (Stage 3) Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals. Required Activities Required Resources Ten-Minute Math (TMM)





http://nlvm.usu.edu


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Title of Unit Measurement and Data Grade Level 4



4.MD.A.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ... 4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Create a picture made entirely of centimeters SOCIAL STUDIES: Discuss different measurements, such as perimeter, using the U.S. Department of Defense, The Pentagon SCIENCE: Draw a garden plan, exploring different arrangements for 24 marigolds to be planted HEALTH: Have an Area Relay MUSIC: Use CDs to measure the length and width of the classroom 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.



U1 - the size of the unit used to measure has an effect on the number of units in the answer. U2 - area and perimeter measure different things therefore the types of label on the answers are different. U3 - the region covered by square units in an array is the same as the area of the rectangle.

Q1 - What can be measured? Q2 - Why does one need to measure things?


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K1 - relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. K2 - the larger the unit used to measure, the smaller the number of units in the answer and vice versa. K3 - area of a rectangle is equal to the length x the width (A = l x w).

S1 - express measurements in a larger unit in terms of a smaller unit. S2 - record measurement equivalents in a two-column table. S3 - find the area of a rectangle using the formula. S4 - find the perimeter of a rectangle using the formula.



U1 – U3 Q1 – Q2 K1 – K3



Transfer Task(s)

Solve problems involving measurement Solve problems involving conversion of measurements from a larger unit

to a smaller unitS1 – S4

Learning Plan (Stage 3)Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals. Required Activities Required Resources Ten-Minute Math (TMM)


Investigations3 Unit 2: 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 Unit 4: Investigation 1, 4.5. 4.6 Unit 5: 1.1, 1.2, 1.3, 2.1, 2.6, 2.7, 3.4, 3.5, 3.6 Unit 6: 3.5, 3.6, 4.2. 4.3, 4.4 Unit 7: 1.1, 1.2, 3.6 Unit 8: TMM 1.6, 1.7, TMM 1.7, 1.8, TMM 1.8, TMM 1.9, TMM 1.10

Grade 4 Mathematics Curriculum Binder Suggested Activities Suggested Resources Illuminations lessons http://illuminations.nctm.org

http://nlvm.usu.edu


21




4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books SOCIAL STUDIES: Take a look at your play money and figure out how much of each type of coin or bill you have. Record results in a bar graph and compare bar graphs with other groups in the class SCIENCE: Write down what the weather was like every day for the past week and graph it MUSIC: Take a poll to see how many CDs each student owns in the class. Make a poster showing your group’s musical data. Find the landmarks for your data HEALTH: Take a poll to see how many servings of fruit and vegetables your groups eats in a day. Create a tally chart using pictures to record your results21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to represent and interpret data.



U1 - a line plot is a visual display of data used to help see trends in the data. Q1 - When would a line plot be used? Q2 - Why does one need to display data graphically?



K1 - the scale of a line plot must be equally spaced as in a number line. K2 - the scale of a line plot can contain fractions.

S1 - Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). S2 - Solve problems involving addition and subtraction of fractions by using information presented in line plots.


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U1 Q1 – Q2 K1 – K2



Transfer Task(s)

Represent and interpret dataS1 – S2

Learning Plan (Stage 3)Checks for alignment Summary of Key Learning Events and Instruction and best practice The teaching and learning needed to achieve the unit goals. Required Activities Required Resources


Investigations3 Unit 2: 1.1, 2.3, 2.5, 2.6 Unit 6: 3.3



http://nlvm.usu.edu


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4.MD.C.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books HEALTH: Angle Relays-record the time it takes for your group to complete the relay. Using the clock for the finish time, determine what type of angle is on the clock 21st Century Interdisciplinary Themes:


Transfer Students will be able to independently use their learning to geometric measurement: understand concepts of angle and measure angles.



U1 - the measure of an angle is the measure of the turn. Q1 - Why would one need to measure an angle?


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K1 - that an angle is formed wherever two rays share a common endpoint. K2 - angle measure is additive. K3 - an angle decomposed into non-overlapping parts is the sum of the measure of each parts. K4 - an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. K5 - an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. K6 - an angle that turns through n one-degree angles is said to have an angle measure of n degrees.

S1 - measure angles in whole-number degrees using a protractor. S2 - sketch angles of specified measure. S3 - solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.



U1 Q1 K1 – K6



Transfer Task(s)

Understand concepts of angle Measure angles

S1 – S3



Investigations3 Unit 4: 3.1, 3.2, 3.3, 3.4, 4.6



http://nlvm.usu.edu


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Title of Unit Geometry Grade Level 4



4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Primary Interdisciplinary ConnectionsLAL: Connect math and literacy through reading books ART: Design your ideal school building using two-dimensional drawings and polygons SCIENCE: Observe different crystals from iodized salt, kosher salt, and sugar-discuss different shapes seen and compare MUSIC: Musical instruments are all made using different two- and three-dimensional figures. Can you recognize them all? HEALTH: Make your own customized Food Pyramid. Divide your pyramid into levels and for each level, write the kinds of foods you like that fall into each category 21st Century Interdisciplinary Themes:


TransferStudents will be able to independently use their learning to draw and identify lines and angles, and classify shapes by properties of their lines and angles.



U1 - characteristics of a figure enables one to identify it by a name. Q1 - Why does one need to classify shapes? Q2 - Why does one need to identify lines of symmetry?


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K1 - a right triangle is a category of triangles. K2 - a line of symmetry is such that the figure can be folded along the line into matching parts.

S1 - draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. S2 - identify these in two-dimensional figures. S3 - classify two-dimensional figures based on properties of parallel and perpendicular lines and sizes of angles. S4 - identify right triangles. S5 - identify line-symmetric figures. S6 - draw lines of symmetry.



U1 Q1 – Q2 K1 – K2



Transfer Task(s):

Draw lines and angles Identify lines and angles Classify shapes by properties of their lines Classify shapes by properties of their angles

S1 – S6






http://nlvm.usu.edu

bloomfield public schools · bloomfield grade 4 (2016-2017) 4 title of unit operations &...

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