Fifth Grade Math Curriculum Map Quarter 1 · Fifth Grade Math Curriculum Map . Quarter 1 . ... MAFS.5.NBT.1.2 Explain patterns in the number of ... • Students may not distribute

Fifth Grade Math Curriculum Map Quarter 1

Table of Contents Quarter 1 ................................................................................................................................................................................................................................................. 1

MAFS 5. NBT.1.1 ................................................................................................................................................................................................................................ 2

MAFS.5.NBT.1.2 ................................................................................................................................................................................................................................. 4

MAFS.5.NBT.2.5 ................................................................................................................................................................................................................................. 6

MAFS.5.NBT.2.6 ................................................................................................................................................................................................................................. 8

MASF.5.OA.1.1 ................................................................................................................................................................................................................................. 10

MASF.5.OA.1.2 ................................................................................................................................................................................................................................. 12

MAFS.5.NF.2.3……………………………………………………………………………………………………………………………………………………...14

MASF.5.NBT.1.3 ............................................................................................................................................................................................................................... 16

MASF.5.NBT.1.4 ............................................................................................................................................................................................................................... 18

MAFS.5.NBT.2.7……………………………………………………………………………………………………………………………………………………20

Fifth Grade Math Curriculum Map Quarter: 1 Cognitive Complexity: DOK Level 1

Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Understand the place value system.

Standard

MAFS.5.NBT.1.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. MP1: Make sense of problems and persevere in solving them. MP8: Look for and express regularity on repeated reasoning.

Learning Goal

• Recognize that a digit in one place represents 10 times as much as the place to its right. • Recognize that a digit in one place represents 1/10 as much as the place to its left.

Misconceptions

Students may confuse directions for finding place values. For example, to fins a number that is ten times as much as 20, a student may divide by ten instead of multiply by ten. Go Math A misconception directly related to comparing whole numbers is the idea that the longer the number the greater the number. With whole numbers, a 5-digit number is always greater that a 1-, 2-, 3-, or 4-digit number. However, with decimals a number with one decimal place may be greater than a number with two or three decimal places. For example, 0.5 is greater than 0.12, 0.009 or 0.499. One method for comparing decimals it to make all numbers have the same number of digits to the right of the decimal point by adding zeroes to the number, such as 0.500, 0.120, 0.009 and 0.499. A second method is to use a place-value chart to place the numerals for comparison. Kansas Flipbook

Vocabulary

Content Vocabulary Vocabulary Resources Multiply Place Value Period

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Assessments

Formative Assessments

Other Assessment Options

Resources

Math Talk Questions Math Literature Spiraling Resources to Support Differentiation and Stations

Reflection/ Notes

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Fifth Grade Math Curriculum Map

Quarter: 1 Cognitive Complexity: DOK Level 2 Basic Application of Skills and Concepts

Critical Area


Standard

MAFS.5.NBT.1.2 Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. MP 1: Make sense of problems and persevere in solving them. MP 4: Model with mathematics. MP 7: Look for and make sense of structure. MP 8: Look for and express regularity on repeated reasoning.

Learning Goal • Explain patterns in the number of zeroes in a product when multiplying a number by a power of ten. • Explain patterns in the placement of the decimal point when a decimal is multiplied by a power of ten. • Explain patterns in the placement of the decimal point when a decimal is divided by a power of ten. • Use exponents to show powers of ten.

Misconceptions

• Students may misinterpret bases and exponents. • Students may not include the correct number of zeroes in a product because the basic fact has a zero in its

product. • Students may forget to include the decimal point when multiplying by decimal numbers.

Vocabulary

Content Vocabulary Vocabulary Resources Base Decimal Tenths Expanded Form Exponent Thousandths Hundredths Multiplication Ones Pattern Place Value Product

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Resources


Reflection/ Notes

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Quarter: 1 Cognitive Complexity: DOK Level 1 Recall

Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Perform operations with multi-digit whole numbers and with decimals to hundredths.

Standard

MAFS.5.NBT.2.5 Fluently multiply multi-digit whole numbers using the standard algorithm 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. MP 1: Make sense of problems and persevere in solving them. MP 8: Look for and express regularity on repeated reasoning.

Learning Goal

• Fluently multiply multi-digit whole numbers • Multiply multi-digit whole numbers using the standard algorithm

Misconceptions

Students may overlook the place value of digits, or forget to use zeroes as place holders, resulting in an incorrect partial product and ultimately the wrong answer. Georgia Standards

Vocabulary

Content Vocabulary Vocabulary Resources Estimate

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Assessments



Resources


Reflection/ Notes

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Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Perform operations with multi-digit whole numbers and with decimals to hundredths.

Standard

MAFS.5.NBT.2.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-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. MP 1: Make sense of problems and persevere in solving them. MP 8: Look for and express regularity on repeated reasoning.

Learning Goal

• Use strategies to divide whole numbers. • Show and explain the relationship between multiplication and division. • Show and explain division using place value. • Solve a division problem using an equation. • Show and explain division using a rectangular array. • Show and explain division using an area model.

Misconceptions • Students may not distribute the first factor to each addend when applying the Distributive Property. • When the Distributive Property is used to divide, the sum of the products may not equal the dividend. • Students may not understand how to break apart a dividend.

Vocabulary

Content Vocabulary Vocabulary Resources Area Model Place Value Distributive Property Product Dividend Quotient Divisor Rectangular Arrays Factor Inverse Operations

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Assessments



Resources


Reflection/ Notes

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Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Write and interpret numerical expressions.

Standard

MAFS.5.OA.1.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. MP: 1 Make sense of problems and persevere in solving them. MP: 8 Look for and express regularity in repeated reasoning.

Learning Goal

• Use parentheses in numerical expressions. • Use brackets in numerical expressions. • Use braces in numerical expressions. • Evaluate expressions with parentheses. • Evaluate expressions with brackets. • Evaluate expressions with braces.

Misconceptions

Students may believe the order in which a problem with mixed operations is written is the order to solve the problem. Allow students to use calculators to determine the value of the expression, and then discuss the order the calculator used to evaluate the expression. Do this with four-function and scientific calculators. Kansas Flipbook Students may evaluate expressions from left to right without consideration of the type of operation. GO Math! Students do not find the values of the expressions using the correct order of operations. GO Math!

Vocabulary

Content Vocabulary Vocabulary Resources Evaluate Order of Operations

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Assessments



Resources


Reflection/ Notes

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Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Write and interpret numerical expressions.

Standard

MAFS.5.OA.1.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. MP: 1 Make sense of problems and persevere in solving them. MP: 8 Look for and express regularity in repeated reasoning.

Learning Goal • Write simple expressions that record calculations with numbers. • Interpret the meaning of numerical expressions.

Misconceptions

Students may believe the order in which a problem with mixed operations is written is the order to solve the problem. Allow students to use calculators to determine the value of the expression, and then discuss the order the calculator used to evaluate the expression. Do this with four-function and scientific calculators. Kansas flipbook Students do not place parentheses correctly. GO Math!

Vocabulary

Content Vocabulary Vocabulary Resources Calculations Evaluating Numerical Expression

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Assessments



Resources


Reflection/ Notes

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Quarter: 1 Cognitive Complexity: DOK Level 2 Basic Application and Skill Concepts

Critical Area

Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions). Apply and extend previous understanding of multiplication and division to multiply and divide fractions.

Standard

MAFS.5.NF.2.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. MP 1: Make sense of problems and persevere in solving them MP 4: Model with mathematics MP 7: Look for and make use of structure

Learning Goal

• Understand that a fraction bar can mean to divide. • Find an equivalent whole number, mixed number, or decimal for a fraction by dividing the numerator by the

denominator. • Solve division word problems where the quotient is a fraction or a mixed number.

Misconceptions Students may reverse the divisor and dividend when doing a division problem.

Vocabulary

Content Vocabulary Vocabulary Resources Interpret Mixed numbers

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Assessments



Resources


Reflection/ Notes

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Quarter: 1 Cognitive Complexity: DOK Level 2 Basic Application and Skill Concepts

Critical Area


Standard

MAFS.5.NBT.1.3 Read, write, and compare decimals to thousandths. MACC.5.NBT.1.3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). MP 1: Make sense of problems and persevere in solving them. MP 3: Construct viable arguments and critique the reasoning of others. MP 8: Look for and express regularity on repeated reasoning.

Learning Goal • Read and write decimals to thousandths using base-ten numerals. • Read and write decimals to thousandths using number names. • Read and write decimals to thousandths using expanded form.

Misconceptions Students may think that the value of a decimal increases by adding a zero to the end of it.

Vocabulary

Content Vocabulary Vocabulary Resources Compare Decimals Place Value Number Names Expanded Form Thousandths

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Assessments



Resources


Reflection/ Notes

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Critical Area


Standard

MAFS.5.NBT.1.4 Use place value understanding to round decimals to any place. MP 1: Make sense of problems and persevere in solving them. MP 8: Look for and express regularity on repeated reasoning.

Learning Goal

• Round decimals to any place.

Misconceptions Students may not attend to precision of place value when rounding decimals.

Vocabulary

Content Vocabulary Vocabulary Resources Estimate Place Value Round

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Assessments



Resources


Reflection/ Notes

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Quarter: 1 Cognitive Complexity: DOK 2 Basic Application of Skills and Concepts

Critical Area

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Perform operations with multi-digit whole numbers and with decimals to hundredths

Standard

MAFS.5.NBT.2.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. MP: 3 Construct viable arguments and critique the reasoning of others. MP: 7 Look for and make use of structure. MP: 8 Look for and express regularity in repeated reasoning.

Learning Goal • Add decimals to hundredths and write an explanation of the reasoning used. • Subtract decimals to hundredths and write an explanation of the reasoning used. • Multiply decimals to hundredths and write an explanation of the reasoning used.

Misconceptions

Students may compute the sum or difference of decimals by lining up the right-hand digits as they would whole number. Kansas flipbook Students may place the decimal point in a sum or difference incorrectly. GO Math! Students may not align place values correctly. GO Math! Students may forget to place the decimal point after multiplying as with whole numbers. GO Math!

Vocabulary

Content Vocabulary Vocabulary Resources Benchmark Sequence Term

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Assessments



Resources


Reflection/ Notes

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Documents

Fifth Grade Math Curriculum Map Quarter 1 · Fifth Grade Math Curriculum Map . Quarter 1 . ... MAFS.5.NBT.1.2 Explain patterns in the number of ... • Students may not distribute