images.pcmac.orgimages.pcmac.org/sisfiles/schools/nv/whitepine/normanelem... · web viewconvert...

5th Grade – Math – Singapore Ch 1 – 1 day. Ch 2 – 3 days

Learner Goals: Singapore Page CitationsRead, write in words, standard, and expanded notation, and identify place values of digits and round numbers in the billions.

TB-A: Unit 1, Ch 1, 9-10WB-A: 5-6

EP: 13-16

Round large numbers to the nearest 10, 100, 1000, 10,000, or 100,000. TB-A: Unit 1, Ch 2, 11-14WB-A:

Use estimation to verify the reasonableness of calculated results in addition and subtraction, check subtraction problems using addition.

TB-A: Unit 1, Ch 2, 11-16WB-A: 7-8

EP: 17-20

Add/subtract numbers in the billions.

5th Grade Math – Singapore Ch 3 – 1 day. Ch 4 – 2 days

Learner Goals: Singapore Page Citations

Number and Operations in Base Ten 5.NBTUnderstand the place value system. 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.

Vocabularybillion period estimate estimationapproximation expanded form

Grade 6 Learner Goals:

Teacher Notes

WHOLE NUMBERSCh 1 and Ch 2

Suggested LiteratureMath Curse by jon ScieszkaThe King’s Chessboard by David BirchOne Grain of Rice: A mathematical Folktale by Demi

Grade 4 Learner Goals: Use place-value models to represent numbers to 100,000. Read, write in words, standard, and expanded notation, identify place

values of digits, and compare and order numbers within 100,000. Complete or extend regular number patterns for numbers within 100,000. Use place-value models to represent numbers to 1,000,000. Use place-value models to represent numbers to 1,000,000,000. Read, write in words, standard, and expanded notation, identify place

values of digits, and compare and order numbers within 1,000,000,000. Complete or extend regular number patterns for numbers within

1,000,000,000. Round numbers within 1,000,000,000 to the nearest 10, 100 or 1000.

Materials


Find the factors and common factors of whole numbers within 100. TB-A: Unit 1, Ch 3, 17-18WB-A: 12-13

EP: 21-22Find multiples and common multiples of whole numbers within 100.Find the lowest common multiple of up to 3 numbers within 100.Find the greatest common factor of up to 3 numbers within 100.Identify prime numbers. TB-A: Unit 1, Ch 4, 19-22

WB-A: 14-17EP: 25-26

Determine the prime factors of numbers within 100 and write the numbers as products of prime numbers, using exponents.

5th Grade – Math – Singapore Ch 5 – 1 day. Ch 6 – 2 days, R – 1 day

Learner Goals: Singapore Page CitationsMultiply/divide numbers within 1,000,000 by tens, hundreds, or thousands. TB-A: Unit 1, Ch 5-6, 23-27

WB-A: 16-19EP: 25-26EP: 27-28Use estimation to verify the reasonableness of calculated results in

multiplication and division problems.

Operations and Algebraic Thinking 5.OAGenerate and analyze patterns.

none

Vocabularygreatest common factor lowest common multipleprime factors prime factorization factor treecontinuous division exponent base power


Teacher Notes

Suggested Literature

Grade 4 Learner Goals: Find the factors and common factors of whole numbers within 100. Identify prime numbers. Find multiples and common multiples of whole numbers within 100.

Materials Appendix 1.4a


Check division problems using multiplication.

5th Grade – Math – Singapore Ch 1 – 3 days. Ch 2 – 3 days

Learner Goals: Singapore Page CitationsUse order of operations to solve mathematical expressions with or without parentheses.

TB-A: Unit 2, Ch 1, 29-31WB-A: 22-23

Understand the distributive property. TB-A: Unit 2, Ch 1, 31-32WB-A: 24

EP: 35-36

Use the commutative and associative properties to perform mental calculations and check results.

TB-A: Unit 2, Ch 2, 34-37WB-A: 25-28

EP: 37-38

Use the distributive property to perform mental calculations and check

Number and Operations in Base Ten 5.NBTUnderstand the place value system. 2. Explain patterns in the number of zeros 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. Perform operations with multi-digit whole numbers and with decimals to hundredths.5. Fluently multiply multi-digit whole numbers using the standard algorithm.

Vocabularyalgorithm area model array dividenddivision product divisor multiplicationquaotient factor


Teacher Notes

Suggested LiteratureMath Curse by Jon Scieszka

Grade 4 Learner Goals: Use estimation to verify the reasonableness of calculated results in

multiplication and division problems. Check division problems using multiplication.

Materials Appendix 1.5a

MORE CALCULATIONS WITH WHOLE NUMBERS Ch 1-2

results.Add/subtract a number close to a multiple of 100 (e.g. 498).Multiply by 99 or by 25.Multiply by a number one less than a multiple of 10 or 100 (e.g. 49, 499).

Operations and Algebraic Thinking 5.OAWrite and interpret numerical expressions.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.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. Number and Operations in Base Ten 5.NBTPerform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm.

Vocabularyvalues order of operations operation signsparentheses distributive porperty bracesbrackets expression


Teacher Notes

Suggested LiteratureThe Fly on the Ceiling by Dr. Julie Glass

Grade 4 Learner Goals: Use order of operations to solve mathematical expressions with or without

parentheses. Use the commutative and associative properties to perform mental

calculations and check results. Use the distributive property to perform mental calculations and check

results. Multiply by 99 or by 25.

Materials Counters

5th Grade Math – Singapore Ch 3 – 3 days

Learner Goals: Singapore Page CitationsSolve multi-step word problems involving all four operations on whole numbers, fractions, decimals, percentage, and ratios.

TB-A: Unit 2, Ch 3, 38-41WB-A: 29-34

EP: 39-44

Represent unknown quantities with bar diagrams and solve word problems involving whole numbers using bar diagrams.

Teacher Notes

Operations and Algebraic Thinking 5.OAGenerate and analyze patterns. none

Vocabularymodel comparison part/whole

MORE CALCULATIONS WITH WHOLE NUMBERS Ch 3

Suggested LiteratureMaterials

5th Grade Math – Singapore Ch 4 – 3 days, Ch 5 – 5 days, R – 1-2 days

Learner Goals: Singapore Page CitationsMultiply numbers within 10,000 by a 2-digit number. TB-A: Unit 2, Ch 4, 42-43

WB-A: 35-36EP: 45-46

Divide numbers within 10,000 by a 2-digit number. TB-A: Unit 2, Ch 5, 44-48WB-A: 37-40

EP: 47-50

Operations and Algebraic Thinking 5.OAGenerate and analyze patterns. none

Vocabularymodel comparison part/whole

Grade 6 Learner Goals: Solve multi-step word problems involving all four operations on

whole numbers, fractions, decimals, percentage, and ratios. Represent unknown quantities with bar diagrams and solve

word problems involving whole numbers using bar diagrams.

Teacher Notes

Grade 4 Learner Goals: Solve 2-step word problems which involve the four operations

on whole numbers. Represent unknown quantities with bar diagrams and solve

word problems involving whole numbers using bar diagrams.

Number and Operations in Base Ten 5.NBTPerform operations with multi-digit whole numbers and with decimals to hundredths. 5. Fluently multiply multi-digit whole numbers using the standard algorithm. 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.

Vocabularyremainder estimate quotient estimated quotientdividend divisor factor productdivision multiplication

MORE CALCULATIONS WITH WHOLE NUMBERS Ch 4 - 5


Materials

5th Grade Math – Singapore Ch 1 – 2-3 days, Ch 2 – 1-2 days

Learner Goals: Singapore Page CitationsCompare and order fractions with different denominators. TB-A: Unit 3, Ch 1, 51-53

WB-A: 46-49EP: 57-58

Relate division to fractions. TB-A: Unit 3, Ch 2, 54-57WB-A: 50-51

EP: 59-62


Teacher NotesGrade 4 Learner Goals:

Multiply numbers within 10,000 by a 2-digit number.

Number and Operations—Fractions 5.NF Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 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. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Vocabularyfraction numerator denominatorequivalent fraction simplest form like fractionsmixed number proper fraction improper fractiondivision

FRACTIONSCh 1 - 2


Grade 4 Learner Goals: Understand mixed numbers and improper fractions, convert

between them, locate them on a number line. Find equivalent fractions and simplest form of a fraction. Compare and order fractions with different denominators.

Materials

5th Grade – Math – Singapore Ch 3 – 3 days, Ch 4 – 2-3 days, Ch 5 – 1-2 days

Learner Goals: Singapore Page CitationsAdd/Subtract unlike fractions. TB–A: Unit 3, Ch 3, 58-60

WB–A: 52-55EP: 63-64

Add/subtract mixed numbers. TB–A: Unit 3, Ch 4, 61-63WB–A: 56-59

EP: 65-68

Multiply a fraction by a whole number. TB–A: Unit 3, Ch 5, 64-66WB–A: 60-63

EP: 69-70

Use bar diagrams to solve word problems involving fractions. TB–A: Unit 3, Ch 3, 60, Ch 4, 63WB–A:Solve multi-step word problems involving all four operations on whole

numbers, fractions, decimals, percentage, and ratios.

Grade 6 Learner Goals: Compare and order fractions with different denominators.

Teacher Notes

Grade 4 Learner Goals: Understand mixed numbers and improper fractions, convert

between them, locate them on a number line. Find equivalent fractions and simplest form of a fraction. Compare and order fractions with different denominators.

Number and Operations—Fractions 5.NF Use equivalent fractions as a strategy to add and subtract fractions. 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Measurement and Data 5.MD Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit

Vocabularylike fractions unlike fractions sumdifference multiply number linesmixed numbers improper fraction

FRACTIONSCh 3-5


Materials Fraction circles

Number and Operations—Fractions 5.NF Use equivalent fractions as a strategy to add and subtract fractions. 1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Measurement and Data 5.MD Represent and interpret data. 2. Make a line plot to display a data set of measurements in fractions of a unit

Grade 6 Learner Goals: Compare and order fractions with different denominators. Add/Subtract unlike fractions. Add/subtract mixed numbers. Multiply a fraction by a whole number. Solve multi-step word problems involving all four operations on

whole numbers, fractions, decimals, percentage, and ratios. Use bar diagrams to solve word problems involving fractions.

Teacher Notes

Grade 4 Learner Goals: Add/Subtract related fractions. Multiply a fraction by a whole number. Solve 2-step word problems which involve decimals and

fractions. Use bar diagrams to solve word problems involving fractions.

5th Grade – Math – Singapore Ch 6 – 6 days, Ch 7 – 2 days, R – 1-2 days

Learner Goals: Singapore Page CitationsMultiply a fraction by a whole number. TB–A: Unit 3, Ch 6, 67-70

WB–A: 64-65Find fraction of a set for measurements (e.g. 10 minutes as a fraction of one hour).

TB–A: Unit 3, Ch 6, 70-73WB–A: 66-71

EP: 71-74

Find the fraction of a set where the answer is a whole number or a mixed number.Use bar diagrams to solve word problems involving fractions. TB–A: Unit 3, Ch 6, 73, Ch 7, 74-76

WB–A: 72-75EP: 75-78

Solve multi-step word problems involving all four operations on whole numbers, fractions, decimals, percentage, and ratios.

Teacher Notes

Number and Operations—Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Measurement and Data 5.MDConvert like measurement units within a given measurement system. 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Vocabularycommon factor cancellation conversion factormixed number improper fraction

Grade 6 Learner Goals: Find the fraction of a set where the answer is a whole number or a

mixed number. Multiply a fraction by a whole number.

FRACTIONSCh 6-7


Grade 4 Learner Goals: Multiply a fraction by a whole number. Find fraction of a set for measurements (e.g. 10 minutes as a fraction

of one hour).

Materials Fraction circles Various measuring devices

5th Grade – Math - Singapore Ch 1 – 3 days, Ch 2 – 2 days, Ch 3 – 2 days, Ch 4 – 5 days, Ch 5 – 2 days, R – 1-2 days

Learner Goals: Singapore Page Citations

Grade 6 Learner Goals: Find the fraction of a set where the answer is a whole number or a

mixed number. Multiply a fraction by a whole number.

Teacher Notes

Grade 4 Learner Goals: Multiply a fraction by a whole number. Find fraction of a set for measurements (e.g. 10 minutes as a fraction

of one hour).

MULTIPLY AND DIVIDE FRACTIONS

Multiply a fraction by a fraction. TB–A: Unit 4, Ch 1, 80-83WB–A: 79-82

EP: 85-86

Divide a fraction by a whole number. TB–A: Unit 4, Ch 3, 88-90WB–A: 87-90

EP: 89-90

Divide a whole number or a fraction by a fraction. TB–A: Unit 4, Ch 4, 91-98WB–A: 91-95

EP: 91-92

Use bar diagrams to solve word problems involving fractions. TB–A: Unit 4, Ch 1, 83, Ch 2, 84-87Ch 3, 90, Ch 4, 98, Ch 5, 99-103WB–A: 83-86, 96-101

EP: 87-88EP: 93-96Solve multi-step word problems involving all four operations on whole

numbers, fractions, decimals, percentage, and ratios.

Number and Operations—Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5. Interpret multiplication as scaling (resizing), by:

Vocabularyreciprocal denominator numeratordivision multiplication mixed numberimproper fraction area quotientproduct

Grade 6 Learner Goals: Multiply a fraction by a fraction. Multiply a fraction by a whole number. Divide a fraction by a whole number. Divide a whole number or a fraction by a fraction. Solve multi-step word problems involving all four operations on

whole numbers, fractions, decimals, percentage, and ratios. Use bar diagrams to solve word problems involving fractions.


Grade 4 Learner Goals: Multiply a fraction by a whole number. Solve 2-step word problems which involve decimals and

fractions. Use bar diagrams to solve word problems involving fractions.

Grade 4 Learner Goals: Index cards Fraction squares Sheets of paper Appendix 4.r

5th Grade – Math – Singapore Ch 1 – 1 day, Ch 2 – 2 days, Ch 3 – 4 days, Ch 4 – 1 day, Ch 5 – 1 day, R – 2 daysLearner Goals: Singapore Page CitationsFind the area of shapes by covering them with unit squares or by counting squares.

TB-A: Unit 5, Ch 1, 108-110WB-A: 106-107

EP: 105-106

Understand and use units of area, such as square centimeter and square inch.Find the area, perimeter, and unknown sides of rectangles. TB-A: Unit 5, Ch 2, 111-114 EP: 107-108

Number and Operations—Fractions 5.NFApply and extend previous understandings of multiplication and division to multiply and divide fractions. 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. 5. Interpret multiplication as scaling (resizing), by:

Teacher Notes

PERIMETER, AREA, & SURFACE AREA

WB-A: 108Find the area and perimeter of composite figures made from squares and rectangles.Derive the formula for area of a triangle and find the area of triangles. TB-A: Unit 5, Ch 3, 115-122

WB-A: 109-118EP: 109-112

Derive the formula for area of a parallelogram and find the area of parallelograms.

TB-A: Unit 5, Ch 4, 123-126WB-A: 119-120

EP: 113-114

Find the surface area of cubes and rectangular prisms. TB-A: Unit 5, Ch 5, 127-130WB-A: 121-122

EP: 115-116

Use and interpret formulas to answer questions about quantities and their relationships.

throughout

Measurement and Data 5.MD none

Vocabularyarea perimeter square unit complete squaresheight base share square unitrelated rectangle perpendicular distance vertexparallelogram congruent triangles composite figuresfaces prisms pyramids net total areasurface area sum cubes cuboids


Teacher Notes


Grade 4 Learner Goals: Find the area of shapes by covering them with unit squares or

by counting squares. Understand and use units of area, such as square centimeter

and square inch. Find the area, perimeter, and unknown sides of rectangles. Find the area and perimeter of composite figures made from

squares and rectangles. Use and interpret formulas to answer questions about quantities

and their relationships.

Materials Square grids

5th Grade – Math – Singapore Ch 1 – 1 day, Ch 2 – 3 days, Ch 3 – 2 days, R – 1-2 days

Learner Goals: Singapore Page CitationsUse ratios to compare two quantities. TB-A: Unit 6, Ch 1, 135-138

WB-A: 129-130EP: 119-120

Find equivalent ratios and simplify ratios. TB-A: Unit 6, Ch 2, 139-143WB-A: 131-134

EP: 121-124

Use ratios to compare three quantities. TB-A: Unit 6, Ch 3, 144-146WB-A: 135-137

EP: 125-126Use ratios to solve problems.Use bar diagrams to solve word problems involving ratio.Solve multi-step word problems involving all four operations on whole numbers, fractions, decimals, percentage, and ratios.

Teacher Notes

RATIO

5th Grade Math – Singapore Ch 1 – 2 days, Ch 2 – 1 day, Ch 3 – 1 day

Learner Goals: Singapore Page CitationsUnderstand tenths, hundredths, thousandths, locate decimal numbers on a number line, compare decimal numbers.

TB-B: Unit 7, Ch 1, 8-12WB-B: 5-6

EP: 141-146

Convert a decimal to a fraction and simplify.Convert a fraction to a decimal number (denominators are a factor of 10, 100, or 1000).Compare and order decimal numbers of up to 3 decimal places and fractions.Round decimal numbers up to 3 decimal places to the nearest whole number, to 1-decimal place, or to 2-decimal places.

TB-B: Unit 7, Ch 2, 13-15WB-B: 7

EP: 147-148

Measurement and Data 5.MD

none

Vocabularyratio quantities units

Grade 6 Learner Goals: Use ratios to compare two quantities. Find equivalent ratios and simplify ratios. Use ratios to compare three quantities. Relate ratios to fraction of a quantity. Solve problems involving changing ratios. Relate ratios to proportions. Use ratios to solve problems. Use bar diagrams to solve word problems involving ratio. Solve multi-step word problems involving all four operations on

whole numbers, fractions, decimals, percentage, and ratios.

Teacher Notes



Materials Appendix 6.r

Number and Operations in Base Ten 5.NBT Vocabulary

DECIMALSCh 1-3

Add/Subtract decimal numbers of up to 3 decimal places. TB-B: Unit 7, Ch 3, 16-17WB-B: 8

EP: 149-150

Use bar diagrams to solve word problems involving decimals. throughout

Number and Operations in Base Ten 5.NBT Vocabulary

Grade 6 Learner Goals: Use bar diagrams to solve word problems involving decimals.

Teacher Notes


Grade 4 Learner Goals: Understand tenths, hundredths, thousandths, locate decimal

numbers on a number line, compare decimal numbers. Convert a decimal to a fraction and simplify. Convert a fraction to a decimal number (denominators are a factor

of 10, 100, or 1000). Compare and order decimal numbers of up to 3 decimal places and

fractions. Round decimal numbers of up to 2 decimal places to the nearest

whole number or to 1-decimal place. Add/Subtract decimal numbers of up to 2 decimal places. Use bar diagrams to solve word problems involving decimals.

Materials A square cardboard divided into 10 equal parts A square cardboard divided into 100 equal parts Fraction squares 2 fruits Digital weighing scale Tape measure (long enough to measure height Appendix pages:

o 7.3a-1o 7.3a-2

5th Grade Math – Singapore Ch 4 – 4 days, Ch 5 – 2 days, Ch 6 – 2 days, Ch 7 – 1 day, Ch 8 – 1 day

Learner Goals: Singapore Page CitationsMultiply/Divide decimal numbers of up to 2 decimal places by a whole number.

TB-B: Unit 7, Ch 4, 18-22WB-B: 9-12

EP: 151-152

Find the quotient of a division problem correct to 2-decimal places. TB-B: Unit 7, Ch 4, 19-20WB-B: 9-11

Convert fractions to decimals correct to 2-decimal places. TB-B: Unit 7, Ch 4, 20-21WB-B: 12

Multiply/Divide decimal number by tens, hundreds, or thousands. TB-B: Unit 7, Ch 5, 23-26, Ch 6, 27-30WB-B: 13-15, 16-18

EP: 153-154EP: 155-156

Use estimation to verify the reasonableness of calculated results in problems involving decimal numbers.

TB-B: Unit 7, Ch 4, 22, Ch 7 and 8WB-B:

EP: 151-152

Multiply/divide a decimal number by a 2-digit whole number. TB-B: Unit 7, Ch 7, 31-32, Ch 8, 33-34WB-B: 19-21, 22-23

EP: 157-160EP: 161-162

Use bar diagrams to solve word problems involving decimals. throughout

Teacher Notes

Number and Operations in Base Ten 5.NBTUnderstand the place value system.

Vocabularymultiply product estimate division

DECIMALS Ch 4-8

Number and Operations in Base Ten 5.NBTUnderstand the place value system.

Vocabularymultiply product estimate division


Teacher Notes


Grade 4 Learner Goals: Multiply/Divide decimal numbers of up to 2 decimal places by a

whole number. Find the quotient of a division problem correct to 1 decimal place. Use estimation to verify the reasonableness of calculated results in

problems involving decimal numbers. Use bar diagrams to solve word problems involving decimals.

Materials Appendix pages:

o 7.4a-1o 7.4b-1


Learner Goals: Singapore Page CitationsMultiply/divide a whole number or a decimal by a decimal. TB-B: Unit 7, Ch 9, 35-37, Ch 10,

38-41WB-B: 24-26, 27-29

EP: 163-164EP: 165-166Use bar diagrams to solve word problems involving decimals.

Teacher Notes

Number and Operations in Base Ten 5.NBT Perform operations with multi-digit whole numbers and with decimals to hundredths.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.

Vocabularymultiply partial product product quotientmove decimal points to the left divide divisordividendTeacher Notes

DECIMALSCh 9-10

Materials


Learner Goals: Singapore Page CitationsConvert units involving decimals within a measuring system. TB-B: Unit 8, Ch 1, 44-47

WB-B: 34-35EP: 171-172

Understand and use units of volume, such as cubic centimeter and cubic inch.Convert units within a metric system using multiplication.Convert fractional measurements to a different unit or a compound unit, within a measuring system.Convert units involving decimals within a measuring system.Find the volume of rectangular prisms. TB-B: Unit 8, Ch 2, 48-52

WB-B: 37Find the side of a rectangular prism given the volume and two sides or area of one side.

TB-B: Unit 8, Ch 2, 52-53WB-B: 38

Understand the relationship between cubic centimeters, milliliters, and liters.

TB-B: Unit 8, Ch 2, 54-55WB-B: 40

Solve problems involving the change in height of liquids and volume of liquids in rectangular tanks, including rate problems.

TB-B: Unit 8, Ch 2, 56-57WB-B: 41-42

EP: 173-182

Use and interpret formulas to answer questions about quantities and their relationships.


Teacher Notes



MEASURES AND VOLUMES

Measurement and Data 5.MD Convert like measurement units within a given measurement system.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure, which can be packed without gaps or overlaps using n unit cubes, is said to have a volume of n cubic units. 4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems. c. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole- number edge lengths in the context of solving real world and mathematical problems.

Grade 6 Learner Goals: Find the volume of rectangular prisms. Find the volume of triangular prisms and cylinders. Find the volume of composite figures involving prisms and cylinders.

Teacher Notes

Suggested LiteratureCounting on Frank by Rod ClementMillions to Measure by David M. SchwartzInchworm and a Half by Elinor J. PinczesHow Tall, How Short, How Far Away by David A. Adler

Grade 4 Learner Goals: Understand and use units of volume, such as cubic centimeter and

cubic inch. Find the volume of rectangular prisms. Understand the relationship between cubic centimeters, milliliters,

and liters. Use and interpret formulas to answer questions about quantities and

their relationships.

5th Grade Math – Singapore Ch 1 – 3 days, Ch 2 – 3 days, Ch 3 – 4 days, R – 1-2 days

Learner Goals: Singapore Page CitationsUnderstand and use percent. TB-B: Unit 9, Ch 1, 61-63

WB-B: 47-51EP: 185-190

Find decimal and fraction equivalents for percentages.Write fractions as percentages. TB-B: Unit 9, Ch 2, 64-66

WB-B: 52-55Solve multi-step word problems involving all four operations on whole numbers, fractions, decimals, percentage, and ratios.

TB-B: Unit 9, Ch 2, 67-68WB-B: 56-57

EP: 191-196

Solve multi-step word problems involving average, rate, and percentage.Solve problems involving percentage of a quantity. TB-B: Unit 9, Ch 3, 69-73

WB-B: 58-64EP: 197-200

Use bar diagrams to solve word problems involving percentage.Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, percentage increase or decrease.

Teacher Notes

Number and Operations in Base Ten 5.NBT

none

Vocabularyfraction percentage percent decimal“of” part of a whole discount interest ratesdecrease increase

PERCENTAGE

Suggested LiteratureMaterials 10 x 10 grid Displayable 10 x 0 grids Appendix pages:

o 9.3do 9.r

Vocabularyfraction percentage percent decimal“of” part of a whole discount interest ratesdecrease increase

Grade 6 Learner Goals: Solve problems involving percentage of a quantity. Solve problems involving part of a whole as a percentage. Solve problems involving one quantity as a percentage of another. Solve percentage problems using a unitary method. Solve multi-step word problems involving all four operations on

whole numbers, fractions, decimals, percentage, and ratios. Solve multi-step word problems involving average, rate, and

percentage. Use bar diagrams to solve word problems involving percentage. Calculate given percentages of quantities and solve problems

involving discounts at sales, interest earned, percentage increase or decrease.

Teacher Notes


5th Grade Math – Singapore Ch 1 – 1 day, Ch 2 – 2 days, Ch 3 – 2 days, Ch 4 – 1 day Ch 5 – 1 day, Ch 6 – 1 day, Ch 7 – 2 days, Ch 8 – 1 day

Learner Goals: Singapore Page CitationsMeasure and construct angles. TB-B: Unit 10, Ch 1, 76-77

WB-B: 69-74EP: 211-212

Find unknown angles in figures based on identifying vertical, adjacent, complementary, or supplementary angles.

TB-B: Unit 10, Ch 2, 78-81WB-B: 75-76

EP: 213-214

Know and use angle properties of intersecting lines, triangles, parallelograms, rhombuses, and trapezoids to solve problems involving finding find unknown angles.

Throughout chapters 3-8

Identify attributes of triangles and quadrilaterals. TB-B: Unit 10, Ch 3, 82-85, Ch 4,86-89, Ch 6,93-94, Ch 7, 95-98WB-B: 77-79, 80-83, 85, 86-90

EP: 215-218EP: 219-222EP: 225-226EP: 227-230

Construct triangles, parallelograms, and rhombuses with specified angles.

TB-B: Unit 10, Ch 5, 90-92, Ch 8,99-102WB-B: 84, 91-92

EP: 223-224EP: 231-232

Geometry 5.G Classify two-dimensional figures into categories based on their properties.

Vocabularyprotractor acute angle obtuse angle reflex angle

Grade 6 Learner Goals: Identify acute, obtuse, and right angles and relate 90°, 180°, 270°,

and 360° with quarter, half, three-quarter, and whole turn.

ANGLES

Suggested LiteratureThe Greedy Triangle by Marilyn Burns

Grade 4 Learner Goals: Measure and construct angles. Identify attributes of triangles and quadrilaterals.

Materials Protractor Appendix pages:

o 10.1a 10.3a 10.4a 10.6a 10.7a

o 10.r Ruler Sret square

5th Grade Math - Singapore Ch 1 – 6 days, Ch 2 – 6 days, R – 2-4 days

Geometry 5.G Classify two-dimensional figures into categories based on their properties.

Vocabularyprotractor acute angle obtuse angle reflex angle

Grade 6 Learner Goals: Identify acute, obtuse, and right angles and relate 90°, 180°, 270°,

and 360° with quarter, half, three-quarter, and whole turn.

Teacher Notes

Grade 4 Learner Goals: Measure and construct angles. Identify attributes of triangles and quadrilaterals.

AVERAGE AND RATE

Learner Goals: Singapore Page CitationsFind the average of a set of data. TB-B: Unit 11, Ch 1, 106-108

WB-B: 97-100Find the average of measurement in compound units. TB-B: Unit 11, Ch 1, 108-109

WB-B: 101-102Understand rate as the measure of one quantity per unit value of another.

TB-B: Unit 11, Ch 2, 111-112WB-B:

Solve problems involving rate. TB-B: Unit 11, Ch 2, 113-117WB-B: 104-111

EP: 239-242Use a unitary approach to solve rate problems.Solve discontinuous rate problems involving time.Solve multi-step word problems involving average, rate, and percentage.Find a data value given the average and the other values.

TB-B: Unit 11, Ch 1, 109-110, Ch 8,99-102, Ch 2, 113-117WB-B: 103, 104-111

EP: 235-238EP: 239-242

Number and Operations in Base Ten 5.NBT

none

Vocabularytotal average rate …per…rate table

Grade 6 Learner Goals: Understand rate as the measure of one quantity per unit value of another. Solve problems involving rate. Use a unitary approach to solve rate problems. Solve discontinuous rate problems involving time.



Materials Counters that can be displayed Paper bowls or plates Measuring tools, e.g., yard stick, meter stick, stopwatch Rate charts, such as postage rates Appendix 11.r

5th Grade Math – Singapore Ch 1 – 1 day, Ch 2 – 1 day, Ch 3 – 1 day, Ch 4 – 2-3 days, R – 1-2 days

Learner Goals: Singapore Page CitationsUnderstand, find, and compare mean, median, and mode of a set of data.

TB-B: Unit 12, Ch 1, 122-123WB-B: 116-117

EP: 249-250

Ask and solve questions related to data representation, including finding

Grade 6 Learner Goals: Understand rate as the measure of one quantity per unit value of another. Solve problems involving rate. Use a unitary approach to solve rate problems. Solve discontinuous rate problems involving time.

Teacher Notes

DATA ANALYSIS

the range and mode.Collect, organize, and analyze data using line plots.Collect, organize and display data in histograms. TB-B: Unit 12, Ch 2, 124-127

WB-B: 118-121EP: 251-252

Collect, organize, and analyze data using line graphs. TB-B: Unit 12, Ch 3, 128-130WB-B: 122

EP: 253-254

Collect, organize and display data in pie charts. TB-B: Unit 12, Ch 4, 131-134WB-B: 123-133

EP: 255-260

Geometry 5.G Graph points on the coordinate plane to solve real-world and mathematical problems.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Vocabularymean median mode dataline plot histogram line graph horizontal axisvertical axis circle graph pie chart

Grade 6 Learner Goals: Understand, find, and compare mean, median, and mode of a set of

data. Find the range of a set of data. Understand how additional data added to data sets may affect

measures of central tendency. Understand how the inclusion or exclusion of outliers affects

measures of central tendency.


Grade 4 Learner Goals: Ask and solve questions related to data representation, including

finding the range and mode. Collect, organize, and analyze data using line plots. Collect, organize, and analyze data using line graphs.

Materials Graph paper Rulers Data collected over time Examples of pie charts from other subjects Appendix pages:

o 12.4bo 12.4co 12.r

5th Grade Math – Singapoare Ch 1 – 6 days, Ch 2 – 4 days, Ch 3 – 4 days, R – 1-2 days,Learner Goals: Singapore Page CitationsUse letters to stand for unknown numbers in equations and solve for the unknown numbers using properties of the four operations.

TB-B: Unit 13, Ch 1, 140-148WB-B: 139-145

EP: 269-274

Write simple equations involving related changes in quantities (e.g. y = 3x + 5) and solve for the dependent value when given the independent value.Write and evaluate simple algebraic expressions in one variable using substitution.Use the distributive property in expressions with variables

Grade 6 Learner Goals: Understand, find, and compare mean, median, and mode of a set of

data. Find the range of a set of data. Understand how additional data added to data sets may affect

measures of central tendency. Understand how the inclusion or exclusion of outliers affects

measures of central tendency.

Teacher Notes

ALGEBRA

Simplify algebraic expressions in one variable.Solve problems involving simple linear functions with whole numbers values, write the equation, and graph the resulting ordered pairs on a grid.

TB-B: Unit 13, Ch 3, 156-163WB-B: 151-154

EP: 279-282

Understand the coordinate grid, locate points, and write ordered pairs (first quadrant).Understand the coordinate grid, locate points, and write ordered pairs (all four quadrants).Identify ordered pairs of data from a graph.Collect, organize, and analyze data using coordinate graphsUnderstand and interpret negative numbers, locate negative numbers on a number line, compare and order integers.

TB-B: Unit 13, Ch 2, 150-155WB-B: 146-150

EP: 275-278

Find the numerical value of negative numbers.Add and subtract positive and negative integers.Solve problems involving linear functions with integer values, write the equation, and graph the resulting ordered pairs on a grid.

Operations and Algebraic Thinking 5.OAAnalyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Geometry 5.GGraph points on the coordinate plane to solve real-world and mathematical problems.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that

Grade 6 Learner Goals: Use letters to stand for unknown numbers in equations and solve for

the unknown numbers using properties of the four operations. Write simple equations involving related changes in quantities (e.g. y

= 3x + 5) and solve for the dependent value when given the independent value.

Write and evaluate simple algebraic expressions in one variable using substitution.

Use the distributive property in expressions with variables. Write and evaluate simple algebraic expressions for a given situation,

using up to three variables. Solve simple algebraic equations in one variable. Solve problems involving simple linear functions with whole numbers

values, write the equation, and graph the resulting ordered pairs on a grid.


Operations and Algebraic Thinking 5.OAAnalyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Geometry 5.GGraph points on the coordinate plane to solve real-world and mathematical problems.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that




Write and evaluate simple algebraic expressions in one variable using substitution.

Use the distributive property in expressions with variables. Write and evaluate simple algebraic expressions for a given situation,

using up to three variables. Solve simple algebraic equations in one variable. Solve problems involving simple linear functions with whole numbers

values, write the equation, and graph the resulting ordered pairs on a grid.

Teacher Notes




Solve problems involving simple linear functions with whole numbers values, write the equation, and graph the resulting ordered pairs on a grid.

Understand the coordinate grid, locate points, and write ordered pairs (first quadrant).

Identify ordered pairs of data from a graph. Collect, organize, and analyze data using coordinate graphs. Understand and interpret negative numbers, locate negative

numbers on a number line, compare and order integers. Recognize and extend regular number patterns that include negative

images.pcmac.orgimages.pcmac.org/sisfiles/schools/nv/whitepine/normanelem... · web viewconvert...

Documents