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4th Grade Math SingaporeCh 1 6 days, Ch 2 3 days

WHOLE NUMBERS

Vocabulary

patternrounddigitsplace value

expanded formsumcomparerepresent

amountcomposecount by 100sdecompose

roundingskip-countvaluebase-ten numeral

comparisonexpanded notationfront-end digit

ten thousands placehundred thousands place

millions placeexpanded formtens place

hundreds placeones placemissing number

Materials

Number discs

Place value chart

Learner Goals:

Singapore Page Citations

Use place-value models to represent numbers to 100,000.

TB-A: Unit 1, 8-21

WB-A: 7-18

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.

TB-A: Unit 1, 22-25

WB-A: 19-20

Suggested Literature

One Hundred Hungry Ants by Elinor J. Pinczes

Amanda Beans Amazing Dream by Cindy Neuschwander

4th Grade Math Singapore Ch 3 2 days, Ch 4 3 days

FACTORS AND MULTIPLES

Learner Goals:


Find the factors and common factors of whole numbers within 100.

TB-A: Unit 1, 26-37

WB-A: 21-27

Identify prime numbers.

Find multiples and common multiples of whole numbers within 100.

Complete or extend regular number patterns for numbers within 100,000.

TB-A: Unit 1, 33

WB-A: 15

Operations and Algebraic Thinking 4.OA

Gain familiarity with factors and multiples.

4. Find all factor pairs for a whole number in the range 1100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1100 is prime or composite. Generate and analyze patterns.

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.

Vocabulary

productfactorcompositeprime

common factormultiplecommon multiple

term (of a sequence)patternrule

whole numberfactor pair

greatest common factorleast common multiple


The Best of Times by Greg Tang

Grade 3 Learner Goals:

Materials

Connect-a-cubes

Some square grid paper

Laminated hundreds boards

Transparent counters or a dry-erase marker

Opaque counters

Materials for each group of about 4 students:

Counters, a different color for each student

Number cards 1-10, 4 sets per group (or a 10 sided number cube)


Find the factors and common factors of whole numbers within 100.

Find the greatest common factor of up to 3 numbers within 100.

Identify prime numbers.

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

Find multiples and common multiples of whole numbers within 100.

Find the lowest common multiple of up to 3 numbers within 100.

Teacher Notes

4th Grade Math Singapore Ch 5 3 days

ORDER OF OPERATIONS

Learner Goals:


Use order of operations to solve mathematical expressions with or without parentheses.

TB-A: Unit 1, 38-41

WB-A: 28-33

Vocabulary

equationexpressionorder of operations

additionsubtractionmultiplication

divisionparentheses


Materials

Operation cards +, -, x, and , =, and parentheses cards ( and ), eight sets per group

Number cards 0-9, four sets per group

Teacher Notes




Use order of operations to solve mathematical expressions with or without parentheses.

4th Grade Math SingaporeCh 6 3 days, R 1-2 days

NEGATIVE NUMBERS

Learner Goals:


Understand and interpret negative numbers, locate negative numbers on a number line, compare and order integers.

TB-A: Unit 1, 42-47

WB-A: 34-37

Recognize and extend regular number patterns that include negative numbers.

Vocabulary

positive numbersnegative numbers


Materials

A set of 10 number cards for each group with random numbers between -100 and +100


Teacher Notes



Understand and interpret negative numbers, locate negative numbers on a number line, compare and order integers.

Find the numerical value of negative numbers.

Add and subtract positive and negative integers.

4th Grade Math SingaporeCh 1 4 days

4 OPERATIONS OF WHOLE NUMBERS

ADDITION AND SUBTRACTION

Learner Goals:


Add/Subtract numbers within 10,000.

TB-A: Unit 2, 51-58

WB-A: 40-50

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

TB-A: Unit 2, 55-56

WB-A: 47-48

Determine whether an estimate is sufficient for a specific problem situation.

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

TB-A: Unit 2, 54-55

WB-A: 44-46

Mentally subtract from 1000.

Mentally add/subtract a number close to 1000 (e.g. 998).

Solve 2-step word problems which involve the four operations on whole numbers.

TB-A: Unit 2, 51, 57-58

WB-A: 49-50

Use boxes and other symbols to stand for unknown numbers in expressions and equations.

Throughout

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

TB-A: Unit 2, 51-53, 57

WB-A: 49-50

Vocabulary

sumdifferenceadditionround

digitequationplace valuesubtraction

addendcomposedecomposeminuend

representoperation2-step problem more

reasonableestimationestimateless

altogethermental calculationsreasonableexact number


Use the four operations with whole numbers to solve problems.

3. Solve multistep 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. Number and Operations in Base Ten 4.NBT

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

4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Materials

Number discs (discs with 1, 10, and 100 written on them)


Teacher Notes



Add/subtract numbers in the billions.

Use letters to stand for unknown numbers in equations and solve for the unknown numbers using properties of the four operations.


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

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

Add/subtract a number close to a multiple of 100 (e.g. 498).


Add/Subtract numbers within 10,000.



Solve problems involving numeric equations or inequalities.

Select appropriate operational symbol to make an expression true.

Use boxes and other symbols to stand for unknown numbers in expressions and equations.


4th Grade Math Singapore Ch 2 4 days


MULTIPLICATION AND DIVISION

Materials


Place value cards

Vocabulary

multipleproductdivisionmultiplication

quotientequationpatternrule

divisorestimaterounddividend

factorremaindercomparedivide

Learner Goals:


Multiply numbers within 10,000 by a 1-digit number.

TB-A: Unit 2, 59-67

WB-A: 51-55

Divide numbers within 10,000 by a 1-digit number, including situations where there is a remainder.

Use estimation to verify the reasonableness of calculated results in multiplication and division problems.

TB-A: Unit 2, 61, 63-64, 66-67

WB-A: 51-55

Check division problems using multiplication.

throughout


TB-A: Unit 2, 65-67

WB-A: 54-55


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

TB-A: Unit 2, 62-63

WB-A:

Use divisibility rules for 2, 3, 5, 6, 9, and 10.

throughout



Divide and Ride by Stuart J Murphy

A Remainder of One by Elinor J Pinczes

Minnies Diner: A Multiplying Menu by Dayle Ann Dodds


Use the four operations with whole numbers to solve problems.

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. 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.

3. Solve multistep 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. Number and Operations in Base Ten 4.NBT

Generalize place value understanding for multi-digit whole numbers.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. Use place value understanding and properties of operations to perform multi-digit arithmetic.

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.

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.


Relate division to multiplication.

Recognize and extend regular linear patterns.

Understand quotient and remainder.

Understand the properties of 0 and 1 in multiplication and division.

Multiply numbers within 1000 by a 1-digit number. Multiply numbers within 10,000 by a 1-digit number.

Divide numbers within 1000 by a 1-digit number, including situations where there is a remainder. Divide numbers within 10,000 by a 1-digit number, including situations where there is a remainder.





Teacher Notes



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

Multiply/divide numbers within 1,000,000 by tens, hundreds, or thousands.




Understand the distributive property.


Multiply by 99 or by 25

Multiply by a number one less than a multiple of 10 or 100 (e.g. 49, 499).


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


MULTIPLICATION by a 2-DIGIT NUMBER

Vocabulary

multipleproductdivisionmultiplication

quotientequationpatternrule

divisorestimaterounddividend

factorremaindercompare

Number and Operations in Base Ten 4.NBT

Generalize place value understanding for multi-digit whole numbers.

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.

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

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.

Learner Goals:



TB-A: Unit 2, 68-73

WB-A: 56-62

Multiply by 99 or by 25.

Multiply 10's by 10's or 100's.




Divide and Ride by Stuart J Murphy

A Remainder of One by Elinor J Pinczes

Minnies Diner: A Multiplying Menu by Dayle Ann Dodds

Materials


Appendix 2.r

Teacher Notes



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

Multiply/divide numbers within 1,000,000 by tens, hundreds, or thousands.




Understand the distributive property.


Multiply by 99 or by 25

Multiply by a number one less than a multiple of 10 or 100 (e.g. 49, 499).


Relate division to multiplication.

Recognize and extend regular linear patterns.

Understand quotient and remainder.

Understand the properties of 0 and 1 in multiplication and division.

Multiply numbers within 1000 by a 1-digit number. Multiply numbers within 10,000 by a 1-digit number.

Divide numbers within 1000 by a 1-digit number, including situations where there is a remainder. Divide numbers within 10,000 by a 1-digit number, including situations where there is a remainder.




4th Grade Math Singapore Ch 1 3 days, Ch 2 3 days, Ch 3 1 day, Ch 4 4 days

FRACTIONS

Ch 5 2 days, Ch 6 9 days, R 1-2 days

Learner Goals:


Understand mixed numbers and improper fractions, convert between them, locate them on a number line.

TBA: Unit 3, 88-93

WBA: 77-87

Find equivalent fractions and simplest form of a fraction.

TBA: Unit 3, 7780

WBA: 6770

Find the fraction of a set where the answer is a whole number.

TBA: Unit 3, 98-104

WBA: 90-109

Find fraction of a set for measurements (e.g. 10 minutes as a fraction of one hour).

Add/Subtract related fractions.

TBA: Unit 3, 8182, 87, 88-89, 92-93

WBA: 7576, 77-78, 83-85

Compare and order fractions with different denominators.

TBA: Unit 3, 7980

WBA: 70, 87

Relate division to fractions.

TBA: Unit 3, 94-96

WBA: 88-89

Multiply a fraction by a whole number.

TBA: Unit 3, 98-100

WBA: 91-97

Solve 2-step word problems which involve fraction of a set.

TBA: Unit 3, 101105

WBA: 98109

Solve 2-step word problems which involve decimals and fractions.

Use bar diagrams to solve word problems involving fractions.

Materials

Fraction bars and circles

Rulers in cm and inches

Apples or other objects

20 cards with improper fractions and 20 cards with corresponding mixed numbers, per group

Paper plates

Coins

Meter stick

Ruler (12 in.)

Vocabulary

common ___ comparisondenominatorequivalentestimation

productfractionmixed numbermultiplicationimproper number linenumeratorsimplest formimproper fraction

Teacher Notes


Piece = Part = Portion by Scott Gifford

One Riddle, One Answer by Lauren Thompson

Number and Operations - Fractions 4.NF

Extend understanding of fraction equivalence and ordering. 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. 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 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. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 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?


Compare and order fractions with the same denominator or with the same numerator.

Find equivalent fractions and simplest form of a fraction.


Recognize and name the fraction of a set.

Find the value given the fraction of a set, using objects or drawings.

Find the fraction of a set where the answer is a whole number.

Add/Subtract like fractions.



Find the fraction of a set where the answer is a whole number or a mixed number.

Find fraction of a set for measurements (e.g. 10 minutes as a fraction of one hour).

Add/Subtract unlike fractions.

Relate division to fractions.

Add/subtract mixed numbers.

Multiply a fraction by a whole number.

Multiply a fraction by a fraction.

Divide a fraction by a whole number.

Divide a whole number or a fraction by a fraction.

Use bar diagrams to solve word problems involving fractions.

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

GEOMETRY

Ch 6 1 day, Ch 7 1 day, Ch 8 1 day, Ch 9 2 days, R 1-2 days

Learner Goals:


Describe and classify common 3-dimensional shapes according to number and shape of faces, edges, and vertices. Visualize, describe, and draw geometric solids.

TBA: Unit 4, 130-131

WBA: 146-147

Identify acute, obtuse, and right angles and relate 90, 180, 270, and 360 with quarter, half, three-quarter, and whole turns.

TBA: Unit 4, 116-121

WBA: 123131

Measure and construct angles.

Identify perpendicular and parallel lines.

TBA: Unit 4, 116-121

WBA: 132-139

Name different types of triangles and quadrilaterals. Identify attributes of triangles and quadrilaterals.

TBA: Unit 4, 122-127

WBA: 140-143

Find the lengths of unknown sides given the length of other sides or the perimeter of triangles and quadrilaterals.

Identify the radius and diameter of a circle, find one given the other.

TBA: Unit 4, 128-129

WBA: 144-145

Identify nets of solids, or solids of nets.

TBA: Unit 4, 132-136

WBA: 148-155

Teacher Notes

Materials

Folding meter stick or 2 strips of cardboard attached with a brad at one end

Protractors, compasses, rulers, rulers (cm)

Large demonstration protractor or overhead projector

Worksheets with angles to measure

Worksheets each with a large rectangle on it

Set-squares

Square grid paper such as cm graph paper

Scissors, straws, paperclips, string and pins

Worksheet with lines crossing each other some perpendicular to each other

worksheet with various rectilinear figures

worksheets with pairs of lines, some crossing each other, some parallel to each other

Paper for cut-out triangles

Paper circles of various diameters

Models of solids prisms, pyramids, cylindres

Appendix pages

4.5a-14.9b-14.r


Describe and classify common 3-dimensional shapes according to number and shape of faces, edges, and vertices.

Identify common 3-dimensional shapes within compound shapes.

Identify intersecting and parallel lines.

Identify and describe polygons.

Identify attributes of triangles and quadrilaterals.

Identify right angles and compare angles to right angles.

Measurement and Data 4.MD

Geometric measurement: understand concepts of angle and measure angles.

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. 6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

7. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Geometry 4.G Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 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.

Vocabulary

acute anglecenterendpointmeasurerhombus

anglecircleright anglearcrhombi

obtuse angledegreeprotractordiametercylinder

radiusradiiperpendicularparallelcubes

quadrilateraltriangleisoscelesequilateralarea

scaleneperimeterrectangularprism

triangularpyramidsquareface

edgeverticesnetset-square

intersectingnon-intersectingparallelogramtrapezoid


Sir Cumference and the Isle of Inmeter by Cindy Neuschwander

Sir Cumference and the Great Knight of Angleland by Cindy Neuschwander

The Greedy Triangle by Marilyn Burns


Identify attributes of triangles and quadrilaterals.

Measure and construct angles.

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

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

Construct triangles, parallelograms, and rhombuses with specified angles.

Visualize, describe, and draw geometric solids.

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

Area and Perimeter

Learner Goals:


Find the area of shapes by covering them with unit squares or by counting squares.

TB-A: Unit 5, 141-144

WB-A: 162-164

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, 145-150

WB-A: 165-171

Find the area and perimeter of composite figures made from squares and rectangles.

TB-A: Unit 5, 151-156

WB-A: 172-176

Vocabulary

areaperimetersquare unitdimension

widthlengthmeasurementsquare unit

distancerectanglesquarecomposite figures

path

Measurement and Data4.MD

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

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.


Materials

Square grid paper such as centimeter graph paper

Rectangular cards 8 cm x 5 cm, 6 cm x 3 cm, squares 4 cm x 4 cm for each student

Centimeter graph paper

Appendix 5.r

Teacher Notes


Find the perimeter of polygons.



Count unit cubes in 2-dimensional representations of 3-dimensional solids.




Find the area, perimeter, and unknown sides of rectangles.

Find 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.

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

Find the surface area of cubes and rectangular prisms.

4th Grade Math Singapore Ch 1 4 days, Ch 2 6 days, Ch 3 3 days, Ch 4 2 days,

DECIMALS

R 1-2days

Learner Goals:


Understand tenths, hundredths, thousandths, locate decimal numbers on a number line, compare decimal numbers.

TBB: Unit 6, 8-27

WBB: 7-33

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.

TBB: Unit 6, 28-30

WBB: 34-36

Find coin amounts as a fraction of a dollar.

Vocabulary

hundredthcompareequivalentdecimalones

tenthdecimal pointroundtenths place

thousandthwhole number partfractional partcentimeter

millimeterdigitsvaluedotdollarcent

sumnumber patternconstant amount

numeratordenominatorsimplest formsimplify

factorgreatersmallermore/less than

make 100count onplace valuerename

round up/downhundredth place

Number and OperationsFractions 4.NF

Understand decimal notation for fractions, and compare decimal fractions.

5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

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. 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 , =, or

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