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# Math Grade 4 Flip Chart

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Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Grade Grade Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-4001 444 \|xiBAHBDy01217nzW Sturdy, Free-Standing Design, Perfect for Learning Centers! Reverse Side Features Questions, Math Problems, Vocabulary Review & more!

Phone: 800-507-0966 • Fax: 800-507-0967 www.newpathlearning.com NewPath Learning® products are developed by teachers using research-based principles and are classroom tested. The company’s product line consists of an array of proprietary curriculum review games, workbooks, posters and other print materials. All products are supplemented with web-based activities, assessments and content to provide an engaging means of educating students on key, curriculum-based topics correlated to applicable state and national education standards. Copyright © 2009 NewPath Learning. All Rights Reserved. Printed in the United States of America. Curriculum Mastery® and NewPath Learning® are registered trademarks of NewPath Learning LLC. Math Curriculum Mastery® Flip Charts provide comprehensive coverage of key standards-based curriculum in an illustrated format that is visually appealing, engaging and easy to use. Curriculum Mastery® Flip Charts can be used with the entire classroom, with small groups or by students working independently. Each Math Curriculum Mastery® Flip Chart Set features • 10 double-sided laminated charts covering grade-level specific curriculum content on one side plus write-on/wipe-off charts on reverse side for student use or for small-group instruction. • Built-in sturdy free-standing easel for easy display • Spiral bound for ease of use • Activity Guide with black-line masters of the charts for students to fill-in, key vocabulary terms, corresponding quiz questions for each chart, along with answers Ideal for • Learning centers • In class instruction for interactive presentations and demonstrations • Hands-on student use • Stand alone reference for review of key science concepts • Teaching resource to supplement any program HOW TO USE Classroom Use Each Curriculum Mastery® Flip Chart can be used to graphically introduce or review a topic of interest. Side 1 of each Flip Chart provides graphical representation of key concepts in a concise, grade appropriate reading level for instructing students. The reverse Side 2 of each Flip Chart allows teachers or students to fill in the answers and summarize key concepts. Note: Be sure to use an appropriate dry-erase marker and to test it on a small section of the chart prior to using it. The Activity Guide included provides a black-line master of each Flip Chart which students can use to fill in before, during, or after instruction. On the reverse side of each black-line master are questions corresponding to each Flip Chart topic which can be used as further review or as a means of assessment. While the activities in the guide can be used in conjunction with the Flip Charts, they can also be used individually for review or as a form of assessment or in conjunction with any other related assignment. Learning Centers Each Flip Chart provides students with a quick illustrated view of grade-appropriate curriculum concepts. Students may use these Flip Charts in small group settings along with the corresponding activity pages contained in the guide to learn or review concepts already covered in class. Students may also use these charts as reference while playing the NewPath’s Curriculum Mastery® Games. Independent student use Students can use the hands-on Flip Charts to practice and learn independently by first studying Side 1 of the chart and then using Side 2 of the chart or the corresponding graphical activities contained in the guide to fill in the answers and assess their understanding. Reference/Teaching resource Curriculum Mastery® Charts are a great visual supplement to any curriculum or they can be used in conjunction with NewPath’s Curriculum Mastery® Games. Chart # 1: Chart # 2: Chart # 3: Chart # 4: Chart # 5: Chart # 6: Chart # 7: Chart # 8: Chart # 9: Chart #10: Place Value – Understanding Numbers Multiplying Two-digit Numbers Dividing Two-digit Numbers Adding & Subtracting Decimals Polygons Lines & Angles Area, Volume & Perimeter Fraction Concepts Adding & Subtracting Fractions Customary & Metric Units of Measurement

Thousands 10 hundreds make up 1 thousand Hundreds 10 tens make up 1 hundred Tens 10 ones make up 1 ten Ones 1 Standard Form Expanded Form Number Word 372,512,489 300,000,000 + 70,000,000 + 2,000,000 + 500,000 + 10,000 + 2,000 + 400 + 80 + 9 three hundred seventy-two million, five hundred twelve thousand, four hundred eighty-nine 11 2 2 6 6 . hundredths tenths ones tens 1 one 2 tenths 6 hundredths 3 7 2 5 1 2 4 8 9 3 7 2 5 1 2 4 8 9 ones tens hundr eds ones tens hundr eds thousands thousands ten thousands ten thousands millions millions ten millions ten millions hundr ed millions hundr ed millions hundr ed thousands hundr ed thousands Ones Period Thousands Period Millions Period • Place value is the value assigned to the position of a digit in a written number. • A digit is a symbol used to write a number 0 to 9. • A period is a group of three digits separated by a comma. Base–ten Place Value Decimal Place Value • Our place value system is based on groups of ten. • Each place represents ten times the value of the place to the right. 1.1 1.2 1.21 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.22 1.24 1.26 1.28 1.23 1.25 1.27 1.29 1.3 1.4 0 1.0 2.0 © Copyright NewPath Learning. All Rights Reserved. 93-4401 www.newpathlearning.com Place Value - Understanding Numbers

\|xiBAHBDy01658ozX 10 hundreds make up 10 tens make up 10 ones make up Standard Form Expanded Form Number Word 372,512,489 11 2 2 6 6 . hundredths tenths ones tens 1.26 Key Vocabulary Terms • base-ten • decimal • expanded form • hundreds • hundredths • millions • millions period • number word • ones • ones period • place value • standard form • tens • tenths • thousands • thousands period 3 7 2 5 1 2 4 8 9 3 7 2 5 1 2 4 8 9 Ones Period Thousands Period Millions Period • Place value is the value assigned to the position of a digit in a written number. • A digit is a symbol used to write a number 0 to 9. • A period is a group of three digits separated by a comma. Base–ten Place Value Decimal Place Value • Our place value system is based on groups of . • Each place represents the value of the place to the right. 1.1 1.2 1.21 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.22 1.24 1.26 1.28 1.23 1.25 1.27 1.29 1.3 1.4 0 1.0 2.0 ___________ + _________ + ________ + ______ + _____ + _____ + ____ + ___ + __ © Copyright NewPath Learning. All Rights Reserved. 93-4401 www.newpathlearning.com Place Value - Understanding Numbers

Multiplication Arrays Using the Distributive Property Distributive Property of Multiplication • An array is one way to show the product of two numbers. • An array is used to break apart greater factors to make numbers easier to multiply. 4 x 5 4 x (3 + 2) = 4 x 5 = 20 4 x (3 + 2) = (4 x 3) + (4 x 2) = 12 + 8 = 20 Step 1 Step 2 Step 3 12 x 18 96 12 x 18 96 120 12 x 18 96 + 120 216 1 Multiply (8 x 12) 2 Multiply (10 x 12) 3 Add 96 and 120 to find the final product Remember the expanded form of 18 is (10 + 8). Each addend is multiplied by 12. 12 x 8 10 10 180 216 96 2 x 8 = 16 10 x 8 = 80 10 x 10 = 100 2 x 10 = 20 120 36 8 2 © Copyright NewPath Learning. All Rights Reserved. 93-4402 www.newpathlearning.com Multiplying Two-digit Numbers

\|xiBAHBDy01656kzU Multiplication Arrays Using the Distributive Property Distributive Property of Multiplication • An is one way to show the of two numbers. • An array is used to break apart greater factors to make numbers easier to . 4 x 5 4 x (3 + 2) = 4 x 5 = 20 4 x (3 + 2) = (4 x 3) + (4 x 2) = 12 + 8 = 20 Step 1 Step 2 Step 3 12 x 18 96 12 x 18 96 12 x 18 96 1 Multiply (8 x 12) 2 Multiply (10 x 12) 3 Add 96 and 120 to find the final product Remember the expanded form of 18 is (10 + 8). Each addend is multiplied by 12. 12 x 8 Key Vocabulary Terms • add • expanded form • array • factor • digit • multiply • distributive property • product + 10 10 180 216 96 2 x 8 = 16 10 x 8 = 80 10 x 10 = 100 2 x 10 = 20 120 36 8 2 © Copyright NewPath Learning. All Rights Reserved. 93-4402 www.newpathlearning.com Multiplying Two-digit Numbers

Divisibility Rules Division 3 + 3 + 3 + 3 = 12 3 x 4 = 12 • Division is repeated subtraction and the inverse operation of multiplication. Divide 8 tens by 6. Each group gets 1 ten, with 2 tens remaining. To check your answer, multiply the quotient by the divisor and add the remainder if any. Bring down the ones and divide. 12 ÷ 4 = 3 number of items number of items in each group number of groups dividend divisor quotient Step 1 Step 2 Step 3 4 3 12 84 1 2 – 6 6 84 1 4 24 24 – – 6 6 0 14 6 x 84 • multiply: 6 x 4 • subtract: 24 – 24 • compare: 0 < 6 The answer checks if the product is the same as the dividend 2 • Dividend is the number that is divided. • Divisor is the number by which the dividend is being divided. • Quotient is the answer to a division problem. dividend divisor quotient Find 84 ÷ 6 • multiply: 1 x 6 • subtract: 8 – 6 • compare: 2 < 4 2 3 4 5 6 7 8 9 10 If the ones (last) digit is even If the sum of the digits are divisible by 3 If the sum of its digits is divisible by 9 If the number is divisible by both 2 and 3 If the number ends in 0 If the last two digits are divisible by 4 If the last three digits are divisible by 8 A whole number is divisible by: If the ones (last) digit is 0 or 5 If the number is divisible by 7 © Copyright NewPath Learning. All Rights Reserved. 93-4403 www.newpathlearning.com Dividing Two-digit Numbers

Divisibility Rules Division 3 + 3 + 3 + 3 = 12 3 x 4 = 12 • Division is and the inverse operation of multiplication. Divide 8 tens by 6. Each group gets 1 ten, with 2 tens remaining. To check your answer, multiply the quotient by the divisor and add the remainder if any. Bring down the ones and divide. 12 ÷ 4 = 3 number of items number of items in each group number of groups Step 1 Step 2 Step 3 4 3 12 84 1 2 – 6 6 84 – – 6 6 14 6 x • multiply: 6 x 4 • subtract: 24 – 24 • compare: 0 < 6 The answer checks if the product is the same as the dividend • Dividend is the number that is divided. • Divisor is the number by which the dividend is being divided. • Quotient is the answer to a division problem. Find 84 ÷ 6 • multiply: 1 x 6 • subtract: 8 – 6 • compare: 2 < 4 2 3 4 5 6 7 8 9 10 A whole number is divisible by: Key Vocabulary Terms • digit • multiplication • dividend • quotient • division • remainder • divisor • repeated subtraction • inverse operation © Copyright NewPath Learning. All Rights Reserved. 93-4403 www.newpathlearning.com Dividing Two-digit Numbers \|xiBAHBDy01644rzu

16.58 + 27.8 27.8 – 16.58 Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 • Line up the decimal points. • Write zeros as place holders, if needed. • Add the hundredths. • Carry (regroup) if needed. • Add the tenths. • Carry (regroup) if needed. 0.62 + 0.34 = 0.96 1.8 – 1.2 = 0.6 Decimal Models Adding Decimals with Grids Adding Decimals Subtracting Decimals Subtracting Decimals with Grids 1.0 one whole (1) 0.1 . 01 1 10 hundredths 1 100 thousandths 1 1000 + + ones tens tenthshundr edths ones tens tenthshundr edths 1 1 1 6 5 8 . 2 7 8 0 4 4 3 8 . + 1 1 6 5 8 . 2 7 8 0 . 3 8 + 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . 8 • Line up the decimal points. • Write zeros as place holders, if needed. • Regroup if needed. • Subtract the hundredths. • Regroup if needed. • Subtract the tenths. • Regroup if needed. • Subtract the ones, then the tens. • Drag the decimal point straight down. – – ones tens tenthshundr edths ones tens tenthshundr edths 1 7 10 7 10 7 10 6 5 8 . 2 7 8 0 1 1 2 2 . – 1 6 5 8 . 2 7 8 0 . 2 2 – 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . 2 . . © Copyright NewPath Learning. All Rights Reserved. 93-4404 www.newpathlearning.com Adding & Subtracting Decimals 0.001

16.58 + 27.8 27.8 – 16.58 Step 1 Step 2 Step 3 Step 4 Step 1 Step 2 Step 3 Step 4 • Line up the decimal points. • Write zeros as place holders, if needed. • Add the hundredths. • Carry (regroup) if needed. • Add the tenths. • Carry (regroup) if needed. 0.62 + 0.34 = 0.96 1.8 – 1.2 = 0.6 Decimal Models Adding Decimals with Grids Adding Decimals Subtracting Decimals Subtracting Decimals with Grids 1.0 one whole (1) 0.1 . 01 1 10 hundredths 1 100 thousandths 1 1000 + + ones tens tenthshund redths ones tens tenthshund redths 1 6 5 8 . 2 7 8 0 . + 1 6 5 8 . 2 7 8 0 . + 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . • Line up the decimal points. • Write zeros as place holders, if needed. • Regroup if needed. • Subtract the hundredths. • Regroup if needed. • Subtract the tenths. • Regroup if needed. • Subtract the ones, then the tens. • Drag the decimal point straight down. – – ones tens tenthshund redths ones tens tenthshund redths 1 6 5 8 . 2 7 8 0 . – 1 6 5 8 . 2 7 8 0 . – 1 6 5 8 . 2 7 8 0 . 1 6 5 8 . 2 7 8 0 . . . © Copyright NewPath Learning. All Rights Reserved. 93-4404 www.newpathlearning.com Adding & Subtracting Decimals 0.001 Key Vocabulary Terms • add • decimal • decimal point • hundredth • regroup • subtract • tenth • thousandth \|xiBAHBDy01634sz\

equilateral triangle isosceles triangle right triangle obtuse triangle acute triangle scalene triangle square rectangle parallelogram rhombus trapezoid Triangles – Polygons with three sides Quadrilaterals – Polygons with four sides vertex side • Polygons are plane figures (flat shapes) with three or more sides. • A polygon is made by joining line segments. Each line segment is a side. • A vertex is the point where the sides meet. Polygon equilateral triangle isosceles triangle right triangle obtuse triangle acute triangle scalene triangle square rectangle parallelogram rhombus trapezoid © Copyright NewPath Learning. All Rights Reserved. 93-4405 www.newpathlearning.com Polygons All three sides have equal length One of the angles is a right angle (90º) All three angles are acute angles (less than a right angle) One of the angles is an obtuse angle (greater than a right angle) At least two sides have equal length A four-sided polygon with two pairs of parallel sides Four sides of equal length and four right angles A four-sided polygon with four right angles A four-sided polygon with one pair of parallel sides Opposite sides are parallel and all four sides have equal length All three sides have different lengths

\|xiBAHBDy01659lz[ Key Vocabulary Terms • acute triangle • rectangle • equilateral triangle • rhombus • isosceles triangle • right triangle • line segment • scalene triangle • obtuse triangle • side • parallelogram • square • plain figure • trapezoid • polygon • triangle • quadrilateral • vertex Triangles – Polygons with three sides Quadrilaterals – Polygons with four sides • Polygons are (flat shapes) with three or more sides. • A polygon is made by joining . Each line segment is a . • A is the point where the sides meet. © Copyright NewPath Learning. All Rights Reserved. 93-4405 www.newpathlearning.com Polygons All three sides have length One of the angles is a angle (90º) All three angles are angles (less than a right angle) One of the angles is an angle (greater than a right angle) At least two sides have length A four-sided polygon with two pairs of sides Four sides of length and four angles A four-sided polygon with four angles A four-sided polygon with one pair of sides Opposite sides are and all four sides have length All three sides have lengths

Pairs of Lines Angles right angle straight angle acute angle obtuse angle Parallel lines right angle A D G H E F I Definition Examples How to write it How to say it An angle is made up of two rays that share the same endpoint called the vertex. A straight angle forms a straight line. A right angle forms a square corner. never intersect or cross one another Intersecting lines meet at the same point Perpendicular lines cross each other and form right angles An acute angle is less than a right angle. An obtuse angle is greater than a right angle. A ray is part of a line with one endpoint and goes on forever in the other direction. A line segment is part of a line between two endpoints. A line is a straight collection of points that extend in two opposite directions without end. A point is a location in space. Line Segment Line Ray Angle Point • line segment AB • line segment CD • line segment EF or or or or • line AB • line CD • line EF AB CD EF • ray AB • ray CD • ray EF • angle BAC • angle CAB • angle A BAC CAB A • point A • point B • point A • point B AB CD EF AB CD EF A A B D C F E B C vertex endpoint side side A B C F E A B D A B C D F E © Copyright NewPath Learning. All Rights Reserved. 93-4406 www.newpathlearning.com Lines & Angles

\|xiBAHBDy01649mzV Pairs of Lines Angles A D G H E F I Definition Examples How to write it How to say it Line Segment Line Ray Angle Point Key Vocabulary Terms • acute angle • parallel line • angle • perpendicular line • intersecting line • point • line • ray • line segment • right angle • obtuse angle • straight angle © Copyright NewPath Learning. All Rights Reserved. 93-4406 www.newpathlearning.com Lines & Angles

Volume = length x width x height Perimeter = 2 + 2w Perimeter = (2 x length) + (2 x width) Area = length x width Volume = 36 cubic feet Area = 45 square feet Perimeter = 42 meters P = 14 + 7 + 14 + 7 = 42m Perimeter Volume Area Area formula Volume formula Perimeter formula width (w) height (h) width (w) width (w) width (w) width (w) 5ft 4ft 3ft 3ft 9ft A = l x w A = 9 x 5 A = 45 V = x w x h V = 4 x 3 x 3 V = 36 P = 2 + 2 P = 2(14) + 2(7) P = 28 + 14 P = 42 7m 7m 14m 14m Area is the number of square units needed to cover the inside of a figure. Volume is the number of cubic units that fill up a solid figure. Perimeter is the distance around a plane figure. To find the perimeter you may also add the lengths of all sides. Volume = x w x h Area = x w length ( ) length ( ) length ( ) length ( ) length ( ) © Copyright NewPath Learning. All Rights Reserved. 93-4407 www.newpathlearning.com Area, Volume & Perimeter

Volume = cubic feet Area = square feet Perimeter = meters P = + + + = Perimeter Volume Area 5ft 4ft 3ft 3ft 9ft A = l x w A = 9 x 5 A = 45 V = x w x h V = 4 x 3 x 3 V = 36 P = 2 + 2 P = 2(12) + 2(6) P = 24 + 12 P = 36 7m 7m 14m 14m Area is the number of s needed to cover the inside of a figure. Volume is the number of that fill up a solid figure. Perimeter is the a plane figure. To find the perimeter you may also add the lengths of all sides. Volume = length x width x height Perimeter = (2 x length) + (2 x width) Area = length x width Volume formula Perimeter formula width (w) width (w) Area formula Area = x Volume = x x Perimeter = + length ( ) length ( ) Key Vocabulary Terms • area • solid figure • cubic unit • plane figure • height • square unit • length • volume • perimeter • width • side © Copyright NewPath Learning. All Rights Reserved. 93-4407 www.newpathlearning.com Area, Volume & Perimeter \|xiBAHBDy01640tz]

Mixed Numbers & Impr oper Fractions Fractions in Simplest Form To subtract fractions with the same denominator: + = – = 3 6 2 6 5 6 = + 2 6 5 6 + 3 8 2 8 1 8 = – 3 8 2 8 1 8 = – Parts of a Whole Part of a Group A fraction is used to describe a part of a whole. A fraction can also describe part of a group or set. Equivalent fractions are fractions with different numerators and denominators but have the same value. To find an equivalent fraction, multiply or divide the numerator and denominator of a fraction by the same number. Equivalent Fractions To find the simplest form of a fraction, keep dividing until 1 is the only number that divides both the numerator and denominator. Fractions in Simplest Form Improper Fractions & Mixed Numbers 8 16 4 8 2 4 1 2 = = = = = = ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 ÷2 6 16 6 16 3 8 3 8 = = 2 4 2 4 1 2 1 2 = = 10 3 1 3 6 16 6 16 3 8 3 8 = = x2 x2 x2 x2 2 4 2 4 1 2 1 2 = = ÷2 ÷2 ÷2 ÷2 2 6 green sections (numerator) total number of sections (denominator) 5 12 apples (numerator) total number of fruit (denominator) • divide the numerator by the denominator • write the remainder as the numerator of the mixed number To change an improper fraction to a mixed number: improper fraction mixed number = 3 1 whole 3 3 ( ) 1 whole 3 3 ( ) 1 whole 3 3 ( ) of a whole 1 3 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 16 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4