Math: Math Facts Flip Chart

Copyright © NewPath Learning. All rights reserved. www.newpathlearning.com Charts Charts Mathfacts Mathfacts Curriculum Mastery Flip Charts Combine Essential Math Skills with Hands-On Review! ® 33-2005 \|xiBAHBDy01262nzW 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: Adding Two-digit Numbers Subtracting Two-digit Numbers Adding & Subtracting Three-digit Numbers Multiplication Concepts & Strategies Multiplication Table Division Concepts & Strategies Adding & Subtracting Number Sense Multiplying Two-digit Numbers Dividing Two-digit Numbers Problem Solving Strategies

Digit Place Value Place 24 and 18 blocks in the tens and ones columns. Add the ones. Regroup 10 ones as 1 ten. Write a 1 in the tens column. Add the tens and write the sum. 1. 2. 3. 14 ones = 1 ten & 4 ones 24 + 18 = ? 24 + 12 = ? addends addends sum has two digits digits Regroup 1 2 1 + 4 8 2 1 2 1 + 4 8 2 4 2 1 4 2 6 3 12 + There are 2 tens and 4 ones in 24. Adding with Regrouping Adding without Regrouping tens ones tens ones tens ones tens ones tens ones tens ones tens ones © Copyright NewPath Learning. All Rights Reserved. 93-4201 www.newpathlearning.com Adding Two-digit Numbers

\|xiBAHBDy01613nzW Place Value Place 24 and 18 blocks in the tens and ones columns. Add the ones. Regroup 10 ones as 1 ten. Write a 1 in the tens column. Add the tens and write the sum. 1. 2. 3. = 24 + 18 = ? 24 + 12 = ? Regroup 2 1 + 4 8 2 1 + 4 8 2 1 4 2 + There are and in 24. Adding with Regrouping Adding without Regrouping tens ones tens ones tens ones tens ones tens ones tens ones tens ones © Copyright N ewPath Learning. All Rights Reserved. 93-4201 www.newpathlearning.com Adding Two-digit Numbers Digit has two digits 12 digits Key Vocabulary Terms • addends • regroup • add • sum • digit • tens • ones • two-digit • place value

tens ones tens ones tens ones tens ones tens ones Number Line Subtracting with Regrouping Place 32 blocks in the tens and ones columns. 1. 1 ten = 10 ones 34 – 13 = ? 32 – 7 = ? Regroup Counting Back tens ones 3 – 2 7 Regroup 1 ten as 10 ones. 2. 3 – 2 2 12 7 tens ones 3 – 2 2 12 7 5 3 – 2 2 12 7 5 2 difference 3 1 – 4 2 1 3 Subtract the ones. 3. Subtract the tens. When subtracting 1, 2, or more from a number, you can subtract by counting back. 4. 0 1 2 3 4 5 6 7 8 9 10 tens ones tens ones tens ones tens ones tens ones Example: 6 – 2 = 4 Subtracting without Regrouping © Copyright NewPath Learning. All Rights Reserved. 93-4202 www.newpathlearning.com Subtracting Two-digit Numbers

\|xiBAHBDy01628rzu tens ones tens ones tens ones tens ones tens ones Key Vocabulary Terms • count back • regroup • difference • subtract • number line • tens • ones Subtracting with Regrouping Place 32 blocks in the tens and ones columns. 1. 1 ten = 34 – 13 = ? 32 – 7 = ? Regroup tens ones 3 – 2 7 Regroup 1 as . 2. 3 – 2 7 tens ones 3 – 2 7 3 – 2 7 5 2 difference 3 1 – 4 3 Subtract the ones . 3. Subtract the tens . 4. tens ones tens ones tens ones tens ones tens ones Subtracting without Regrouping Number Line Counting Back When subtracting 1, 2, or more from a number, you can subtract by counting back. 0 1 2 3 4 5 6 7 8 9 10 Example: 6 – 2 = 4 © Copyright NewPath Learning. All Rights Reserved. 93-4202 www.newpathlearning.com Subtracting Two-digit Numbers

Adding Three-digit Numbers Subtracting Three-digit Numbers Add the ones: Regroup: What is the total number of marbles? How many more marbles does Sue have than Mike? A B Ungroup: B 7 ones + 8 ones = 15 ones Subtract the ones: A 1 ten = 10 ones Ungroup: B Subtract the tens: A 1 hundred = 10 tens Subtract the hundreds: A 16 ones – 8 ones = 12 tens – 4 tens = Add the tens: A 1 ten + 4 tens + 7 tens = 12 tens Add the hundreds: A 1 hundred + 1 hundred + 2 hundreds = 4 hundreds 15 ones = Regroup: B 12 tens = Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 1 4 1 7 2 + 5 ones tens hundr eds 1 1 1 2 + 7 8 5 2 ones tens hundr eds 1 4 7 + 7 8 5 ones tens hundr eds 2 4 425 total number of marbles 1 2 16 3 4 4 2 8 ones tens hundr eds x xx x xx xx xx 3 16 4 2 6 8 8 ones tens hundr eds 12 2 16 3 4 6 8 8 8 1 ones tens hundr eds 12 278 Sue’s marbles 147 Mike’s marbles 7 8 4 7 1 2 6 8 2 3 4 8 xx hundreds – hundreds = 3 2 16 ones – 8 ones = 8 ones 12 tens – 4 tens = 8 tens hundreds – hundreds = hundred 3 2 1 3 4 2 © Copyright NewPath Learning. All Rights Reserved. 93-4301 www.newpathlearning.com Adding & Subtracting Three-digit Numbers 248 436 Mike’s marbles Sue’s marbles

Adding Three-digit Numbers Subtracting Three-digit Numbers Add the ones: Regroup: What is the total number of marbles? How many more marbles does Sue have than Mike? A B Ungroup: B 7 ones + 8 ones = 15 ones Subtract the ones: A 1 ten = 10 ones Ungroup: B Subtract the tens: A 1 hundred = 10 tens Subtract the hundreds: A 16 ones – 8 ones = 8 ones 12 tens – 4 tens = 8 tens Add the tens: A 1 ten + 4 tens + 7 tens = 12 tens Add the hundreds: A 1 hundred + 1 hundred + 2 hundreds = 4 hundreds 15 ones = 1 ten and 5 ones Regroup: B 12 tens = 1 hundred and 2 tens Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 4 1 7 2 + ones tens hundr eds 1 2 + 7 8 5 2 ones tens hundr eds 4 7 + 7 8 ones tens hundr eds 425 total number of marbles 2 16 3 4 4 2 8 ones tens hundr eds x xx x xx xx xx 3 16 4 2 6 8 8 ones tens hundr eds 2 16 3 4 6 8 ones tens hundr eds 278 Sue’s marbles 147 Mike’s marbles 7 8 4 7 1 2 6 8 2 3 4 8 xx hundreds – hundreds = hundred 3 2 1 3 4 2 Key Vocabulary Terms • add • ones • total • digit • regroup • ungroup • hundreds • subtract • more • tens © Copyright NewPath Learning. All Rights Reserved. 93-4301 www.newpathlearning.com Adding & Subtracting Three-digit Numbers 248 Mike’s marbles 436 Sue’s marbles \|xiBAHBDy01633lz[

Number Line 4 x 5 Using a Pattern to Multiply Array Diagram 4 x 5 = 20 number of groups number in all number in each group • • Count by 5’s four times • • Numbers that are multiplied are called factors. 4 groups of 5 The answer is the product. } 0 5 10 15 20 25 1 2 3 4 0 1 2 3 4 5 6 7 8 9 1 x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9 0 2 4 6 8 10 12 14 16 18 2 x 0 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9 0 3 6 9 12 15 18 21 24 27 3 x 0 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9 0 4 8 12 16 20 24 28 32 36 4 x 0 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9 Area Model Addition Sentence Equal Shares Multiplication is repeated addition • 4 5 4 x 5 = 20 20 factor factor Product Multiply 4 x 5 4 x © Copyright NewPath Learning. All Rights Reserved. 93-4302 www.newpathlearning.com Multiplication Concepts & Strategies

Number Line x Using a Pattern to Multiply Array Diagram 4 x 5 = • • Count by 5 ’s times • • Numbers that are multiplied are called factors. 4 groups of 5 The answer is the product. } 0 21 1 x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9 2 x 0 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9 3 x 0 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9 4 x 0 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9 Area Model Addition Sentence Equal Shares Multiplication is repeated • 4 5 4 x 5 = 20 20 Multiply 4 x 5 4 x Key Vocabulary Terms • addition sentence • area model • array diagram • equal shares • factor • multiplication • number line • product • times © Copyright NewPath Learning. All Rights Reserved. 93-4302 www.newpathlearning.com Multiplication Concepts & Strategies \|xiBAHBDy01652mzV

1 X 0 2 3 4 5 6 7 8 9 10 1 0 2 3 4 5 6 7 8 9 10 11 00 22 33 44 55 66 77 88 99 10 10 2 0 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 0 x 0 0 x 1 0 x 2 0 x 3 0 x 4 0 x 5 0 x 6 0 x 7 0 x 8 0 x 9 0 x 10 1 x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9 1 x 10 2 x 0 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9 2 x 10 3 x 0 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9 3 x 10 4 x 0 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9 4 x 10 5 x 0 5 x 1 5 x 2 5 x 3 5 x 4 5 x 5 5 x 6 5 x 7 5 x 8 5 x 9 5 x 10 6 x 0 6 x 1 6 x 2 6 x 3 6 x 4 6 x 5 6 x 6 6 x 7 6 x 8 6 x 9 6 x 10 7 x 0 7 x 1 7 x 2 7 x 3 7 x 4 7 x 5 7 x 6 7 x 7 7 x 8 7 x 9 7 x 10 8 x 0 8 x 1 8 x 2 8 x 3 8 x 4 8 x 5 8 x 6 8 x 7 8 x 8 8 x 9 8 x 10 9 x 0 9 x 1 9 x 2 9 x 3 9 x 4 9 x 5 9 x 6 9 x 7 9 x 8 9 x 9 9 x 10 10 x 0 10 x 1 10 x 2 10 x 3 10 x 4 10 x 5 10 x 6 10 x 7 10 x 8 10 x 9 10 x 10 • The numbers along the first column and top row are factors. The numbers inside the table are products. • To find the product of two factors, locate one of the factors in the first column and then find the other factor in the top row. The number in the square where the column and row meet is the product. © Copyright NewPath Learning. All Rights Reserved. 93-4303 www.newpathlearning.com Multiplication Table

1 X 0 2 3 4 5 6 7 8 9 10 1 0 2 3 4 5 6 7 8 9 10 11 00 22 33 44 55 66 77 88 99 10 10 2 0 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100 0 x 0 0 x 1 0 x 2 0 x 3 0 x 4 0 x 5 0 x 6 0 x 7 0 x 8 0 x 9 0 x 10 1 x 0 1 x 1 1 x 2 1 x 3 1 x 4 1 x 5 1 x 6 1 x 7 1 x 8 1 x 9 1 x 10 2 x 0 2 x 1 2 x 2 2 x 3 2 x 4 2 x 5 2 x 6 2 x 7 2 x 8 2 x 9 2 x 10 3 x 0 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 x 6 3 x 7 3 x 8 3 x 9 3 x 10 4 x 0 4 x 1 4 x 2 4 x 3 4 x 4 4 x 5 4 x 6 4 x 7 4 x 8 4 x 9 4 x 10 5 x 0 5 x 1 5 x 2 5 x 3 5 x 4 5 x 5 5 x 6 5 x 7 5 x 8 5 x 9 5 x 10 6 x 0 6 x 1 6 x 2 6 x 3 6 x 4 6 x 5 6 x 6 6 x 7 6 x 8 6 x 9 6 x 10 7 x 0 7 x 1 7 x 2 7 x 3 7 x 4 7 x 5 7 x 6 7 x 7 7 x 8 7 x 9 7 x 10 8 x 0 8 x 1 8 x 2 8 x 3 8 x 4 8 x 5 8 x 6 8 x 7 8 x 8 8 x 9 8 x 10 9 x 0 9 x 1 9 x 2 9 x 3 9 x 4 9 x 5 9 x 6 9 x 7 9 x 8 9 x 9 9 x 10 10 x 0 10 x 1 10 x 2 10 x 3 10 x 4 10 x 5 10 x 6 10 x 7 10 x 8 10 x 9 10 x 10 • The numbers along the first column and top row are factors. . The numbers inside the table are pro duct. • To find the of two factors, locate one of the factors in the first column and then find the other factor in the top row. The number in the square where the column and row meet is the . Multiplication Table © Copyright NewPath Learning. All Rights Reserved. 93-4303 www.newpathlearning.com \|xiBAHBDy01653tz]

Division Sentence Using Multiplication to Divide How Many Groups? 1. 2. 3. How Many in Each Group? 12 – 4 = 8 8 – 4 = 4 4 – 4 = 0 Using a Number Line • Count back to divide • Start at 12 • Count back in 3s 0 5 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19 15 20 4 3 2 1 Bob, Sue and Mike picked 12 apples to share equally. How many will each get? We use repeated subtraction to find out how many groups of 4 are in 12. We subtracted 4 three times. Therefore, there are 3 groups of 4 in 12. • 3 equal groups • 4 in each group 12 ÷ 3 = 4 number of apples number of apples in each basket number of baskets dividend divisor quotient We use division to find the number in each group. 1 2 3 4 5 6 7 8 9 10 11 12 factor factor product dividend divisor quotient number of equal groups number in each group group size total number total number number of groups 12 ÷ 3 = 4 Bob Sue Mike 3 x 4 = 12 3 x 4 = 12 12 ÷ 3 = 4 12 ÷ 3 = 4 © Copyright NewPath Learning. All Rights Reserved. 93-4304 www.newpathlearning.com Division Concepts & Strategies

Division Sentence Using Multiplication to Divide How Many Groups? 1. 2. 3. How Many in Each Group? 12 – 4 = 8 8 – 4 = 4 Using a Number Line • Count back to divide • Start at 12 • Count back in 3s 0 5 1 2 3 4 6 7 8 9 10 11 12 13 14 15 4 3 2 1 Bob, Sue and Mike picked 12 apples to share equally. How many will each get? We use to find out how many groups of 4 are in 12. We subtracted 4 three times. Therefore, there are 3 groups of 4 in 12 . • 3 equal groups • 4 in each group 12 ÷ 3 = 4 We use to find the number in each group. 1 2 3 4 5 6 7 8 9 10 11 12 12 ÷ 3 = 4 8 – 4 = 4 Key Vocabulary Terms • dividend • division • division sentence • divisor • factor • group • number line • product • quotient • repeated subtraction Division Concepts & Strategies Bob Sue Mike © Copyright NewPath Learning. All Rights Reserved. 93-4304 www.newpathlearning.com \|xiBAHBDy01645ozX

Problem Solving Strategies Using Multiplication to Divide How Many Groups? $ 3 + $ 2 = $ 5 Using a Number Line • Count back to divide • Start at 12 • Count back in 3s 0 5 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19 15 20 4 3 2 1 12 ÷ 3 = 4 Jane spent $3 to buy a hot dog and $2 to buy an ice cream. How much did she spend? whole part part • Add to find the whole $ 12 – $ 3 = $ 9 • Subtract to find a part Ken had $12. He bought a ball for $3. How much money does he have left? Commutative Property of Addition Identity (zero) Property Relating Addition & Subtraction Associative Property of Addition • Adding 4 and 5 to get 9 is the opposite of 9 minus 5, leaving 4. • The sum of any number and zero is that same number. • Add the addends in any order and the sum will be the same. • Group the addends in any way and the sum will be the same. • 4 + 5 has the same sum as 5 + 4 • Although the addends were grouped in different ways, the sum is the same. whole part part addends difference sum addend addend sum 33 12 12 22 33 ?? 99 44 55 ?? 4 + 5 = 9 4 5 9 5 + 4 = 9 5 4 9 4 + 5 = 9 and 9 – 5 = 4 8 + ( 2 + 3) = 8 + 5 = 13 ( 8 + 2) + 3 = 10 + 3 = 13 8 + ( 2 + 3) = 8 + 5 = 3 © Copyright NewPath Learning. All Rights Reserved. 93-4306 www.newpathlearning.com Addition & Subtraction Number Sense

Problem Solving Strategies Jane spent $3 to buy a hot dog and $2 to buy an ice cream. How much did she spend? whole part part • to find the whole – • to find a part Ken had $12. He bought a ball for $3. How much money does he have left? Commutative Property of Addition Identity (zero) Property Relating Addition & Subt raction Associative Property of Addition • Adding 4 and 5 to get 9 is the opposite of 9 minus 5, leaving 4. • The sum of any number and zero is that same number. • Add the in any order and the will be the same. • Group the in any way and the will be the same. • 4 + 5 has the same sum as 5 + 4 • Although the addends were grouped in different ways, the sum is the sam . whole part part ? 99 44 55 ? 4 + 5 = 9 4 5 9 5 + 4 = 9 5 4 9 4 + 5 = 9 and 9 – 5 = 4 8 + ( 2 + 3) = 8 + 5 = 13 ( 8 + 2) + 3 = 10 + 3 = 13 Key Vocabulary Terms • add • difference • subtract • addend • identity property • sum • associative property • minus • whole • commutative property • part Addition & Subtraction Number Sense © Copyright NewPath Learning. All Rights Reserved. 93-4306 www.newpathlearning.com \|xiBAHBDy01636mzV

Draw a Picture Read & understand Reflect & check Use your strategy to solve the problem 1 Plan 2 3 4 The Four-Step Method Strategies Make a Graph or Table Find a Pattern Work Backward Write a Number Sentence Day Number of Butterflies N u m b e r o f S tu d e n ts Monday Tuesday Wednesday Thursday 14 8 20 26 ? $ 7 m $ 16 $ 16 $ 7 m Day 1 243 miles 168 miles 212 miles allowance candy drink Day 2 $ 16 – $ 7 = m $ 16 – $ 7 = $ 9 m = $ 9 Day 3 ? • What do I need to find? • Identify and underline clue words • Look for something that changes in a predictable way. • Identify the steps in a problem and work backward doing the reverse of each step. • Make a graph or a table to compare information and to see patterns. • Write a number sentence and solve it to find the missing part. • Did I answer the question? • Is my answer probable? • Which strategy do I use? • Draw a picture • Find a pattern • Make a graph or table • Write a number sentence • Work backwards TOTAL ? – $ 3 – $ 2 • Draw a picture when the problem describes some action. ? + $ 3 + $ 2 $ 5 $ 5 money left allowance candy drink money left Clue Words Clue Words Addition Subtraction Multiplication Division • sum • total • in all • difference • how much more • product • total • times • share • average • quotient © Copyright NewPath Learning. All Rights Reserved. 93-4310 www.newpathlearning.com Problem-Solving Strategies

\|xiBAHBDy01661ozX Draw a Picture Read & understand Reflect & check Use your strategy to solve the problem 1 Plan 2 3 4 The Four-Step Method Strategies Make a Graph or Table Find a Pattern Work Backward Write a Number Sentence N u m b e r o f S tu d e n ts Monday Tuesday Wednesday Thursday 14 8 20 26 ? $ 7 m $ 16 $ 16 $ 7 m Day 1 243 miles 168 miles 212 miles allowance candy drink Day 2 $ 16 – $ 7 = m $ 16 – $ 7 = $ 9 m = $ 9 Day 3 ? • What do I need to find? • Identify and underline clue words • Look for something that changes in a predictable way. • Identify the steps in a problem and work backward doing the reverse of each step. • Make a graph or a table to compare information and to see pattern s . • Write a number sentence and solve it to find the missing part . • Did I answer the question? • Is my answer probable? • Which strategy do I use? • Draw a picture • Find a pattern • Make a graph or table • Write a number sentence • Work backwards TOTAL – $ 3 $ 10 – $ 2 • Draw a picture when the problem describes some action . + $ 3 + $ 2 $ 5 money left allowance candy drink money left Clue Words Clue Words Addition Subtraction Multiplication Division Key Vocabulary Terms • addition • product • average • quotient • difference • share • division • strategy • graph • subtraction • how much more • sum • in all • table • multiplication • times • number sentence • total • pattern • • • • • • • • • • • Day Number of Butterflies Problem-Solving Strategies © Copyright NewPath Learning. All Rights Reserved. 93-4310 www.newpathlearning.com

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

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