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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!
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