Unit 1Multiplication Facts: Use Patterns and Known Facts
13 lessons5 Weeks
Multiplication Facts: Use Patterns and Known Facts
 Week 1
Lesson 1
Lesson 5.1: 2 and 5 as Factors
Students learn to use skip counting or patterns to help them multiply. They find patterns in the products for multiplication with factors of 2 or 5. Students also learn that multiples are the products of a number and other whole numbers. The learners use the patterns in data tables to help them learn the multiplication facts. Students complete multiplication facts with 2 or 5 as factors to help them recall facts to 10 by 10 with automaticity.
Lesson 2
Lesson 5.2: 9 as a Factor
Students learn to use patterns to multiply by a factor of 9 and to remember 9s facts. They analyze data tables to understand the patterns in the products. Learners complete multiplication facts with 9 as a factor to help them recall facts to 10 by 10 with automaticity.
Lesson 3
Lesson 5.3: Multiplying with 0 and 1
Students learn about patterns in the products for multiplication facts with factors of 0 or 1. They use the Identity and Zero Properties of Multiplication to solve problems. They draw a picture to represent a problem, and then solve. Students also write a greater than, less than, or equal sign between 2 multiplication sentences with factors of 0 or 1 to compare the values. Learners complete multiplication facts with 0 or 1 as factors to help them recall facts to 10 by 10 with automaticity.
 Week 2
Lesson 4
Lesson 5.4: Patterns for Facts
Students learn there are patterns in the products of multiplication facts with factors of 2, 5, or 9. They view patterns on a hundred chart. Students then learn to skip count to find multiples of 2, 5, or 9. They practice skip counting by writing the next number in a sequence. Students also complete multiplication facts with factors of 2, 5 or 9 to help them learn the multiplication facts up to 10 by 10 with automaticity.
Lesson 5
Lesson 5.5: 10 as a Factor
Students learn to use patterns to multiply by 10. They analyze a table of 10s facts to identify patterns. They learn to write a 0 to the right of the other factor when multiplying a number by 10. They learn that products of problems with 10 as a factor have a 0 in the ones place. Learners also skip count on number lines to help find the products. Learners complete multiplication facts with 10 as a factor to help them recall facts to 10 by 10 with automaticity.
Lesson 6
Lesson 5.6: The Distributive Property
Students learn to use the Distributive Property to break larger multiplication facts into the sum of two smaller multiplication facts. They break a large array of counters into two smaller arrays, write new facts, and find the sum. They use the Distributive Property to write the missing factor in multiplication sentences. 
 Week 3
Lesson 7
Lesson 5.7: 3 as a Factor
Students learn to multiply with 3 by breaking a multiplication fact into the sum of a 1s fact and a 2s fact. They view arrays representing problems, and they use counters or draw pictures to multiply by 3. Students also use a data table that shows 3s facts. Learners complete multiplication facts with 3 as a factor to help them recall facts to 10 by 10 with automaticity.
Lesson 8
Lesson 5.8: 4 as a Factor
Students learn to multiply with 4 by doubling a 2s fact. Learners view or create arrays representing multiplication problems, and then solve. They also use a data table that shows 4s facts. Learners complete multiplication facts with 4 as a factor to help them recall facts to 10 by 10 with automaticity.
Lesson 9
Lesson 5.9: 6 and 7 as Factors
Students learn to multiply with 6 or 7 by breaking apart a 6s or 7s fact into the sum of two smaller known multiplication facts. They break apart arrays with 6 or 7 as factors into two parts, find the product in each part, and add the sums to solve. Learners draw pictures or use counters to help multiply by 6 or 7. Learners complete multiplication facts with 6 or 7 as factors to help them recall facts to 10 by 10 with automaticity.
 Week 4
Lesson 10
Lesson 5.10: 8 as a Factor
Students learn to multiply with 8 by doubling a 4s fact or by breaking up the 8s fact into other smaller facts. Learners view or draw arrays representing multiplication problems with a factor of 8, and then solve. Students also use a data table that shows 8s facts. Learners complete multiplication facts with 8 as a factor to help them recall facts to 10 by 10 with automaticity.
Lesson 11
Lesson 5.11: Multiplying with 3 Factors
Students learn about the Associative Property of Multiplication, which says they can group and multiply three or more numbers in any way and the product will be the same. Learners group and multiply numbers to find the amount represented in two sections of an array or in two arrays. They use objects and draw pictures to solve multiplication problems with 3 factors. 
Lesson 12
Lesson 5.12: Multiplication Facts
Students use patterns and known facts to complete multiplication facts. They practice solving problems by breaking a larger multiplication fact into the sum of two smaller known multiplication facts. They also use arrays to represent problems and find patterns by skip counting to find products. Learners recall multiplication facts to multiply up to 10 by 10 with automaticity.
 Week 5
Lesson 13
Lesson 5.13: Problem Solving: Draw a Strip Diagram, Write an Equation
Students learn to solve multi-step problems by first finding the hidden question, answering the hidden question, and then using that answer to solve the problem. They use strip diagrams and write equations to represent each part of the problem. Students use symbols and mathematical language to communicate their mathematical ideas and reasoning.
Unit 2Meanings of Division
5 lessons2 Weeks
Meanings of Division
 Week 5
Lesson 14
Lesson 6.1: Division as Sharing
Students learn that division is an operation that is used to find how many equal groups there are or how many are in each group. They learn that sharing involves separating into equal groups, and is one way to think about division. Students solve real-world division problems by drawing pictures, using counters, or using strip diagrams. Learners determine the number of objects in each group when a set of objects is shared equally.
Lesson 15
Lesson 6.2: Division as Repeated Subtraction
Students learn that one way to divide is to repeatedly subtract equal-sized groups of objects and then count to find the number of groups. They solve real-world problems by drawing pictures, using counters, or drawing strip diagrams to represent repeated subtraction of equal groups. They also write division equations. Learners determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally.
 Week 6
Lesson 16
Lesson 6.3: Finding Missing Numbers in a Multiplication Table
Students learn to use a multiplication table to solve division problems. They learn that any division problem can be thought of as a multiplication equation showing a missing factor. Students rewrite the division problem as a missing factor equation. They then use the multiplication table to solve in three steps: locate the known factor, locate the product, and then find the missing factor. Learners determine a quotient using the relationship between multiplication and division.
Lesson 17
Lesson 6.4: Writing Division Stories
Students learn to write real-world division stories to show how many are in each group or how many groups there are in all. They plan and write a division story for an equation with a missing quotient, and then they use counters or draw a picture to solve. Learners solve problems involving division using strategies based on objects; pictorial models, including arrays and equal groups, properties of operations; or recall of facts.
Lesson 18
Lesson 6.5: Problem Solving: Draw a Strip Diagram, Write an Equation
Students learn that some word problems can be solved by drawing a strip diagram and then writing a division equation based on that representation. They analyze a word problem, plan how to solve by drawing a strip diagram to show what they know and what they don’t know, and then write a corresponding division equation to solve. This method allows students to visualize the quantitative relationships involved in the word problem. 
Unit 3Division Facts
8 lessons3 Weeks
Division Facts
 Week 7
Lesson 19
Lesson 7.1: Relating Multiplication and Division
Students learn that multiplication and division have an inverse relationship. They see how to use related multiplication facts to help divide. Learners analyze arrays to help explain the relationship between multiplication and division. They identify and write fact families, and they complete fact families by providing missing numbers. Students determine the unknown number in a multiplication or division equation when the unknown is either a missing factor or product.
Lesson 20
Lesson 7.2: Dividing with 2, 3, 4 and 5
Students learn to use the inverse relationship between multiplication and division to complete division facts. Students analyze a word problem with the divisor 2, 3, 4, or 5 and think about a related multiplication fact to help solve. Then they write an appropriate division equation. Learners also draw arrays to help solve problems. They are reminded of the two notations for writing division problems. 
Lesson 21
Lesson 7.3: Dividing with 6 and 7
Students learn to use multiplication facts to solve division problems and learn there is an inverse relationship between multiplication and division. They see that every multiplication fact is part of a fact family that also contains division facts. They analyze word problems and division equations with 6 or 7 as divisors and use related multiplication and division facts to find the quotients. Students also use strip diagrams to represent division problems. 
 Week 8
Lesson 22
Lesson 7.4: Dividing with 8 and 9
Students learn to use strip diagrams and the inverse relationship between multiplication and division to help solve division problems. Students analyze word problems when the divisors are 8 or 9. They think about an appropriate multiplication fact and then write the related division equation. Learners also see that division can be represented with arrays and pictures of equal groups. Learners recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts.
Lesson 23
Lesson 7.5: Even and Odd Numbers
Students learn that even numbers can be divided by 2, and odd numbers cannot be divided by 2. Students use the divisibility rule for 2. The rule states that even numbers have a 0, 2, 4, 6, or 8 in the ones place, and odd numbers have a 1, 3, 5, 7, or 9 in the ones place. Only an even number of objects can be put into groups of 2 with nothing left over. Students analyze numbers up to 10,000 to determine if a number is divisible by 2, and then write whether the number is even or odd.
Lesson 24
Lesson 7.6: Division Involving 0 and 1
Students learn to divide with 0 and 1 using related multiplication facts. They learn the division rules for 0 and 1: any number (except 0) divided by itself is equal to 1; any number divided by 1 is that number; and zero divided by any number (except 0) is 0. Zero cannot be a divisor. Learners first solve multiplication sentences to find quotients for related division sentences, and use division rules for dividing with 0 and 1 to help solve problems. 
 Week 9
Lesson 25
Lesson 7.7: Multiplication and Division Facts
Students learn that division facts can be recalled by thinking of related multiplication facts. They practice using multiplication and division fact families to solve real-world problems. Learners model problems with strip diagrams and then solve problems with related multiplication and division sentences using patterns and known facts. They learn that they can write a division problem as a missing-factor multiplication problem. 
Lesson 26
Lesson 7.8: Problem Solving: Two-Step Problems
Students learn to solve real-world two-step problems involving all four operations by first finding the answers to hidden questions and then using those answers to solve the given problem. Learners start by analyzing a word problem. They draw a strip diagram to represent the quantities in the hidden question. Then they compute the answer to the hidden question. They use that answer to draw a second strip diagram and compute the answer to original problem. 
Unit 4Number Sense: Multiplying 2-Digit by 1-Digit Numbers
5 lessons2 Weeks
Number Sense: Multiplying 2-Digit by 1-Digit Numbers
 Week 9
Lesson 27
Lesson 8.1: Multiplying by Multiples of 10
Students learn to use basic multiplication facts and place-value patterns to multiply a 1-digit number by a multiple of 10. They multiply the 1-digit number by the digit in the 10s place, and write 1 zero after this product. If the product of the basic fact ends in a zero, the answer will have 2 zeros. Learners apply the Associative Property of Multiplication, which states that the way factors are grouped does not affect the product. 
 Week 10
Lesson 28
Lesson 8.2: Breaking Apart to Multiply
Students learn that a 2-digit by 1-digit multiplication problem can be broken apart in two simpler problems. Students break the 2-digit number apart by place value and multiply each part by the 1-digit number. Then they add the partial products to arrive at the product of the original problem. Learners use arrays of place-value blocks to model the problem. 
Lesson 29
Lesson 8.3: Using Mental Math to Multiply
Students learn there is more than one way to multiply mentally. They use compensation to multiply a 2-digit number by a 1-digit number. Learners substitute numbers close to the numbers in the problem to make the computation easier, and then they use compensation to adjust the product using addition or subtraction to find the answer. Learners use mental math to multiply a 2-digit number by a 1-digit number.
Lesson 30
Lesson 8.4: Using Rounding to Estimate
Students learn to estimate products of a 2-digit number by a 1-digit number by combining the strategies of rounding numbers and multiplying by multiples of 10. Learners identify halfway numbers on number lines to help them round the 2-digit number to the nearest 10. They multiply the multiple of 10 by the 1-digit number to arrive at the estimated product. Learners use strategies including mental math to multiply a 2-digit number by a 1-digit number.
Lesson 31
Lesson 8.5 Problem Solving: Reasonableness
Students learn to check whether an answer to a real-world problem is reasonable by both comparing the actual answer to an estimate and deciding if the right question was answered. Learners practice analyzing problems and then justifying and evaluating the reasonableness of the solutions. They estimate solutions and check the answers against the questions and conditions in the problems.