Unit 1Numeration
9 lessons3 Weeks
Numeration
 Week 1
Lesson 1
Lesson 1.1: Representing Numbers
Students read and write 3- and 4-digit numbers. They learn that our number system is based on groups of 10, all numbers are made from digits, and a place value is the value of the place a digit has in a number. Students show numbers with place-value blocks. They write 3- and 4-digit numbers in standard form, expanded form, and word form. Students learn to use a place-value chart. They solve problems to demonstrate their understanding.
Lesson 2
Lesson 1.2: Ways to Name Numbers
Learners use place value to name numbers in different ways. Learners name numbers as so many thousands, so many hundreds, so many tens, and so many ones. They name some numbers, including years and addresses, using thousands and hundreds, and only hundreds. They also name some numbers using only tens and only ones. Throughout the lesson, learners use place-value blocks to help them solve problems.
Lesson 3
Lesson 1.3: Greater Numbers
Students read and write numbers in the ten thousands and hundred thousands. They learn how a number s digits are grouped in periods for ones and thousands. Learners use a place-value chart to represent numbers in standard form, word form, and expanded form. They use place value to show different ways to compose and decompose numbers.
 Week 2
Lesson 4
Lesson 1.4: Place Value Relationships
Students learn how digits within a multi-digit whole number relate to each other by their place value. Learners analyze the values of different digits and recognize that when two digits next to each other in a number are the same, the value of the digit on the left is ten times that of the digit to the right. Students write place values for given digits in numbers through six digits to verify place value relationships.
Lesson 5
Lesson 1.5: Comparing Numbers
Learners compare numbers having as many as five digits and designate the comparisons using the >, <, and = symbols. Students use place-value charts, place-value blocks, and number lines to help them compare numbers. They learn that they can compare numbers by comparing the number of digits in the numbers and the values of the digits.
Lesson 6
Lesson 1.6: Ordering Numbers
Students order 3-digit, 4-digit, and 5-digit numbers. They use a place-value chart to help them arrange the numbers from greatest to least and from least to greatest. Students show numbers on a number line to show number order. Learners analyze data given in pictures and charts to solve problems involving ordering numbers.
 Week 3
Lesson 7
Lesson 1.7: Counting Numbers
Students determine the value of a collection of coins and bills. They count bills and coins including: $5 and $1 bills, half dollars, quarters, dimes, nickels, and pennies. Learners count on from greatest to least value using skip logic. They write the value of money with a dollar sign and a decimal point. They solve story problems and show different ways to add bills and coins to reach the total. Students draw bills and coins to show the sum.
Lesson 8
Lesson 1.8: Rounding on the Number Line
Students round numbers up to five-digits to the nearest ten, hundred, thousand or ten thousand. Students represent a number on a number line as being halfway between two consecutive multiples and round. Students describe the relative size of numbers with words such as: about, close to, or nearly. If a number is halfway between, students round to the greater number. Learners solve story problems by rounding.
Lesson 9
Lesson 1.9: Problem Solving: Writing to Explain
Students write mathematical explanations using words, pictures, numbers, and symbols to communicate their reasoning. Their explanations are correct, simple, complete, and easy to understand. They analyze, plan, solve, and evaluate problems using place-value charts, place-value blocks and number lines. Learners explain the concepts of rounding, multiples of 10, count on, and relative value. 
Unit 2Number Sense: Adding and Subtracting Whole Numbers
8 lessons3 Weeks
Number Sense: Adding and Subtracting Whole Numbers
 Week 4
Lesson 10
Lesson 2.1: Addition Properties
Some real-world can be solved using the commutative, associative, and identity properties of addition. Two or more numbers can be grouped and added in any order, and the sum of any number and 0 is that number. Students use the concepts of addition to model the commutative, associative, and identity properties of addition. They identify the addition property in an addition sentence. 
Lesson 11
Lesson 2.2: Using Mental Math to Add
Students solve problems by adding 2- and 3-digit numbers with mental math. They use place value and properties of addition to help solve problems. Techniques for doing addition calculations mentally, such as breaking apart numbers and making tens, involve changing the numbers or the expressions so that the calculation is easy to do mentally and has the same answer as the original conclusion. 
Lesson 12
Lesson 2.3: Using Mental Math to Subtract
Students solve problems by subtracting 2- and 3-digit numbers with mental math. They show more than one way to do a mental calculation. Techniques for doing subtraction calculations mentally, such as compensation and equal additions, involve changing the numbers or the expressions so that the calculation is easy to do mentally. The new problem has the same answer as the original. 
 Week 5
Lesson 13
Lesson 2.4: Estimating Sums
Students solve problems by estimating sums in more than one way. They solve by rounding to the nearest 10, 100, or using compatible numbers to estimate the sum for addition problem. Learners solve problems by estimating the sums.
Lesson 14
Lesson 2.5: Estimating Differences
Students solve problems by estimating differences in more than one way. Rounding and substituting compatible numbers are two ways to estimate differences by replacing numbers with other numbers that are close and easy to compute mentally. Learners round to the nearest 10 or 100, or use compatible numbers to estimate solutions to subtraction problems.
Lesson 15
Lesson 2.6: Relating Addition and Subtraction
Sums and differences can be estimated and calculated using a variety of procedures. Students use inverse operations to check subtraction and addition. They estimate to solve a problem, then add or subtract to find the answer. Students check their work using the inverse operation. The learners use strip diagrams to model and solve problems. Students solve with fluency one-step and two-step problems involving addition, using strategies based on properties of operations.
 Week 6
Lesson 16
Lesson 2.7: Adding and Subtracting on a Number Line
Sums and differences can be represented by lengths on a number line. Students create and use a number line to add and subtract. They solve problems by marking numbers on a number line with arrows to show the sum or difference. Learners write and solve a word problem that is modeled on a number line. They represent one- and two-step problems involving addition and subtraction of whole 2- and 3-digit numbers using pictorial models, number lines, and equations.
Lesson 17
Lesson 2.8: Problem Solving: Use Representations
Students use representations to solve problems. Some problems can be solved by writing and completing a number sentence or equation. Students use strip diagrams to show addition and subtraction. They analyze a problem, then draw a strip diagram to plan and solve. They estimate to evaluate the answer. Learners create and use representations to organize, record, and communicate mathematical ideas.
Unit 3Developing Proficiency: Adding and Subtracting Whole
9 lessons4 Weeks
Developing Proficiency: Adding and Subtracting Whole
 Week 6
Lesson 18
Lesson 3.1: Adding with an Expanded Algorithm
Students learn to add 3-digit numbers with the expanded algorithm. As modeled with place-value blocks, students learn that any 3-digit addition problem can be broken into a series of smaller problems based on place value: add the hundreds, add the tens and add the ones. Then the answers to the smaller problems are added together to determine the final sum. Students solve real-world and mathematical addition problems using the expanded algorithm, a strategy which involves place-value concepts.
 Week 7
Lesson 19
Lesson 3.2: Models for Adding 3-Digit Numbers
Students learn to use place-value blocks to model addition problems with two 3-digit numbers. They break apart whole numbers according to place value, then add the ones, the tens, and the hundreds. They learn when and how to regroup. Students use place-value blocks and place-value concepts to solve real-world and mathematical addition problems with 3-digit numbers.
Lesson 20
Lesson 3.3: Adding 3-Digit Numbers
Students learn to use the standard addition algorithm to solve addition problems with 3-digit numbers. They first add the ones, then the tens, then the hundreds, and regroup as needed. Students use rounding to estimate answers to the nearest ten or hundred, and then use the estimates to check whether the final answers are reasonable. 
Lesson 21
Lesson 3.4: Adding 3 or More Numbers
Students learn to use the standard addition algorithm to add three or more numbers. They first add the ones, then the tens, then the hundreds, and regroup as needed. Students also use rounding to estimate answers to the nearest ten or hundred, and then use the estimates to check whether the final answers are reasonable. They learn that a strip diagram can be used to represent a problem with three addends. 
 Week 8
Lesson 22
Lesson 3.5: Subtracting with an Expanded Algorithm
Students learn to subtract 3-digit numbers with the expanded algorithm. They learn that any 3-digit subtraction problem can be broken into a series of smaller problems based on place value: subtract the hundreds, from that result subtract the tens, and then from that result subtract the ones. Regrouping is done within the steps as needed. Students solve real-world and mathematical subtraction problems using the expanded algorithm, a strategy which involves place-value concepts.
Lesson 23
Lesson 3.6: Models for Subtracting 3-Digit Numbers
Students learn to use place-value blocks to model subtraction problems with two 3-digit numbers. They break apart whole numbers according to place value, then subtract the ones, the tens, and the hundreds. They learn when and how to regroup. Students use place-value blocks and place-value concepts to solve real-world and mathematical subtraction problems with 3-digit numbers.
Lesson 24
Lesson 3.7: Subtracting 3-Digit Numbers
Students learn to use the standard subtraction algorithm to solve subtraction problems with 3-digit numbers. They first subtract the ones, then the tens, then the hundreds, and regroup as needed. Students also estimate answers and then use the estimates to check whether the final answers are reasonable. Students solve mathematical and real-world subtraction problems with 3-digit numbers using the place-value concepts involved in rounding, estimates, and the standard algorithm.
 Week 9
Lesson 25
Lesson 3.8: Subtracting Across Zero
Students learn how to use the standard algorithm to subtract from numbers with one or more zeros. They learn to subtract from a number with one zero, and then from a number with two zeros. Students first subtract the ones, then the tens, and then the hundreds, regrouping as needed. Students use place-value concepts to solve real-world and mathematical subtraction problems involving numbers with zeros.
Lesson 26
Lesson 3.9: Problem Solving: Draw a Strip Diagram, Write an Equation
Students learn how to draw a strip diagram and write an equation to represent and solve addition and subtraction problems. They draw a strip diagram showing the parts they know and the part they do not know. They learn to represent the parts they do not know with an unknown, a symbol that stands for a number in an equation. Students add or subtract to find the unknown and solve the problem.
Unit 4Multiplication Meanings
6 lessons2 Weeks
Multiplication Meanings
 Week 9
Lesson 27
Lesson 4.1: Multiplication as Repeated Addition
Students learn to multiply by using repeated addition. They learn that multiplication is an operation that gives the total number when you join equal groups. Students learn that the numbers that are being multiplied are called factors, and the answer to a multiplication problem is called the product. They write both an addition sentence and a multiplication sentence to represent a multiplication situation. 
 Week 10
Lesson 28
Lesson 4.2: Arrays and Multiplication
Students learn that arrays, which show items arranged in equal rows, are one way to display objects in equal groups. Each row in an array has an equal number of items in it. The total number of items can be found by multiplying the number of rows by the number of items in each row. Students use arrays to solve real-world and mathematical multiplication problems.
Lesson 29
Lesson 4.3: Skip Counting on the Number Line
Students learn to use a number line and skip counting to show multiplication. Skip counting on the number line involves joining equal groups and is one way to think about multiplication. Students represent multiplication facts with equal jumps on a number line. Students use number lines and skip counting to solve real-world and mathematical multiplication problems.
Lesson 30
Lesson 4.4: The Commutative Practice
Students learn about the Commutative (Order) Property of Multiplication. The Commutative Property says that you can multiply numbers in any order and the product is the same. Students use arrays to help them understand this concept. Students use the Commutative Property to write multiplication facts and solve real-world and mathematical multiplication problems.
Lesson 31
Lesson 4.5: Writing Multiplication Stories
Students learn that stories can be written to describe multiplication facts. They learn to represent multiplication with verbal language and the symbolic language of mathematics. They use pictures to help them find products. Given a multiplication expression or sentence, students write multiplication stories involving equal groups, arrays, or comparison.
Lesson 32
Lesson 4.6: Problem Solving: Two-Step Problems
Students learn how to solve multiple-step problems. They learn that some word problems can be solved by first finding and solving a hidden problem, t and then using that answer to solve the original problem. Students learn to apply multiplication principals to problems arising in everyday life. They analyze, plan, solve, evaluate, and justify problems. Students solve real-world problems.