• Elementary Mathematics Grade 3 Unit 1

    Subject: Mathematics
    Grade: 3 
    Timeline: 16 days
    Unit 1 Title: Place Value and Problem Solving with Addition and Subtraction

    Unit Overview: 
    This unit will give the opportunity for students to identify, compare, and order numbers through 10,000 including comparing total value of coin combinations, add and subtract using regrouping with 2- and 3-digit numbers to solve problems including two-step word problems (use equations with a symbol standing for the unknown quantity), also create word problem to match a combination of symbols and numbers, as well as identify missing numbers and symbols, round and estimate to the nearest 10 and 100 to solve problems. 

    Unit Objectives:
    At the end of this unit, all students must be able to use their prior knowledge of place value to identify the value of numbers. They will have to be able to order, round, and compare numbers.  Students must be able to add and subtract using regrouping with up to three digits.

    Focus Standards:
    PA.CCSS.Math.Content.CC.2.1.3.B.1 Apply place value understanding and properties of operations to perform multi-digit arithmetic. (3.NBT.1, 3.NBT.2)
    PA.CCSS.Math.Content.CC.2.2.3.A.4 Solve problems involving the four operations, and identify and explain patterns in arithmetic. (3.OA.8, 3.OA.9)
    PA.CCSS.Math.Content.CC.2.4.3.A.3 Solve problems and make change using a combination of coins and bills. 

    Mathematical Practice Standards:  
    #1 Make sense of problems and persevere in solving them.  
    Mathematically proficient students start by explaining to themselves the meaning of a problem and look for an entry point to its solution.  They then plan a solution pathway rather than jumping into a solution attempt.  They monitor and evaluate their progress and change course, if needed. Students might rely on using concrete objects or pictures to help conceptualize and solve a problem.  They then check their answers to problems using a different method, and continually ask themselves, “Does this make sense?”  These students can also understand the approaches of others to solving complex problems and identify correspondences between different approaches.
    #2 Reason abstractly and quantitatively.  
    Mathematically proficient students make sense of quantities and their relationships in problem situations.  They bring two complementary abilities to bear on problems, the ability to decontextualize-to abstract the given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and contextualize-to pause as needed to during the manipulation process in order to probe into the referents for the symbols involved.
    #3 Construct viable arguments and critique the reasoning of others.  
    Mathematically proficient students understand and use states assumptions, definitions, and previously established results in constructing arguments. They make a statement that they believe to be true but not yet proved and then build a progression of statements to explore its truth.  They justify their conclusions, communicate them to others and respond to the arguments of others.  Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.  
    #4 Model with mathematics.   
    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation.
    #5 Use appropriate tools strategically. 
    Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, or a calculator. Proficient students are sufficiently familiar with tools appropriate for their grade to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.   
    #6 Attend to Precision.  
    Mathematically proficient students try to communicate precisely to others.  They use clear definitions in discussions with others and in their own reasoning.  They state the meaning of the symbols they choose, including the equals sign, consistently and appropriately.  They calculate accurately and efficiently and give carefully formulated explanations to each other.
    #7  Look for and make use of structure.  
    Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. 
    # 8 Look for and express regularity in repeated reasoning.
    Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts... They continually evaluate the reasonableness of their intermediate results. 

    Concepts - Students will know:
    • A number up to 9,999 consists of an amount of thousands,  hundreds, tens and ones
    • Each digit in a number up to 9,999 has a value
    • To round a number to the nearest 10 or hundred, you must know the two closest tens or hundreds to that number and locate in that sequence how close or far the number is to those tens or hundreds. 
    • Numbers fall into an order on a number line 
    • Addition causes the value of a number to increase
    • Subtraction causes the value of a number to decrease
    • More than one step or operation may be needed to solve a problem
    Competencies -Students will be able to:
    • Build or draw representations of numbers to 9,999
    • Write numbers to 9,999 in standard, word and expanded form
    • Round two- or three-digit numbers to the nearest 10 or 100
    • Order numbers to 9,999 from greatest to least or least to greatest
    • Add numbers together using the partial-sums strategy
    • Subtract numbers using a variety of strategies including trade first and counting up
    • Solve one- and two- step problems involving addition and subtraction

    • Unit 1 Progress Check
    • Daily RSA

    Elements of Instruction:
    Students leaving a second grade Common Core Classroom have a deep knowledge of place value up to 1,000, can read, write and show numbers in expanded form, and understand that the three digits of a three digit number represent amounts of hundreds, tens, and one. They have a deep knowledge of addition and subtraction, and have used fact families, Fact Triangles, and games to help them learn addition and subtraction facts. Knowledge of these basic facts is vital to their success in the third grade classroom. They have fluency with subtraction within 100 using strategies. Second grade students can add and subtract two-digit numbers using various strategies.

    Each lesson has differentiation options for each portion of the lesson.  Additional differentiation options are listed with directions and student masters in the Teacher’s Guide to Games.  These games are foundational for this unit and should be used with students who are struggling with these foundations.
    • Base-10 Exchange (Place value concepts; counting and exchanging blocks)
    • Base 10 Trading (Place value concepts counting; and exchanging money)

    Interdisciplinary Connections:

    Additional Resources / Games:
    Students will play a variety of games that directly support the content of the lesson and the overall goals for the unit.
    Games for unit one include:
    • Less Than You
    • Target 50
    • Addition Top-It
    • Roll to 100
    • Name That Number
    • Beat the Calculator
    • Three Addends
    • Subtraction Top-It
    • Number Grid Difference
    • Round to 10
    • Round to 100
    • Money Exchange Game
    • Number Top-It