• Elementary Mathematics Grade 4 Unit 2

    Subject: Mathematics
    Grade: 4 
    Timeline: 17 days
    Unit 2 Title:  Addition, Subtraction, and Time

    Unit Overview: 
    This unit will give students the opportunity to develop an understanding of addition, subtraction, and elapsed time. Students will be using base-ten blocks when working with addition and subtraction. This will give them an understanding of what happens when you add and subtract as well as continue their understanding on place value.  Students will be using number lines when working with rounding numbers. Finally, students will be solving number stories that involve addition and subtraction of mass, volume, and length. They will also solve problems involving elapsed time. All of the activities in this unit are designed to give students a deep understanding of addition, subtraction, and elapsed time.  

    Unit Objectives:
    At the end of this unit students must be able to add and subtract 6 digit numbers. They will be able to use their place-value skills to round numbers up to 100,000. Lastly, students will be able to use their understanding of time, liquid, mass, and length or distance to solve number stories.      

    Focus Standards:
    PA.CCSS.Math.Content.CC.2.1.4.B.2 Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.4)
    PA.CCSS.Math.Content.CC.2.2.4.A.1 Represent and solve problems involving the four operations. (4.OA.3)
    PA.CCSS.Math.Content.CC.2.4.4.A.1 Solve problems involving measurement and conversions from a larger unit to a smaller unit. (4.MD.2) 

    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 looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” 
    #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 involving quantitative relationships: the ability to decontextualize—to abstract a 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 the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects
    #3 Construct viable arguments and critique the reasoning of others.  
    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. 
    #4 Model with mathematics.
    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation.  They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
    #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, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course 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 try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.
    #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. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. 

    Concepts - Students will know:
    • the partial-sums algorithm 
    • trade-first subtraction
    • how to solve number stories with addition and subtraction
    • round rules and tendencies
    • estimating
    • the clock and its purpose
    • why clocks are used
    Competencies -Students will be able to:
    • solve multi-digit addition using partial-sums addition 
    • solve multi-digit subtraction problems using trade-first 
    • use a strategy to solve numbers stories involving addition and subtraction
    • round numbers to the nearest 100,000
    • estimate answers to various problems and check their final answers to close proximity 
    • tell time on analog and digital clocks
    • convert times between analog and digital clocks

    • Unit 2 Progress Check
    • Daily RSA

    Elements of Instruction:
    With previous common core standards focusing on single digit addition and subtraction, students will extend their knowledge to the addition and subtraction of multi-digit numbers. They will prove their mastery of partial-sums addition and trade-first subtraction. Students will also have the opportunity to prove their mastery of telling time using both versions of the clock. The rounding up to 100,000 is going to be the first time students are introduced to this concept with six digit numbers. See the differentiation section for some misconceptions that struggling students may have throughout this unit.  

    Each lesson has differentiation options for each portion of the lesson. It is necessary to point out some areas that struggling students may have during this unit.  Building a number is the first step to understanding place value, and in turn partial sums and trade first subtraction. Students who struggle with understanding the difference between the minute hand and the hour hand will struggle with telling time. If you notice any of these common problems, the individual students will need to be pulled for some extra focus of their misunderstood skill. 

    Interdisciplinary Connections:
    • Morning message and calendar routines.

    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 two include:
    • Base 10 Trading
    • Addition Top-It
    • Subtraction Top-It
    • Rounding to 100
    • Time Match