• Elementary Mathematics Grade 4 Unit 2


    Subject: Mathematics
    Grade: 4 
    Timeline: 11 days
    Unit 2 Title:  Multiplication

    Unit Overview: 
     
    This unit will give the opportunity for students to learn about factor pairs, multiples, prime and composite numbers.  Students will also build on the number concepts that were developed in the first unit of study through multiplication of multi-digit factors.  Students will be given the opportunity to further develop proficiency in solving number stories.   Examination of patterns will take place as well.  

    Unit Objectives:
     
    At the end of this unit, students must understand multiplication, the importance of arrays, factors, multiples, and divisibility rules. Students are expected to multiply a whole number up to four digits by a one-digit whole number and multiply two two-digit numbers.  Students will be using multiplication and division to solve multi-step word problems and represent these types of problems using equations with a letter standing for the unknown quantity.      

    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.5)
    PA.CCSS.Math.Content.CC.2.2.4.A.1  Represent and solve problems involving the four operations. (4.OA.1, 4.OA.2)
    PA.CCSS.Math.Content.CC.2.2.4.A.2 Develop and/or apply number theory concepts to find factors and multiples (4.OA.4) 
    PA.CCSS.Math.Content.CC.2.2.4.A.4 Generate and analyze patterns using one rule. (4.OA.5)

    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:
    • arrays
    • factors
    • multiples
    • divisibility rules
    • number stories involving multiplication
    Competencies -Students will be able to:
    • draw arrays
    • identify factors in various numbers
    • list the first 10 multiples of various numbers
    • use divisibility rules to begin studying division
    • solve number stories

    Assessments:
    • Unit 2 Progress Check
    • Daily RSA
    • Optional Quizzes (3)
    • 50 Facts Test

    Elements of Instruction:
     
    Learners in 4th grade will use their understanding of basic multiplication facts to enhance their understanding of multiplication.  In third grade, the students were introduced to the basic multiplication facts through 10 x 10.  The knowledge of these facts will allow students to continue to work with multiplication and understand all aspects of multiplication. 

    Differentiation:
     
    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.

    Interdisciplinary Connections:
    • Mental Math and Math message 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:
    • Baseball Multiplication
    • Multiplication Top-It
    • Multiplication BINGO
    • Rugs and Fences