• Elementary Mathematics Grade 1 Unit 8

    Subject: Mathematics
    Grade: 1 
    Timeline: 14 days
    Unit 8 Title: Measurement and Geometry

    Unit Overview: 
    This unit will provide the foundation for students to develop an understanding of the meaning and processes of attributes and measurement.  The first graders will use Non-Standard and Standard objects to measure items.  More focus is spent on non-standard objects in first grade to enhance the students focus on how to measure correctly. 
    First grade students will also use their beginning knowledge of defining and non-defining attributes of shapes to identify, name, build and draw shapes (including triangles, squares, rectangles, and trapezoids). They will understand that defining attributes are always-present and will learn to classify a particular object (e.g., number of sides, angles, etc.). They also will understand that non-defining attributes are features that may be present, but do not identify what the shape is called (e.g., color, size, orientation, etc.).
    Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language.  The terms students should learn to use with increasing precision with this cluster are: measure, order, length, height, more, less, longer than, shorter than, about, a little less than, a little more than, shape, closed, open, side, attribute, feature, two-dimensional, rectangle, square, trapezoid, triangle, half-circle, and quarter-circle and  three-dimensional.

    Unit Objectives:
    Students must be able to:
    • distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
    • identify various attributes by using the knowledge attained during the lessons.
    • order three objects by length; compare the lengths of two objects indirectly by using a third object.
    • indirectly measure objects by comparing the length of two objects by using a third object as a measuring tool.
    • express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
    • use multiple copies of one object to measure a larger object.

    Focus Standards:
    PA.CCSS.Math.Content.CC.2.3.1.A.1 Compose and distinguish between two- and three-dimensional shapes based on their attributes. (1.G.1, 1.G.2)
    PA.CCSS.Math.Content.CC.2.3.1.A.2 Use the understanding of fractions to partition shapes into halves and quarters. (1.G.3)
    PA.CCSS.Math.Content.CC.2.4.1.A.1 Order lengths and measure them both indirectly and by repeating length units. (1.MD.1, 1.MD.2)
    PA.CCSS.Math.Content.CC.2.4.1.A.4 Represent and interpret data using tables/charts. (1.MD.4)

    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.
    #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.  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 and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. 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, 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.

    Concepts - Students will know:
    • The meaning of attributes
    • How to use attributes to categorize shapes
    • The meaning of length
    • Non-standard tools can be used to measure items
    • Complex shapes can be created out of basic shapes
    Competencies -Students will be able to:
    • Distinguish between defining and non-defining attributes
    • Order up to 3 objects by length
    • Use a third object to compare 2 other objects
    • Compose shapes using other shapes either 2 or 3 dimensional

    • Unit 8 Progress Check
    • Daily RSA

    Elements of Instruction:
    Students leaving a Kindergarten Common Core Classroom spent the year gaining understanding in measurement and data.  They were given many opportunities to spent time comparing measureable attributes by describing several measurable attributes of a single object, comparing two objects with a measurable attribute in common and classifying objects into given categories.  Kindergarten geometry standards gave students the experiences they needed to become proficient in identifying and describing shapes and analyzing, comparing, creating, and composing shapes.

    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 eight include:
    • Go Forward
    • Back Up
    • Attribute Spinner
    • Double or Nothing
    • Fact Power Game
    • Shaker Addition Top-It
    • Addition Top-It
    • High Roller
    • Disappearing Train Game