• # Elementary Mathematics Grade 1 Unit 7

Subject: Mathematics
Timeline: 14 days
Unit 7 Title: Algebraic Concepts

Unit Overview:

This unit features many new concepts not normally taught so intensively in 1st grade before.  It is very important to model within this unit since much of it will be “higher-level” for the students.  This unit is very engaging and builds upon the last units taught.

Students will develop an understanding of the concepts of joining, separating, and “the same amount/quantity as”.  Teachers should know that the compare problems are relatively difficult for students to master, so this unit is built to provide students’ time to grapple with the misleading language and difficult contexts involved in algebra type problems.  Once the language and context is developed concretely, first graders are ready to connect the context to the corresponding symbols (+, -, =) used in equations. Thus, students will learn that the equal sign does not mean “the answer comes next”, but that the symbol signifies an equivalent relationship that the left side ‘has the same value as’ the right side of the equation. Teachers should also note that a new concept to this unit is reasoning about whether or not equations are true or false.

Unit Objectives:

By the end of the unit students will develop an understanding of the concepts of joining, separating, and equivalencies.   Students practice problems with a “missing number” where they need to decide if it is an addition or subtraction problem before solving it.  Furthermore, students will learn that the equal sign does not always mean “the answer comes next”, but that the symbol signifies an equivalent relationship that the left side of an equal sign has the same value as the right side.   Students also use strategies and reasoning in deciding if equations are true or false, and how to make them true if they false.   Finally, students have the opportunity to collect data, create graphs, and then analyze the data collected.

Focus Standards:

PA.CCSS.Math.Content.CC.2.2.1.A.1 Represent and solve problems involving addition and subtraction within 20. (1.OA.2, 1.OA.6)
PA.CCSS.Math.Content.CC.2.2.1.A.2 Understand and apply properties of operations and the relationship between addition and subtraction. (1.OA.4, 1.OA.7, 1.OA.8)
PA.CCSS.Math.Content.CC.2.1.1.B.3 Use place value concepts and properties of operations to add and subtract within 100. (1.NBT.5)
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.

#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.

#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. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Concepts - Students will know:
• The equal signs means the same on both sides
• Multiple equations can equal the same sum
• The relationship between addition and subtraction with unknown numbers
Competencies -Students will be able to:
• Solve missing number equations with the missing number in various positions
• Complete name collection boxes using various equations
• Use addition and subtraction to solve and find unknown numbers

Assessments:
• Unit 7 Progress Check
• Daily RSA

Elements of Instruction:

In the Kindergarten Common Core Curriculum, Student decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). As students worked with First Grade Common Core Curriculum, previous units have provided the foundation for students to understand the basics of addition.  Students were presented with multiple opportunities to use concrete models to represent and solve addition within 20. Students used strategies such as counting on, making ten, and using double facts to solve near doubles. Children began building fluency for addition facts with sums of 10, + 0, + 1, and double facts. The units have also provided the foundation for students to understand the basics of subtraction.  Students began with building number models while engaging in multiple opportunities to use concrete materials to represent and solve subtraction facts within 20.  Students created and analyzed subtraction number model stories while also continuing to reinforce the importance of using a number line while building a foundation with subtraction.

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