• # Elementary Mathematics Grade 1 Unit 6

Subject: Mathematics
Timeline: 14 days
Unit 6 Title: Addition and Subtraction

Unit Overview:

This unit will continue on the foundation established in Unit 4 Addition and Unit 5 Subtraction.  This unit will expect students to build upon the strategies already taught by composing and decomposing numbers using 10 as a benchmark (1.0A.6) and being able to add up to 100.

Young students often believe that there are hundreds of isolated addition and subtraction facts to be mastered. However, when students understand the commutative and associative properties, they are able to use relationships between and among numbers to solve problems. Students should after completing Unit 4 and 6 now apply properties of operations as strategies to add and subtract. Students do not use the formal terms “commutative” and “associative”. Rather, they use the understandings of the commutative and associative property to solve problems.

Vocabulary will be essential to this unit as students learn to solve number stories.  The terms students should be using are: adding to, taking from, putting together, taking apart, comparing, unknown, sum, less than, equal to, minus, subtract, the same amount as, and (to describe (+) symbol).

Unit Objectives:

By the end of the unit students must be able to add within 100.  Students must mentally find 10 more or 10 less.  Student must subtract multiples of 10.  Students must also be able to solve word problems for addition and subtraction.

Focus Standards:

PA.CCSS.Math.Content.CC.2.2.1.A.1 Represent and solve problems involving addition and subtraction within 20. (1.OA.1, 1.OA.5)
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.4, 1.NBT.5, 1.NBT.6)

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:
• How to add and subtract within 100
• 10 more and 10 less
• Word Problems
Competencies -Students will be able to:
• Add and Subtract within 100
• Mentally compute 10 more and 10 less
• Solve word problems using strategies

Assessments:
• Unit 6 Progress Check
• Daily RSA

Elements of Instruction:

In previous units in first grade, students have had work with many Common Core State Standards. 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