• # Elementary Mathematics Grade 1 Unit 5

Subject: Mathematics
Timeline: 15 days
Unit 5 Title: Subtraction

Unit Overview:

This unit will provide the foundation for students to understand the basics of subtraction.  Students will begin with building number models while engaging in multiple opportunities to use concrete materials to represent and solve subtraction facts within 20.  Students will create and analyze subtraction number model stories while also continuing to reinforce the importance of using a number line while building a foundation with subtraction.

Students will then learn how to use strategies such as counting on, counting back, and other subtraction shortcuts to solve math problems. Children will begin building fluency for subtraction facts up to 10 and will then internalize these strategies to further the understanding for subtracting whole numbers up to 20.

Students will demonstrate their understanding of the relationship of addition and subtraction by working with fact families, fact triangles and equivalent names in this unit.  All of these will lead into situations that will develop meaning for the operation of subtraction

Unit Objectives:

At the end of this unit, all Students will then learn how to use strategies such as counting on, counting back, and other subtraction shortcuts to solve math problems.  Children will begin building fluency for subtraction facts up to 10 and will then internalize these strategies to further the understanding for subtracting whole numbers up to 20.  Students will demonstrate their understanding of the relationship of addition and subtraction by working with fact families, fact triangles and equivalent names in this unit.  All of these will lead into situations that will develop meaning for the operation of subtraction.

Focus Standards:

PA.CCSS.Math.Content.CC2.2.1.A.1 Represent and solve problems involving addition and subtraction within 20. (1.OA.1, 1.OA.5, 1.OA.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.  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. 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.

#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:
• Vocabulary for subtraction number models
• How subtraction models represent decomposing a total
• Properties of subtraction
• The relationship between addition and subtraction
Competencies -Students will be able to:
• Decompose a number to subtract within 10
• Use manipulatives, drawings, ten-frames, and decomposing to subtract within 20
• Read and write number models
• Use subtraction shortcuts to gain fluency with facts to 20
• Use fact families, fact triangles, and name collection boxes to connect addition and subtraction

Assessments:
• Unit 5 Progress Check
• Daily RSA

Elements of Instruction:

In the Kindergarten Common Core Curriculum, students gained the understanding of subtraction as taking apart and taking from. They represented subtraction within 10 using objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations. Students were giving opportunities to decompose numbers less than or equal to 10 into pairs in more than one way and record their decompositions with either drawings or an equation. They also were giving experiences to find a number that will make 10 when given a number from 1 to 9. Kindergarten subtraction standards gave students the experiences they needed to gain fluency subtracting within 5.

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.