• # Elementary Mathematics Grade 1 Unit 4

Subject: Mathematics
Timeline: 19 days

Unit Overview:

This unit will provide the foundation for students to understand the basics of addition.  Students will begin with multiple opportunities to use concrete models to represent and solve addition within 20. Students will then use strategies such as counting on, making ten, and using double facts to solve near doubles. Children will begin building fluency for addition facts with sums of 10, + 0, + 1, and double facts.  At the end of this unit, another data lesson (1.MD.4) is again infused to allow the first graders to build more of a foundation for collecting, interpreting and representing data.

Unit Objectives:

At the end of this unit, all students must be able to add within 20, demonstrate fluency for addition facts with sums of 10, +0, +1 and double facts.  Students must be able to represent, solve, and read number models in multiple ways.

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.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.3, 1.OA.5, 1.OA.7)
PA.CCSS.Math.Content.CC.2.1.1.1.B.3 Use place value concepts and properties of operations to add and subtract within
100. (1.NBT.6)
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.  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.

#8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and then look both for general methods and for shortcuts.  They maintain oversight of the process, while attending to the details.  They continually evaluate their reasonableness of their immediate results.

Concepts - Students will know:
• How to add within 20
• How to fluently add basic facts
• Number Models
Competencies -Students will be able to:
• Practice their basic facts including doubles, +1, and +0
• Write Number Models

Assessments:
• Unit 4 Progress Check
• Daily RSA

Elements of Instruction:

In the Kindergarten Common Core Curriculum, students gain the understanding that addition is putting together and adding to, and understand subtraction is taking apart and taking from.  They represent addition and subtraction with manipulatives and drawings, become proficient in adding and subtracting within 20 to solve word problems and fluently add and subtract within 10.  Students can decompose numbers less than or equal to 10 into pairs in more than one way and record their decomposition with either a drawing or an equation. They can also find the number that will make 10 when given a number from 1 to 9.

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.