Mathematical Operations: 1, 2 & 3 Digit Addition & Subtraction Problem Solving & Checking, Author(s): Mary Lou Kallies, Grade Level: Elementary, Grade 3, Subject Area: Mathematics & Technology, - Teacher will launch unit by having students create collages showing visual representation of connection of Mathematics in everyday life, i.e., banking cooking, measuring, estimating, shopping, etc. and lead discussion of practical applications for mathematics in our lives and careers.

Planning Guide

Creating Learner-Focused
Schools

* Madison-Oneida BOCES- This document may not be reproduced in any form without the expressed written consent of the District Superintendent or his designee.

LU Title: Mathematical Operations: 1, 2 & 3 Digit Addition & Subtraction Problem Solving & Checking	Author(s): Mary Lou Kallies
Grade Level: Elementary, Grade 3	School Address: General Herkimer School, Keyes Road, Utica, New York 13502
Subject Area: Mathematics & Technology	School Phone/Fax: 315-792-2160

CONTENT KNOWLEDGE

Declarative	Procedural
Students will name components in an addition equation: addends and sum	Students will add 1, 2 and 3 digit numbers and check answers for accuracy (Optional technology use: Students may use a calculator, if available, to check answers for accuracy upon completion.)
Students will identify components in a subtraction equation: minuend, subtrahend and difference	Students will subtract 1, 2 and 3 digit numbers and check answers for accuracy (Optional: Students may use a calculator, if available, to check answers for accuracy upon completion.)
Students will explain concept of "trading" in the base 10 system when this is required in the solution of addition/subtraction problem	Students will create/solve math word problems involving 1, 2 and 3 digit addition and/or subtraction in their solutions.
Students will explain procedure for checking answers for accuracy: Addition -- Subtracting second addend from sum to equal first addend, and Subtraction -- Adding subtrahend and difference to equal minuend	Optional: Utilizing Computer and Math subject specific software, students may reinforce learning of 1, 2 and 3 digit addition and subtraction with specific programs focusing on these mathematical operations.

ESSENTIAL QUESTIONS

How do addition and subtraction help me function in the real world?
How do I express word problem(s) in the real world?

INITIATING ACTIVITY

Teacher will launch unit by having students create collages showing visual representation of connection of Mathematics in everyday life, i.e., banking cooking, measuring, estimating, shopping, etc. and lead discussion of practical applications for mathematics in our lives and careers.

Connection to State Learning Standards

Content Area: Mathematics & Technology (from NYS Mathematics, Science & Technology Learning Standards)

Level: Elementary, Grade 3

Benchmarks: 1. "Mathematical Reasoning: Students use mathematical reasoning to analyze, construct an argument [and] justify logical reasoning to reach simple conclusions"

Benchmarks: 2. "Number and Numeration: Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world…"

Standard: M.S.T.#3 -- Mathematics: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems thru the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.

Standard: M.S.T.#3 -- Mathematics: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-word settings, and by solving problems thru the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.

Unit Theme:

Mathematical Operations:

1-3 Digit Addition & Subtraction,

Problem Solving and Checking

Standard: M.S.T.#3 -- Mathematics: Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems thru the integrated study of number system, geometry, algebra, data analysis, probability and trigonometry.

Standard: E.L.A. Learning Standard #1: Students will read, write, listen and speak for information and understanding.

Benchmarks: 3. "Operations: Students use mathematical operations and relationships among them to understand mathematics…add, subtract,…..whole numbers."

Benchmarks: "Students will present information clearly…in oral and written form.

Learning Experiences

Declarative Knowledge

What declarative knowledge should e in the process of acquiring & integrating? As a result of the unit, the student will know or understand…

What experiences or activities will be used to help students acquire & integrate this knowledge?

What strategies will be used to help students construct meaning, organize and/or store the knowledge?

Describe what will be done.

1.) Students will name components in an addition equation: addends and sum, 2.) Students will identify components in a subtraction equation: minuend, subtrahend and difference, 3.) Students will explain concept of "trading" in the base 10 system when this is required in the solution of addition/subtraction problem, and 4.) Students will explain procedure for checking answers for accuracy: Addition -- Subtracting second addend from sum to equal first addend, and Subtraction -- Adding subtrahend and difference to equal minuend.

Hands-on learning experiences using math manipulative (counters) to improve understanding of "trading" in addition and subtraction

Mini-Lessons conducted by teacher aimed at clarifying aspects involved in mathematical operations/reasoning and identification of parts of each operation.

Word Web Activity focusing on linking mathematics and real life applications

"3 Minute Pause" Strategy adapted from DOL Learning Unit

"Think-Pair-Share" Strategy adapted from DOL Learning Unit

Teacher will launch unit by aiding students who brainstorm real life connections for using mathematics (i.e., banking, shopping, estimating, etc.) using word web graphic organizer as well as a K-W-L chart to guide instruction. Teacher will use an overhead projector to demonstrate adding and subtracting 1, 2, 3 digit addition and subtraction problems and use a graphic organizer to show part to whole and whole to part relationships to aid students to conceptualize addition and subtraction concepts. Teacher will give mini lessons on trading in a base 10 system, working from right to left -- column by column and checking answers for accuracy. Teacher may use pneumonic devices to learn names of components of operations. Teacher will divide class into pairs to use "Think-Pair-Share" and "3 Minute Pause" strategies for learning to process information and to gain understanding of the math operations. Teacher may offer use of technology to enhance learning, i.e., calculators for checki ng answers for accuracy and/or computers & math course specific software for practice and preparation for ensuing year's NYS Grade 4 Mathematics test.

Learning Experiences

Procedural Knowledge

What procedural knowledge will students be in the process of acquiring & integrating? As a result of this unit, students will be able to:

What will be done to help students construct models, shape & internalize the knowledge?

Describe what will be done.

1.) Students will add 1, 2 and 3 digit numbers and check answers for accuracy (Optional technology use: Students may use a calculator, if available to check answers for accuracy.), 2.) Students will subtract 1, 2 and 3 digit numbers and check answers for accuracy (optional: Students may use a calculator, if available, to check answers for accuracy.), 3.) Students will create/solve math word problems involving 1, 2 and 3 digit addition and/or subtraction in their solutions, and 4.) Optional: Utilizing Computer and Math subject specific software, students may reinforce learning of 1, 2 and 3 digit addition and subtraction with specific programs focusing on these mathematical operations.

"Think-Pair-Share" strategy from DOL Learning Unit

Hands-on Learning Experiences using math manipulative (counters) to show changed values involved in addition and subtraction when "trading". Optional: use of calculators to check accuracy of answers and/or practice/review with computers and math course specific software

Teacher will divide students into pairs to practice solving 1, 2, 3 digit addition and subtraction problems involving trading, and to check answers for accuracy. Groups will use "think-pair-share" strategy to work together as a team to solve problems to share with class at conclusion of lesson. Students may use calculators to check accuracy of answers and/or computer and math course specific software for added review and to prepare for ensuing year's NYS Grad 4 Mathematics Test.

Learning Experiences

Extending and Refining

What knowledge will students be extending and refining? Specifically, they will be extending and refining their understanding of…

What reasoning process will they be using?

Describe what will be done.

Students will work in groups to create their own word problems requiring 1, 2 and 3 digit addition and/or subtraction for solution. The final word problems will be compiled and shared with the class and class will work together to solve.

Comparing
Classifying

Inductive Reasoning

Deductive Reasoning

Error Analysis
Analyzing Perspectives
Constructing Support
Abstracting
Other:

Teacher will divide students into collaborative groups (2-3 students per group) to create their own word problems involving 1, 2 and 3 digit addition and or subtraction for solution. At the conclusion, small groups will share word problems with large group for class solution. Calculators may be used to check answers for accuracy. Number patterns will be reviewed and error analysis conducted to aid students to identify their own errors as well as those of others as they review number concepts and prepare for ensuing year's NYS Grade 4 Mathematics Test.

Planning Guide

Unit:

Step 1	Step 2	Step 3
*What knowledge* will students be using meaningfully? Specifically, they will be demonstrating their understanding of and ability to...........**	What reasoning process will they be using?	Describe student's products and performances and the criteria for evaluation.
	[ ] Decision Making (selecting from seemingly equal alternatives or examining the decisions of others) [ ] Problem Solving (seeking to achieve a goal by overcoming constraints or limiting conditions) [ ] Invention (creating something to meet a need or improve on a situation) [ ] Experimental Inquiry (generating an explanation for a phenomenon and testing the explanation) [ ] Investigation (resolving confusions or contradictions related to a historical event, a hypothetical past or future event, or to the defining characteristics of something) [ ] Systems Analysis (analyzing the parts of a system and how they interact) [ ] Other:	Products/Performances
		Criteria for evaluation

Rubric:

Key Questions:

What are the key elements, traits, or dimensions that will be evaluated?

Are the identified elements of equal importance or will they be weighed differently?

	Element #1	Element #2	Element #3	Element #4
Elements Scale	Students will name parts of addition and subtraction problems	Students will create word problems of own design, solve, check and present to class	Students will add 1, 2, 3 digit addition problems, solve and check	Students will subtract 1, 2, 3 digit subtraction problems, solve and check
Weights	Weighted equally	Weighted equally	Weighted equally	Weighted equally
4
3	Proficient -- Student shows proficiency meeting all Element 1 specifications	Proficient -- Student shows proficiency meeting all Element 2 specifications	Proficient -- Student shows proficiency meeting all Element 3 specifications	Proficient -- Student shows proficiency meeting all Element 4 specifications
2	In Progress -- Student is in progress meeting some of Element 1 specifications	In Progress -- Student is in progress meeting some of Element 2 specifications	In Progress -- Student is in progress meeting some of Element 3 specifications	In Progress --Student is in progress meeting some of Element 4 specifications
1	Emergent -- Student is beginning to meet Element specifications	Emergent -- Student is beginning to meet Element specifications	Emergent -- Student is beginning to meet Element specifications	Emergent -- Students is beginning to meet Element specifications

NOTE: Rubric or other performance assessment instruments may be used.

Constructing a Holistic
Scoring Tool
(Rubric or Activity Specific Key)

Key Questions:

* How many score points are needed to discriminate among the full range of different degrees of understanding, proficiency, or quality?

This response, product, or performance provides evidence of understanding of concept/principle/generalization or proficiency in skill/process/strategy.

Score Point 4	Score Point 3
[ ]Please see above, used the previous rubric form for this unit.	[ ]
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Score Point 2	Score Point 1
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Have You Considered These Yet?

Learn to Learn Skills:

Students may require mini-lessons reviewing/reinforcing place value and how and why "trading" values is necessary when adding and subtracting.

Assessment Modifications:

Rubrics utilized in unit were adapted from Utica City School District Technology and Curriculum Integration Plan, Dec. 1998 Edition.

Unit Schedule/Time Plan:

Approximately 4-6 weeks to achieve mastery level and preparation for these skills in preparation of NYS Grade 4 Mathematics text.

Written Overview:

This unit is designed to aid students to improve students understanding and appreciation of mathematical operations, number systems and information systems as well as to aid in their development of reasoning skills. Overall, this unit should prove to be a valuable guideline for aiding students to meet standards established in the NYS Mathematics, Science and Technology Learning Standards with special focus in this unit on mathematics.