- Apply four basic operations (addition, subtraction, multiplication, and division) with symbols and variables to solve problems and to model, explain, and develop computational algorithms.

Every Excel sheet focuses on one of the four basic operational skills.  In first grade, the focus falls primarily on addition and subtraction.  Every sheet includes addition and subtraction, and the majority of the lessons themself deal with various ways to do addition or subtraction problems, including doubles facts, base ten blocks, and word problems.

Indicator 3: Teachers have knowledge of patterns, relationships, functions, symbols and models. Teachers:

• Understand patterns, relationships, functions, systems, and models,
• Recognize and use likeness and differences in defining and describing patterns with actions, words, objects, numbers, and set,
• Create, extend, and predict using geometrical and numerical patterns and sequences,
• Construct tables to illustrate a relationship,
• Illustrate open number sentences by describing relationships,
• Identify and apply variables, expressions and relationships,
• Use problem solving to give meaning to patterns, functions and relationships, and
• Use appropriate software applications to extend and promote understanding of patterns, functions, and relationships

Through the use of Excel sheets, almost every part of this indicator are met.  Students are writing addition sentences from word problems, and have to create word problems from number sentences.  This shows that they are able to form and describe relationships with number sentences.  They are also requred to create and extend patterns, recognize pattern units, and name patterns. 

Standard 9: Elementary teachers understand and use the processes of problem solving, reasoning and proof, communication, connection, and representation as the foundation for the teaching and learning of mathematics.

Indicator 3: Teachers develop instruction in communication that enable all students to:

• Organize and consolidate their mathematical thinking through communication;
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• Analyze and evaluate the mathematical thinking and strategies of others;
• Use the language of mathematics to express mathematical ideas precisely.

One of the lessons completed by my students (Excel 84) focused on developing number sense, and required students to tell different ways to represent a number.  For example, I would write a number on the board, and if the number was 12, then students would have to say "twelve tally marks" or "Six plus six equals twelve".  They could not say "Six add more is six" but were required to use the correct mathematical language to represent their ideas. 

Indicator 4: Teachers develop instruction in making connections that enables all students to:

• Recognize and use connections among mathematical ideas;
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
• Recognize and apply mathematics in contexts outside of mathematics

Every morning at calendar time, my students are helping me keep a count of the days we have been in school.  This is done through using straws to represent the various place values.  Once we have ten straws, we make a bundle and move it to the tens place, and so on.  One of the lessons (Excel 86) taught through the Excel program is focusing on place value, and counting by tens.  My students had no problem with it, because they were able to take the information they had gleaned from calendar time to use and understand base ten blocks.  They also began to use base ten blocks to represent numbers.  We play a game where I write a number on the board and they come up with various ways to represent it, be it tally marks, the number word, or so on.  Now, they are using base ten blocks to represent the numbers as well. 

Indicator 5: Teachers develop instruction in representation that enables all students to:

• Create and use representations to organize, record, and communicate mathematical ideas;
• Select, apply, and translate among mathematical representations to solve problems;
• Use representations to model and interpret physical, social, and mathematical phenomena

Excel 85 focuses on solving word problems using addition.  During this lesson, my students were learning how to read word problems and write addition sentences to go along with the problem.  Going from the word problem to the addition sentence is not very difficult for most students, and just requires them to follow a step by step procedure.  However, for this lesson, we did the lesson, and then altered it a bit.  I would write a number sentence on the board, and my students worked in groups to write a word problem to go with the addition sentence.  This activity focused on the same math strands, but required students to think about math differently.