K-6 Everyday Mathematics Program

• Scope & Sequence
• Curriculum Features
• Program Components for Grades 1-6
• Lesson Structure
• Lesson Components
• Cross-Curricular Links
• Additional Information about Tools and Pedagogy
• Program Components for Kindergarten

The mathematics program in K-6 is based on the following basic principles:

• Students acquire knowledge and skills, and develop an understanding of mathematics from their own experience. Mathematics is more meaningful when it is rooted in real life contexts and situations, and when children are given the opportunity to become actively involved in learning.
• Children begin school with more mathematical knowledge and intuition than previously believed. A K-6 curriculum should build on this intuitive and concrete foundation, gradually helping children gain an understanding of the abstract and symbolic.
• Teachers, and their ability to provide excellent instruction, are the key factors in the success of any program.

Scope & Sequence

The scope of the K-6 Everyday Mathematics curriculum includes the following mathematical strands:

• Algebra and Uses of Variables
• Data and Chance
• Geometry and Spatial Sense
• Measures and Measurement
• Numeration and Order
• Patterns, Functions, and Sequences
• Operations
• Reference Frames

The curriculum is structured to provide multiple exposures to topics, and frequent opportunities to review and practice skills. A concept or skill that is informally introduced in kindergarten, for example, will be revisited, developed and extended numerous times, and in a variety of contexts, throughout the year and into later grades.

Curriculum Features

Real-life Problem Solving: An emphasis is placed on the application of mathematics to real world situations. Numbers, skills and mathematical concepts are not presented in isolation, but are linked to situations and contexts that are relevant to everyday lives.

• Balanced Instruction: Each lesson includes time for whole-group instruction as well as small group, partner, or individual activities. These activities balance teacher-directed instruction with opportunities for open-ended, hands-on explorations, long-term projects and on-going practice.

• Multiple Methods for Basic Skills Practice: The program provides numerous methods for basic skills practice and review. These include written and choral fact drills, Mental Math, routines, practice with fact triangles (flash cards of fact families), daily sets of review problems called Math Boxes, homework, timed tests and a variety of math games.

• Emphasis on Communication: Students are encouraged to explain and discuss their mathematical thinking, in their own words.

• Enhanced Home/School Partnerships: For grades 1-3, daily Home Links provide opportunities for family members to participate in the students' mathematical learning. Study Links are provided for most lessons in grades 4-6, and all grades include periodic letters to help keep parents informed.

Program Components for Grades 1-6

• Teacher's Reference Manual: The Teacher's Reference Manual provides comprehensive background information about mathematical content, teaching strategies, and classroom management.
• Teacher's Lesson Guide: This guide includes easy-to-follow three-part daily lesson plans. A unit organizer provides learning goals, planning tips, content highlights, and suggestions on problem-solving, cross-curricular links, and support for special student populations.
• Math Masters: This is a collection of Blackline masters that support daily lesson activities, projects, and explorations.
• Math Journal 1 and Math Journal 2: These are consumable books that provide a place for students to record their ongoing experiences and conjectures. They provide a permanent record of each student's mathematical development.
• Student Reference Book (Grades 3-6 only): The grade-level specific Student Reference Book contains mathematical essays providing explanations, illustrations, and examples of math skills and concepts. Students may use these pages during lesson instruction and when they need information to complete independent work.
  
  The Student Reference Book has a Game Section that includes directions for games and examples of how to play. Students use this section to help them clarify rules. Adaptations for some games are included to adjust the games for students' varying needs.
  
  A third section of the Student Reference Book is a collection of data including charts and tables. Students use this section of the book in conjunction with lessons and as a resource for problems and projects. The student glossary is located in the Student Reference Book along with a partial answer key for Check Your Understanding problems, which come at the end of most content pages.
  Minute-Math+ (Grades 1-3 only): This book contains brief activities for transition time and for spare moments throughout the day.
• Assessment Handbook: We encourage a balanced approach to student assessment, one that tracks the development of a child's mathematical understanding while giving the teacher useful feedback about instructional needs. The assessment information also provides adequate documentation for assigning grades.
  
  A variety of assessment techniques are already built into the program as Ongoing Assessment tips. Assessment suggestions are incorporated into the lesson descriptions, compiled for each unit in the Unit Organizers, and discussed in the Assessment Handbook. Feel free to pick and choose from the assessment tools and techniques suggested to design your own balanced assessment plan. The following simple rubric is to be used to categorize progress with any of the assessment activities:

General Rubric
Beginning (B)	Children cannot complete the task independently. They show little understanding of the concept or skill.
Developing (D)	Children show some understanding. However, errors or misunderstandings still occur. Reminders, hints, and suggestions are incorporated with understanding.
Secure (S)	Children can apply the skill or concept correctly and independently.

Lesson Structure

1. Lessons are divided into three parts: Teaching the Lesson: This section contains the main instructional activities for the lesson. This is where most new content is introduced.
2. Ongoing Learning and Practice: This section provides materials and suggestions for essential review, practice, and maintenance activities.
3. Options for Individualizing: This section includes activities for re-teaching, extra skill practice, enrichment, and meeting the needs of particular populations (ESL, etc). These suggested activities relate directly to the main instructional activities in Part 1 of the lesson.

Lesson Components

1. Math Messages: A Math Message is provided at the beginning of each lesson, beginning with Unit 4 in first grade. The Math Message usually leads into the lesson for the day; sometimes it reviews topics previously covered. Children should complete the Math Message before the start of each lesson. You can display Math Messages in a number of ways. You may want to write them on the board, overhead transparencies; or post them on the bulletin board; or duplicate them ahead of time on quarter-sheets as handouts.
2. Mental Math and Reflexes: The term Mental Math and Reflexes refers to exercises, usually oral, designed to strengthen children's number sense and to review and advance essential basic skills. Mental Math and Reflexes sessions should be brief, lasting no more than five minutes. Numerous short interactions are far more effective than fewer prolonged sessions. There are several kinds of Mental Math suggestions provided in the Lesson Guide. Some involve a choral counting routine; many are basic-skills practice with counts, operations, or measures; and some are problem-solving exercises. Ideally, children record their answers to these problems on slates. The Teacher's Lesson Guide suggests Mental Math and Reflexes exercises for almost every lesson. You are encouraged to use these exercises based on your children's needs and your classroom activities.
3. Math Boxes: Math Boxes are an excellent way to review material on a regular basis. They are one of the main components of review and skills maintenance. Math Boxes problems are not intended to reinforce the content of the lesson in which they appear. Rather, they provide continuous distributed practice of all skills and concepts in the program. The Math Boxes page does not need to be completed on the same day as the lesson, but it should not be skipped. These are designed as independent activities. Expect that your guidance will be needed, especially at the beginning of the school year when some problems review skills from prior years. If children struggle with a problem set, it is not necessary to create a lesson to develop these skills. You can modify or skip problems that you know are not review for your children. Lesson activities revisit skills throughout the year. Math Boxes also provide useful assessment information on review skills.
4. Games: We view games as enjoyable ways to practice number skills; especially those that help children develop fact power. Games are an integral part of the program, rather than an optional extra as they are traditionally used in many classrooms. Make sure that all children have time to play games, especially those who work at a slower pace or encounter more difficulty than their classmates. Games can also be played frequently without the same mathematical problems repeating because the numbers in most games are generated randomly. The game format eliminates the tedium typical of most drills. There will be times when certain games do not offer sufficient practice with a concept. On these occasions, we strongly encourage you to employ traditional drill problems. In some instances, you will use timed drills. Always strive for balance in your approach to drills and practice.
5. Home Links: Home Links are the Everyday Mathematics version of homework assignments. Each lesson has a Home Link. The next lesson has a follow-up to the previous Home Link. Home Links consist of active projects and ongoing review problems that show parents what the children can do in mathematics. A blank Home Link form has also been provided for you to create your own. Home Links activities serve three main purposes: They (1) promote follow-up, (2) provide enrichment, and (3) involve parents or guardians in their children's mathematics education. Many Home Links require children to interact with parents, other adults, or older children. Since primary caregivers or those likely to help with the homework are not necessarily "parents," Home Links instruct children to complete the activity with someone at home. At the beginning of the year, send home the introductory Family Letter to acquaint parents with the Everyday Mathematics program. Continue to involve families throughout the year by sending home unit-introduction letters that explain the content that will be covered. Everyday Mathematics also provides Family Letters that are meant to be sent home at the with particular Home Links. These letters explain an idea or an activity that parents might not be familiar with. All Family Letters and Home Links are included in the Math Masters book.
6. Explorations: In Everyday Mathematics, the term Explorations means time set aside for independent, small-group activities. In addition to providing the benefits of cooperative learning, small-group work lets all children have a chance to use manipulatives (such as the pan balance and base-10 blocks) that are limited in supply. As there are frequently not enough materials for everyone, you may decide to have small groups of children working on several Explorations simultaneously. Thus, you will need to plan how you will manage several different activities at the same time. Parent volunteers can be very helpful in these situations.
   The Explorations have been designed so that you can position the various activities at different stations around the room and have groups rotate among the stations (or rotate the materials among the groups).
   Whenever possible, you might find it helpful to organize the materials for each Exploration by keeping them together in a small plastic tub, pan, bin, bucket, or box. After the Explorations have been completed, you can make the materials available for review and free-time activities.
   
   Each Explorations lesson suggests three activities, with the option of adding others. Decide how many stations you will need to accommodate groups of three to five children each. Each station should have one kind of material for children to share. To ensure you have enough stations for all of your groups, you may want to set up two stations for each Exploration activity or set up additional familiar activities or games for children to complete independently while other groups are working on Explorations.
   
   Of all the Exploration activities suggested in the lesson, the first one, Exploration A, contains the main content of the lesson and requires the most teacher involvement at the outset. Try to spend most of your time at this station, although you will likely need to circulate as well, especially if parent volunteers are not available and particularly at the beginning of the year, when children are less independent. If you remain at one station as the children rotate through it, this will enable you to work with every child in a small group and to use the task at that station as an informal assessment opportunity.
   
   Beginning in second grade, Everyday Mathematics supplies instruction masters (found in the Math Masters book) for the Exploration activities. These masters aim to make the groups more independent and to incorporate reading into the Explorations process. The groups will need more help and attention at the beginning of the year. But as the year progresses and children become stronger readers, and as they familiarize themselves with some of the activities, they will become increasingly independent. You may want to mount the instruction sheets on tag board and/or laminate them so you will be able to use them over the course of the school year. You should set aside enough class time so that all of your students can experience the Explorations. Do not set up the Explorations stations solely as optional centers for children to use when they have finished their other work. If you do that, the children who need these experiences the most will get fewer opportunities to participate in Explorations activities.

Cross-Curricular Links

There are a variety of cross-curricular links in lessons including literature, social studies, language arts, history, consumer skills, science, and technology.

Additional Information about Tools and Pedagogy

• Unit Boxes: A unit box is a rectangular box displayed next to a problem or a set of problems. Unit boxes contain the labels or units of measure used in the corresponding problem(s). Unit boxes help children to think symbolically by encouraging them to see numbers as quantities or measurements of real objects.
• Slates: Most children and teachers genuinely enjoy using slates. They afford an excellent opportunity for everyone to quietly answer a question at the same time, and they help you to see at a glance which children may need extra help. Establish a routine for using slates. You might want to use one-word cues, such as Listen, Think, Write, Show, Erase. The following procedure, if used consistently, helps prevent confusion:
  • Explain each exercise aloud. Tell children to LISTEN. If children find the problems too challenging, you may want to write them on the board or overhead.
  • Have the children work the problems mentally. Be sure to give them time to THINK.
  • Instruct the children to WRITE their answers on their slates and keep them covered.
  • When most children have written their answers, tell them to SHOW their slates at the same time by holding them up facing you. Afterward, when appropriate, take a few minutes to have the children share their strategies.
    Have the children ERASE their slates.

Program Components for Kindergarten

• Teacher's Reference Manual: The Teacher's Reference Manual provides comprehensive background information about mathematical content, teaching strategies, and classroom management.
• Teacher's Guide to Activities: This book includes clear and complete explanations for implementing classroom activities and ongoing daily routines. It provides detailed notes, illustrations, and progress guideposts.
• Program Guide and Activity Masters: This provides teacher support material including program overview and philosophy, activity listings by mathematical content strand, curriculum and classroom arrangement strategies and a comprehensive glossary. Ready-to-use masters provide printed material for student activities and Home Links.
• Minute Math: This book contains brief activities for transition time and for spare moments throughout the day.
   

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