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The **decimal system **is the name of the system of counting and measurement that is used commonly throughout the world. The decimal system is a system based on ten numerals.

They are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Because the *MasterPieces* have the abstract number imprinted on each block it makes understanding Number, Values, Shapes, and Space easy!

**Addition** or **adding** is the first level of arithmetic that comes after counting.

A **whole number **is simply the numbers 0, 1, 2, 3 (and higher). When we **add** two or more whole numbers together, it is the action of **combining** which creates another whole number with a greater value. When we combine we use the **plus sign (+) **to indicate the action of adding.

Using the *MasterPieces,* it is easy to see how the combining of two (or more) whole numbers works!

Place value works with counting to help us make larger values beyond 9. In the decimal system we count from zero to 9 and change places after the 9s. Once we get to 9, it changes on the next number to the next place - 8, 9, 10. For example, if we started counting by 10s, we would start 10, 20 . . . 80, 90, 100.

Because the *MasterPieces* have unit cubes, ten bars, and hundred blocks it is easy to show how place value works!

Use the *MasterPieces* in combinations to help students master their math facts for any number!

Just start with a value, in the video the value is 10, now find all of the combinations that make 10!

If students find all of the 2-digit addends, then have them find 3 or more addends that make the sum of 10!

Students learn quickly and easily using the *MasterPieces*!

Word problem and solving for unknowns is the first of many important steps for students to understand in the area of data and statistics. As a teacher, helping students to learn how to ask questions that can return measurable information is important.

The *MasterPieces* will help students to clearly see the answers to questions in a concrete format.

Mathematical symbols like the equal, plus, and minus signs are very important to understand in math. Whenever there is an equal sign, we must create a **balanced equation**. Solving for unknowns is a great way to show creating balanced equations. It is also a great way to prepare students for subtraction and algebra.

The *MasterPieces* will help you show every step in the abstract written format for each equation!

**Multiplication** is *fast adding *or *repeated addition *of the same number. By using the *MasterPieces*, we can see the pattern of rectangles or squares.

**Factoring **is the action of taking the product (number) and separating it into one or more sets of values, that when multiplied, produce the same product.

In** division, **we are given the **dividend** (product) and the **divisor** (one factor). We now look to find how many times the divisor can be counted out of the dividend.

Fractions are an expression of a rational number showing us **How Many ***of ***What Kind**.

It is important that students gain the understanding of the parts of a fraction and what they mean to help with higher operations.

The *MasterFractions* are an amazing tool to help students see each part of a fraction and to easily understand equivalencies, mixed numbers, and much more!

** Perceptions Green **is a multi-grade, multi-concept program covering concepts related to the operations of addition and subtraction facts with regrouping, multiplication and division facts, data and graphing, telling time and elapsed time, along with beginning fractions.

**1st - 3rd Grade Skill Range**

* Perceptions Blue* is a multi-grade, multi-concept program covering concepts related to the operations of multiplication and division with whole numbers and addition, subtraction, multiplication, division with fractions and mixed numbers along with solving for unknowns. 4th & 5th Grade Skill Range

The **Instruction Manual **is the guide for the teacher. It provides lesson specific help, lesson objectives, lesson vocabulary, and solutions.

The **Lesson Videos, **are designed to be watched by **BOTH the teacher and the student**. The videos contain the lesson instruction and are designed to provide a launching platform for teachers to develop differentiated instructional approaches for their students.

Each Instruction Manual comes with a 1-year subscription to the Lesson Videos.

Additional resources, such as progress monitoring forms, are also available on the website.

The **Student Workbook **is designed for REVIEW, PRACTICE, and APPLICATION. The workbook is not designed to teach the students. That is the job of a teacher.

In the Student Workbook the students will be challenged with concrete, representational, and abstract problem solving activities. At the end of each lesson is a Mastery Challenge that will engage the students into more complex applications of the math they have learned.

A student self-assessment rubric is also found in the Student Workbook to help facilitate communication between Teacher and Student.