# Primer, Alpha, and Beta

### Primer – A gentle introduction to “doing math”

In Primer your child will learn how to write numerals and also addition and subtraction, basic counting, skip counting, geometric shapes, telling time, and also be introduced to the manipulative block system. It’s a gentle introduction to “doing math.”

• The Student Workbook has been greatly expanded to include the fun download activities from our website that are designed to engage students and expand their understanding of numbers, addition, and subtraction. These pages, formerly known as “Activities” (with some minor revisions), have been titled Application & Enrichment pages. These follow the Systematic Review for each lesson.
• We added a significant number of suggestions and ideas to the Instruction Manual (although no new pages) that will help students understand key concepts, have fun, and expand their number sense.
• We adjusted diagrams and instructions to ensure clarity.

### Specific Examples

1. We added a paragraph in Lesson 11 recommending that parents/teachers have their students act out numbers (e.g. jump three times). This is to help students expand the concept of a number beyond just a number of physical objects.
2. Clarification of the definition of a square. In the previous edition, the Instruction Manual (in Lesson 16) defined a square as a type of rectangle, but the student text and problems treated squares as non-rectangles. In this new edition we clarified the definition of a square. In a few cases the clarification was as small as changing the diagram that goes with the instructions “count the rectangles” so that there are no squares in it (the previous edition had squares which were not counted in the solution).
3. Another change was to rearrange some of the shapes that students are counting in the worksheets and Application & Enrichment pages, so that the same number is not always arranged the same way (in other words, four blocks are not always shown in a row or in a square formation). This helps students to learn the concept that a number is not a particular arrangement of objects.

### Additional Information and Sample Lessons

Primer Instruction Manual illustrates a new teaching tip in Lesson 13.

Primer Sample Lesson 9 – includes instruction and student materials and solutions. To use with the video lesson above.

### Alpha – Single-Digit Addition and Subtraction

Alpha focuses on teaching the concepts of single digit addition and subtraction. We use systematic teaching strategies to help students commit the addition and subtraction facts to memory.

• We added the “Activities” pages (formerly in the Test booklet) to the Student Workbook, and titled them Application & Enrichment pages. These follow the Systematic Review for each lesson. There is now one per lesson.
• We expanded the Alpha Instruction Manual to include additional content to teach students addition, subtraction, and other concepts at this level. We have clarified and made more accurate explanations and definitions.
• We rewrote a number of problems in the Student Workbook. The solutions to these problems remain the same as in previous editions (for compatibility with older Instruction Manuals) but they now require deeper conceptual understanding of addition and subtraction.

### Specific Examples

1. We added a paragraph to Lesson 14 of the Instruction Manual suggesting that parents/teachers introduce the terms “one-half”, “one-fourth”, and “one-quarter” in the context of everyday life. The Application & Enrichment page for the same lesson (14G) develops these terms in much more detail. The symbolism “1/4″ is not introduced yet, but the concept of a “quarter” as “what you get when you divide something up into four equal shares” is developed in this Enrichment page.
2. A sample of a word problem that was rewritten in the Student Workbook is from Systematic Review 17D, #20: The old version says: “When Eric went to feed the chickens, he noticed that three of them were brown, one was red, and the other seven were white. How many chickens does Eric have?”
The new version says: “When Eric went to feed the chickens, he noticed that three of them were brown, one was red, and the others were white. He has 11 chickens.
How many of the chickens are white? 3 + 1 + ___ = 11″
Notice that the old problem is a simple addition problem with three addends, just like others that students have already seen. The new version is actually a “solving for the unknown addend word problem with more than two known addends.” There are a number of cases like this where a slight adjustment to a word problem allows us to cover a concept which had previously been only assumed. Notice that for purposes of compatibility, the solution in both old and new editions is the same (3 + 1 + 7 = 11).

### Additional Information and Sample Lessons

Alpha Instruction Manual sample page 53, illustrating new teaching tip.

Alpha Student Workbook Lesson 17, illustrating revised word problem #20 vs. the page in the older books.

Alpha Student Workbook sample of a new Application & Enrichment page.

Alpha Sample Lesson 9 – includes instruction and student materials, test pages, and solutions, to be used with the video lesson above.

### Beta – Multi-Digit Addition and Subtraction

Beta builds on the foundation in Alpha by applying students’ mastery of single-digit addition and subtraction to multiple-digit addition and subtraction. One of the stepping stones between these two levels is the concept of place value, which is an important milestone for truly grasping any multiple-digit operation.

• We added the “Activities” pages (formerly in the Test booklet) to the Student Workbook, expanded their number, and titled them Application & Enrichment pages. These follow the Systematic Review for each lesson. There is now one per lesson.
• We expanded the Beta Instruction Manual to include suggestions, ideas, and tips for enhanced teaching.
• We rewrote a number of problems in the Student Workbook. The solutions remain the same (for compatibility with older Instruction Manuals) but they now require deeper conceptual understanding of addition and subtraction.
• There are two new appendices to both the Student Workbook and Instruction Manual covering number lines, measurement, polygons, and fraction concepts (still using
words – not symbols) drawing students into a deeper understanding of such concepts.
• The number of changes to Beta is relatively small, but quite significant in content. To get the full benefit of this new material a customer should use the new versions of both books.
•

### Specific Examples

1. Application & Enrichment page 15G in the Student Workbook introduces measurement in centimeters and at the same time has students estimate the length of objects in both inches and centimeters before actually measuring them.
2. Appendix B in the Instruction Manual not only introduces the number line, but explicitly connects it to the Math-U-See manipulatives and shows how they can be used together to demonstrate addition and subtraction. Appendix B in the Student Workbook provides practice.
3. We rewrote some of the word problems in the Student Workbook to require a deeper understanding of addition and subtraction while keeping the same solutions. These are similar to the ones in Alpha, where we have turned simple addition or subtraction word problems into “solving for an unknown” word problems.

### Additional Information and Sample Lessons

Beta Student Workbook Appendix B shows the introduction of number lines with the use of Manipulative Blocks.