• ʺPositive Realsʺ is the second interval set stressing 0 and continuous positive values
• Children come to understand that anything on a positive number is a positive real number.
• For students in grades 5-8
• Blackline masters for written responses (answer keys included).
• Ten separate pages; typically two pages comprise one exercise.

Verbal, algebraic, and number line expressions depicting continuous positive values including fractions. Incremental introduction of continuous positive equalities and inequalities, including fractions. Students often do two exercises at a sitting.

Blackline masters or Digital PDFs for written responses (answer keys included). (No special preparation required.)
Recommended Storage (not included): File

Blackline masters are good for whole-group instruction, homework, tutoring sessions, and assessments.  Because they are used to reproduce worksheets for multiple students, they include copyright for a given site.   (However, copyright does not permit sharing among different sites.) Blacklines may be stored in a file or binder and kept in the copy room for teachers to copy for their class as needed.  Teachers usually keep a copy of the answer pages in a separate file or binder in the classroom.

Digital PDFs are the same as shipped blackline masters, but emailed as a downloadable digital PDF file to the purchaser's email address.  Since no paper or shipping costs are incurred on our part, digital PDFs can be offered for a lower price.  Files are downloaded through an immediate separate email from the reputable download service SendOwl. Digital PDFs are copyrighted and allow only limited access. As is the case for shipped blackline masters, masters printed from digital PDFs may be shared among teachers at a single site.

Scope and Sequence Chart (Click here)

The teacher's experience and the sequence of skills in the students' basic math program are the best guides in determining which skills should be introduced first. In general, the scope and sequence chart above can be used as a guide.

A number of sets for younger children are "color coded." Some teachers present all the levels with an exercise set, while others prefer to present all the blue (two-digit) exercises, progress to the pink (three-digit), and culminate with the green (four-digit).

Other skills such as Roman Numerals require no prerequisites other rhan an understanding of place value.  Such exercises can be presented any time.