# Making Math Real: Fractions on the Number Line & Decimals on the Number Line Intensive

## Making Math Real:  Fractions on the Number Line & Decimals on the Number Line Intensive

#### Online 5-day mini-course via Zoom

Summer 2020 Dates:  Monday-Friday, June 22-26  |  9:00am to 12:00pm
Registration Fee: \$499

MANDATORY PREREQUISITE:  All students who enroll in this mini-course must have completed: Fractions, Decimals & Advanced Place Value

The focus of the Fractions on the Number Line & Decimals on the Number Line Intensive will be on:

• Levels I-XVI of fractions on the number line
• Labeling fraction number lines in standard form and common denominator form
• Concept applications of extended fraction number lines
• Intro to “Tweeners” for decoding and encoding applications
• Levels I-XVI of decimals on the number line
• The essential fundamentals of decimals on the number line: labeling decimal number lines from landmarks to counting numbers, and from counting numbers to landmarks
• Concept applications of extended decimal number lines
• Intro to “Tweeners” for decoding and encoding applications

Fractions on the Number Line & Decimals on the Number Line Intensive Course Description

Fractions on the number line and decimals on the number line are both synthesis applications requiring full decoding and encoding of the fraction number system and the decimal number system, respectively. Decoding and encoding of these two number systems are required to support sufficient number sense and sequencing to solve the “puzzles” that span the 16 levels of development for each.

The 16 levels of fractions on the number line span 2nd through 5th grade, and the 16 levels of decimals on the number line, 4th through 5th. The 16 levels are structured to develop decoding and encoding of each number system and emphasize students’ abilities to label fraction number lines in standard form (simplest form fraction values) at least through twelfths, and decimal number lines through the thousandths place. Additionally, students need to learn to perceptually extend these number lines in which problem solving requires generating fractions or decimals continuing after, before, or in both directions from given landmark prompts. For example, a given number line divided into 12ths may provide the landmarks of 2 and 3, but the number line may extend beyond 3 and prior to 2, so students must be able to perceive mixed fractions that come after 3 as well as mixed fractions that precede 2.

The ability to label fraction number lines requires students’ full integration of lowest terms and equivalent fractions (generating equivalent fractions from given lowest terms fractions and simplifying equivalent fractions from given equivalent fractions) and transforming between mixed and improper fractions; and for decimal number lines, full integration of decoding and encoding decimals and mixed decimals through the thousandths place, generating equivalent decimals, and decimal place value applications: standard to expanded forms and rounding by whole numbers and decimals.

The highest levels for both fractions on the number line and decimals on the number line present the decoding and encoding of points on the number lines that are placed halfway between hash marks on the number lines. These “Tweener” points represent the highest challenge in solving these puzzles, especially when placed immediately after or before landmarks.

Required Course Materials: The fractions on the number line and the decimals on the number sections of the Fractions, Decimals & Advanced Place Value course binder and all of your notes pertaining to these two sections.  (already in participant’s possession)