Preview Problem-Solving Resources
Grades 6-8 Professional Learning and Instructional Resources
Preview Problem-Solving Resources are designed to review grades 3-5 concepts and strategies involving fractions, decimals, and computation while introducing foundational grade 6-8 math concepts such as rational numbers, ratios, rates, and percents. These resources help teachers to connect review topics, such as locating and labeling fractions and decimals on number lines, directly to essential grade 6 strategies and concepts, such as representing negative rational numbers.
These resources are built around videos that structure a problem-solving talk with a class or small group of students. The video briefly reviews essential representations, strategies, and concepts. Then, students are challenged to build representations and solve problems using a set of magnetic manipulatives on a whiteboard. Instructional notes for the video help teachers focus their questioning strategies and identify pause points in the video to address diagram comprehension, concept development, and vocabulary. Finally, students apply what they have learned through daily problem-solving tasks and practice pages.
PPS Video — Represent Rational Numbers
Reviewed and Previewed Topics
Whole Numbers, Fractions, and Decimals on Number Lines.
Basic Compuation with Fractions and Decimals
Integers and Rational Numbers
Equivalent Ratios and Basic Ratio Problems
Unit Rates and Basic Rate Problems
Equivalent Fractions, Decimals and Percents, and Basic Percent Problems
Included Resources
PPS Videos
Magnetic Whiteboard Manipulative Kit
Video Overview and Instructional Notes
Daily Problem-Solving Tasks
Problem-Solving Practice Pages
PPS Video —Represent and Solve Ratio, Rate, and Percent Problems
Preview Problem-Sloving Video
Structure a Problem Solving Talk
Preview Problem Solving Videos review essential concepts from grades 3-5 and preview representations and strategies from grades 6-8. For example, many students entering middle school have a weak understanding of how measurement is used to locate and label whole numbers, fractions, and decimals on number lines. The sequence of PPS Videos starts with a review of plotting whole numbers, fractions, and decimals on number lines. Then, students apply these strategies to locate and label negative integers, fractions, and decimals.
PPS Resources help teachers implement these problem-solving videos with a class or small group of students. These resources include a magnetic manipulative kit for whiteboards, instructional notes, application tasks, and practice pages.
Sample PPS Video — Measure to Plot and Label Positive and Negative Fractions
Review and Preview Topics in this Sample PPS Video
REVIEW and PREVIEW — Positive and negative fractions on number lines represent their distance and direction from zero.
REVIEW — The length of a unit-fraction bar is defined by the number of equal-length bars that measure a length of 1.
REVIEW — Two numbers that measure the same distance and direction from zero on a number line are said to be equivalent.
REVIEW — Represent fractions greater than 1 .
PREVIEW — Positive fractions can be reflected across the tick mark for zero to locate the opposite negative fraction.
Problem Solving Challenges in this Sample PPS Video
Each PPS Video includes a series of Problem-Solving Challenges that are solved as a class or small group. Students use manipulatives from the Magnetic Manipulative Kit for whiteboards to apply strategies demonstrated in the video.
For this PPS Video, Measure to Plot and Label Positive and Negative Fractions, students:
Use magnetic number line segments to build the number line.
Apply measurement strategies from the video to plot and label fractions on the line.
Learn that measurement strategies to plot and label positive fractions to the right of zero can be applied to measure, plot, and label negative fractions to the left of zero.
CHALLENGE 6.3A.1
CHALLENGE 6.3A.3
CHALLENGE 6.3A.2
CHALLENGE 6.3A.4
Magnetic Whiteboard Manipulative Kit
Number Line Measurement Kit and Proportional Representations Kit
Magnetic Number Line Segments, Measurement Bars, and Fraction Stips
Drawn to scale on a 48 in by 36 in magnetic whiteboard.
Magnetic Grid and Chips for Ratios, Double Number Line for Rates, and Bar Model for Percent
Drawn to scale on a 48 in by 36 in magnetic whiteboard.
Video Overview and Instructional Notes
Develop Questioning Strategies
The Video Overview and Instructional Notes outline the conceptual highlights of the PPS Video and list the essential strategies and concepts that are introduced and reviewed. In addition, video pause points with instructional notes identify important representations, strategies, and concepts and offer suggestions for facilitating discussions and problem-solving with students.
The instructional notes offer questioning strategies for each Problem-Solving Challenge and identify other pause points with notes on:
Diagram Comprehension
Essential Concept Development
Vocabulary Discussion
Problem-Solving
REVIEW Pause Points
The first three pages of this VOIN review the basics for measuring to locate and label fractions on number lines.
Identify unit fractions bars
Measure to fractions less than and greater than one.
Identify equivalent fractions and whole numbers that measure from zero to the same point on the line.
PREVIEW Pause Points
The Preview pause points on this page challenge students to apply the measurement strategies to plot and label negative numbers to the left of zero.
The mirror image of a positive number across zero is the opposite negative number.
Negative numbers measure a distance to the left of zero, where measurement bars represent distance and the arrows (or vectors) represent both distance and direction from zero.
Then, students are Challenged to use magnetic measurement bars and fraction strips to locate and label negative fractions on a whiteboard number line.
