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Pathways from the Past is a pair of teacher’s manuals and two sets of activity sheets
for helping students master various topics in arithmetic, pre-

that often cause trouble. Their approach implements the spirit of the NCTM
document,

Pathways from the Past

I: Using History to Teach

Numbers, Numerals, and Arithmetic

This is a 64-

are basic to the curriculum and assessment guidelines of most
states and are in the

Contents

First Thoughts for Teachers

1. Writing Whole Numbers: Place Value

Sheet 1-

Sheet 1-

Sheet 1-

Sheet 1-

Sheet 1-

2. Zero Is Not Nothing: Properties of Zero

Sheet 2-

Sheet 2-

Sheet 2-

3. Broken Numbers: Fraction Arithmetic

Sheet 3-

Sheet 3-

Sheet 3-

Sheet 3-

Sheet 3-

Sheet 3-

4. Less than Nothing?: Negative Numbers

Sheet 4-

Sheet 4-

Sheet 4-

Sheet 4-

Sheet 4-

― “I loved the materials. I will be able to use these throughout the year in my class.” (a 7th grade teacher)

teacher’s manual

& blackline masters

for 19 two-

activity sheets

$39.95

978-

The Manual

Each of the four major chapters is organized like this:

- Its mathematical focus is stated first.
- “Historical Connections” lists the relevant regions and time frames.
- A summary of the historical ideas comes next.
- A section for each Activity Sheet starts with its main mathematical ideas and its
pedagogical purpose, followed by a detailed solution for

each question.

The Content

Chapter 1 links up well with the “ancient civilizations” part of any social studies
curriculum. Chapters 2, 3, and 4 explore how the mathematics of earlier non-