As an 18-year veteran teacher in Philadelphia public schools, my initial reaction when I first saw Sketchpad was “This would have completely changed the way I taught geometry.”
I phrase it differently today: “This would have completely changed the way students experience mathematics.” a perspective that differs in two important details.
First, I now understand that the emphasis needs to be not on my teaching but on students’ experiences of mathematical objects. Secondly, I now realize the value dynamic mathematical experiences bring not just to geometry students but to students of all ages in all areas of mathematics.
My more mature perspective is due in no small part to my participation in the Dynamic Number project. Daniel Scher and I created and field tested many activities to bring dynamic experiences of number concepts to students from second grade on. While field testing in elementary schools, I watched students manipulate mathematical objects and observe and react to the feedback they received–feedback that came not from any adult but directly from the behavior of the mathematical objects. Students’ excitement was contagious.
So here’s a list of several Common-Core aligned Dynamic Number activities to use with your students in grades 2-5, in different mathematical areas, to establish from the start the value–and fun–of manipulating and experimenting with dynamic mathematical objects. Every activity comes with an activity sketch and extensive Teacher Notes, and most are compatible with the iPad. (Update: Many of the Dynamic Number activities are now available for use in your web browser with no need to install Sketchpad. See here.)
Over the next few days, I’ll post some suggested Dynamic Number activities for middle school and high school use.
- Grade 2, two-digit addition/subtraction: Cross Number Puzzles-Addition and Subtraction (Students solve puzzles in which they add, subtract, and use logical reasoning to find missing numbers in a 3 × 3 grid.) iPad compatible.
- Grade 3, multiplication: Multiplication Strategies—Multipliers 6 through 12 (Students decompose multiplication problems into simpler problems.) iPad compatible.
- Grade 4, multiplication: Two-Digit Multiplication—Using an Array Model (Students use an array model to find products up to 50 × 50.) iPad compatible.
- Grade 4, place value: Zooming Integers—Hundreds, Thousands, and Beyond (Students “zoom in” on a number line to name points with integer locations.) iPad compatible.
- Grade 4, equivalent fractions: Make Your Own Fractions—Equivalent Fractions (Students construct area models of equivalent fractions.)
- Grade 5, decimals and decimal notation: Zooming Decimals—Tenths, Hundredths, and Beyond (Students explore tenths, hundredths, and beyond on a “zooming” number line.) iPad compatible.
- Grade 5, addition of fractions: Fractions on a Number Line—Adding with Unlike Denominators (Students add fractions with unlike denominators on a number line.)