Activities

Numbers and Operations

The following files are from the activities we do in class. Click on the "Preview" thumbnails to see a slideshow of the documents, or click the "PDF" button to download a handout.

Downloadable Files

Title	Content	Preview	Download
Learning Number Systems	Online investigation of ancient numeration systems.
The Land of Treble	A fun game that uses dice and coins to learn a base-3 monetary system.
More with the Babylonian Number System	This is a follow-up to an investigation of the Babylonian number system using the Learning Number Systems applet.
More with the Egyptian Number System	Similar to the in-class More with Babylonians, this includes practice with the Egyptian system and some interesting questions about addition and subtraction.
Sorting Numbers	Completed in-class as an introduction to different classifications of numbers.
Base Ten Riddles	This activity uses "base-10 blocks" to look at multiple ways of represented numbers using place-value concepts.
The 2-Color Counter Game	Activity for working with positive and negative numbers as "two-sides of the same coin".
Fractions with Pattern Blocks	This uses pattern blocks related to hexagons as part of part-to-whole consideration of fractions
Cuisenaire Rods and Equivalent Fractions	Cuisenaire rods can be used to learn how to be flexible in thinking about what constitutes a whole when dealing with fractions.
Parts and Wholes- Cuisenaire Rods	Here we model fractions using wooden blocks of varying length.
Parts and Wholes- Sets	Fractions are closely linked with sets of objects.
Parts and Wholes- Area	The area model is a favorite way to represent fractions… just be careful if you prefer Pies!
Methods for Adding and Subtracting Whole Numbers	Analyze four students' strategies for doing arithmetic.
Analyzing Children's Thinking in Whole Number Arithmetic	Look at actual examples of students' work, with the intention of figuring out the method and whether it always/sometimes/never works.
A Historical Shift in Subtraction	Learn a popular alternative algorithm for subtracting whole numbers.
Inequality of Fractions	Individual activity for comparing fractions
Ordering Fractions	Group activity designed to focus on some rules for comparing fractions.
Representing Decimals	Jigsaw activity including three activities varied by learning style.
One-Step Word Problem Sort	Cut out one-step word problems using whole numbers and addition and subtraction, and then sort them.
Taxonomy of One-Step Word Problems	A categorization system for one-step word problems developed by researchers.
The Number Line Approach to Integers	Positive and negative numbers on the number line, including a nice explanation for why subtracting a negative number corresponds to moving to the right.
Youngsters' Approaches to the Fruit Problem	Invented methods for multiplication
The Lattice Method for Multiplication	An alternative, but fast, method for multi-digit multiplication
Visualizing Multiplication as Counting Possibilities	Here multiplication is represented using decision trees.
The Area Model for Multiplication	Fill up a 23 by 14 grid using flats, longs, and units to see the partial product method of multiplication visually.
Chef Story for Positive and Negative Numbers	Look at addition, subtraction, and multiplication with negative and positive numbers using the analogy of raising and lowering temperature.
Outdoor Number Sense Activity	Completed outside in small groups. The point of the activity is to develop systematic approaches to poorly posed arithmetic problems.
Two Types of Division Problems	Examples of the Measurement and Sharing models of division. In-class discussion also included the Explicit Trading Method of division (handout not available on web).
Interpreting Remainders	A nice reading about the many potential meanings for remainders in division problems.
Students Thinking on Division	Can you figure out these students' invented strategies for doing division? Some of them make a lot of sense.
Waffle Makers	Learn to use a "squaring off" procedure to find the greatest common divisor of two numbers… all involving Waffles too!
Factoring into Primes	Some "good examples" of integers for practicing prime factorizations. (Includes solutions.)
Prime Factorization Worksheet	Learn how to determine factors, multiples and divisibility by looking only at prime factorizations.
Finding the Common Value	Some word problems associated with greatest common divisor (GCD) and least common multiple (LCM).
Illustrating Fraction Multiplication	An in-class activity in which we generated six essentially different ways to represent (a/b)x(c/d). (Multiple versions in one document)
It's All in the Choice of Unit	Using some irregular shapes to generate addition of fractions helps us see the physical meaning of "common denominator".
Some Story Problems with Fractions	Some of these are impossible because they lack important information to remove ambiguity, others are just plain fun.