Below is a complete list of all the interactive elementary-themed activities we’ve offered on our Sine of the Times blog. Most of these activities grew out of the work that we did during our NSF-funded Dynamic Number project.

The list includes links to our original blog posts as well as links that take you directly to the interactive models without the accompanying text.

Our blog also features many interactive Web Sketchpad activities for middle school and high school, so do explore!

### **Place Value**

Zooming Integers: Estimate the location of a tick mark on a number line and then “zoom in” one or more times to identify its integer value precisely. [websketch]

Zooming Decimals: Estimate the location of a tick mark on a number line and then “zoom in” one or more times to identify its value to the nearest tenth, hundredth, thousandth, and beyond. [websketch]

Interactive Dials: Count in base 10 or change the dials to count in base 2 or base 3, or any base of your choice. [websketch]

Odometers (Part 1 and Part 2): Explore place-value concepts with odometers that let you adjust each individual digit on their display. [websketch 1 and 2]

**Addition and Subtraction**

Dynamic Number Chart: Use a 99 chart to model addition and subtraction [websketch]

Helical Number Chart: Print and attach a helical number chart to a can to create a number chart that moves continuously from one number to the next.

Cross Number Puzzles: Addition and subtraction puzzles inspired by the great 1960’s math curriculum, *Math Workshop*. [websketch]

Arranging Addends: Arrange and overlap three circles so that the sum of the numbers in each circle matches the desired totals. [websketch 1, 2, 3, 4, and 5]

Decomposing Numbers: Pair a list of numbers together to form sums of 20, 30, or higher. [websketch]

Adding and Subtracting Integers: Use an animated model to add and subtract integers on the number line. [websketch]

Adding and Subtracting Integers: A number line model helps students visualize and understand addition and subtraction of integers. [websketch]

**Multiplication and Division**

Interactive Arrays: Create arrays of counters to model multiplication [websketch]

Bunny Times: Develop a conceptual understanding of multiplication through this engaging multi-level game.

Multiplication Arrays: Two visual array models of multiplication [websketch 1 and 2]

Construct a Building and Splitting Arrays: Explore and model multiplication problems with arrays that you build yourself. [websketch1 and 2]

Raz’s Magic Multiplying Machine: Experience multiplication dynamically as you drag two pointers along a number line and examine the behavior of the third pointer representing their product. Can you locate 0 and 1 on a number line with no markings? [websketch]

Multiplication Is Not Repeated Addition: A double-number approach to understanding (and relating) multiplication and division. [websketch]

**Multiples and Factors**

Dynamic Number Grid: Explore multiples and least common multiples in a number grid whose dimensions can be changed [websketch].

Open the Lock: As pointers move around the dials of a lock, use your knowledge of multiples to align all the pointers facing straight up. [websketch]

Mystery Number: Deduce the value of a secret number by asking questions about its factors. [websketch]

Factor Rainbows: Find all the different ways for a bunny to hop to a location on a number line. The factor patterns you’ll discover create attractive rainbows. [websketch]

Open the Safe: A grid of lights displays patterns based on multiples. Can you open a lock by creating the desired patterns? [websketch]

Factor Patterns: Explore factor relationships in this dynamic grid that displays the factors of any number. [websketch]

String Art: Explore numerical patterns with an appealing, interactive string art model. [websketch]

Animated Factor Patterns: Create animated geometric models of multiplication. [websketch 1 and 2]

Beam of Light: When a beam of light is aimed into a forest, which trees on the coordinate plane are illuminated by the light? [websketch]

**Fractions**

Dividing and Subdividing: Locate fractions on a number line using tools that divide intervals into equal parts [webksetch]

Make Your Own Fractions: Create area models of fractions using either circles or rectangles. [websketch]

Fraction Identification Game: Match two randomly generated fractions to their area representations. [websketch]

Equivalent Fractions Game: Drag squares into two resizable arrays to shade a specified fraction of each array. [websketch]

Deduce the “Mystery” Fraction: Through repeated estimates of a point’s location on a number line, determine its value, expressed as a fraction. [websketch]

Fraction Addition: Add fractions on a number line [websketch]

Fraction Addition and Subtraction: A modification of the fraction addition model above. [websketch]

Fraction Multiplication: Explore a visual model for multiplying fractions. [websketch]

Color Calculator: Display fractions as decimals with each digit represented as a different color. What color patterns can you find? [websketch]

**Early Algebra and Logical Reasoning**

Find the Secret Number: Develop a logical, efficient approach to finding the value of a secret number on a number line. [websketch]

Balance Scale: Deduce the numerical values of objects on a scale by maintaining balance as you remove objects from the scale. [websketch]

Circles and Squares: Use logical reasoning to solve for the unknown numerical values of a circle and square. For an extra challenge, solve for three unknowns—a circle, square, and triangle. [websketch]

Sneaky Sums: Deduce the numerical values of the symbols in a grid by examining the sum of the symbols in any row or column. [websketch]

Dancing Unknowns: Solve for 10—yes 10!—unknowns as they dance around the screen. [websketch]

Student Height Puzzles: Create and solve visual logic puzzles relating to the relative heights of students. [websketch]

Find the Hidden Treasure: Uncover the location of a hidden treasure on the coordinate plane by piecing together clues about your distance from the treasure. [websketch]

Addition and Multiplication Codes: Each digit from 0 to 9 has secretly been assigned a letter. Can use information about the sum or product of the digits to crack the code? [websketch]

Factor Logic Puzzles: Determine the secret numerical values of *a, b, c,* and *d* if you’re only allowed to see the product of any pair of letters. [websketch]

Two-Pan Balance Puzzles: Determine the weight of a rock by using logical-reasoning skills. [websketch]

**Geometry**

Protect the Sheep: A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons. [websketch]

Circle Tracers: A spinning radius and circumference introduce the fundamental properties of circles [websketch 1 an 2]

Triangle Area Without a Formula: Enclose triangles in rectangles to obtain their areas through subtraction. [websketch]

Triangle Area: Construct multiple altitudes of a triangle to check that the area formula gives consistent results. [websketch 1 and 2]

Hidden Polygons: Create order out of seeming chaos by connecting points with segments to form squares and equilateral triangles. [websketch]

Tessellations: Create tessellations with regular polygons and then explore whether all triangles and quadrilaterals can tessellate the plane.

Angle Estimation: Estimate the measures of simple and reflex angles in a game that emphasizes the angle-as-turn interpretation of angle. [websketch]