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. For a brief overview of each of these activities, go to our YouTube page.

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, 2, and 3]

**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]