## Add and Subtract 1 and 10

This is meant to develop understanding of addition and subtraction of 1 and 10. You are given a starting number and and ending number (the relationship between having been determined by the adjustable "Difficulty"). Your job is to get to the ending number by adding or subtracting one(s) or ten(s). Choose a representation to help your thinking and try to find the most efficient pathway. ## Arranged Ten Frames

A random number of dots (up to 20) are placed into ten frames. Choose whether the dots are "arranged" or "random". Lots of different, randomly generated possibilities. ## Balance (The Farmer's Stone)

There's a sack on a scale. How much does it weigh? Use the weights to find out and explore flexible approaches to equality. ## Balanced Expressions

Explore notions of equality and inequality by dragging expressions to the balance. Select whether you'd like your inequalities recorded with the "not equal" sign (≠) or greater/less than signs (> and <). ## Bar Graphs

Similar to Cats, Cows, Dogs, Horses, but with the data provided as bars (either horizontal or vertical) instead of pictures. You are asked a variety of questions. Feedback provided. ## Broken Hundreds Chart

You are looking at a section of a hundreds chart. Use what you know about the ± 1 and 10 relationships of a hundreds chart to put the numbers in the correct locations. Some numbers won't fit! (Click "Skip" for these.) Check your work as often as you'd like. ## Cash Register

Set the max price, then click start. A random price is generated for an item. Drag the coins onto the cash register to pay for it. Toggle the "Show total" to see how much you've paid (if needed), then click "Check" to see if you've paid the right amount. ## Cats, Cows, Dogs, Horses

A randomly generated graph. Interpret the graph to answer the following questions (feedback provided):

- How many total animals?

- Are there more ____ or ____?

- How many more ____ than ____? ## Clock

A simple tool for exploring how a clock works. How does the minute hand move compared to the hour hand? What do we know about what time it is by looking at the hour hand? ## Comparing Two Whole Numbers

Intended for students to develop understanding of bigger/smaller numbers. Type in two whole numbers. Click "Forward" to see the numbers shown in base-10 blocks, then broken apart into ones, then finally shown overlapping. An interesting example is comparing 3 to 30. ## Commuting Counters

Enter two addends, then click next. The addends will show up as counters. Keep clicking next to see the commutative property in action. ## Comparing and Estimating Whole Numbers

Use the given quantity to estimate the others. Use the sliders to adjust the size of the numbers (10 to 1000) and number of questions. Kindergartners might use this to talk about more/less, while 6th graders might have highly sophisticated approaches involving unit rate. ## Dots in the Box

A missing addend activity. There are ___ dots in a box. Some are red and some are blue. If you know how many blue dots there are, can you figure out how many red dots there should be? ## Five by Five

A 2-player, GeoGebra version of Sara VanDerWerf's game. You will place (up to) 25 numbers in the grid. You score by placing (by clicking) matching numbers in adjacent squares. Decide whether you want to play a timed or untimed game, and whether you'd like the scores to be calculated by sums or products. See Sara's blog post for more information. ## How Many?

A random number of objects (between 0 and the upper limit you specify) flashes on the screen. Estimate how many you saw. Then display the picture again, reconsider your guess, and finally see the answer. Designed to develop solid connection between a number and how "big" it actually is. ## How Many? (with grouping)

An updated version of "How Many?" with a new feature: once you see the squares, you can arrange them into groups. Use this to connect estimation and quantity to skip counting. Or use it to have a conversation about multiplication or division. ## Interactive Number Grid

This grid goes to 120. Click on the numbers to toggle the colors. Click on an arrow to turn the entire row or column red. Explore 1 or 10 more/less, patterns in skip counting or beyond. ## Make a Dollar

Drag coins onto a dollar bill until you've got \$1.00 in pennies, nickels, dimes, and/or quarters. ## Making 10's

Specify an number, then watch as it goes from a collection of "ones" to groups of "tens." See the various forms of a number to build understanding of place value. Alternatively, specify a number, make it into tens, then break the tens into ones to develop understanding of regrouping. See also "Showing Numbers with Place Value" ## Making Numbers with Place Value

Enter any number of hundreds, tens, and ones to see that number drawn in any of three ways. One way of using this is to help students see the difference between a digit and its value. For example, a student might say the number 63 has 60 tens and 3 ones. If you enter that in this applet, you can see a number represented as...

• 60 tens and 3 ones ("How I typed it")

• 6 hundreds and 3 ones ("Standard place value")

• 603 ones ("All ones") ## Move the Number

This activity is meant to develop flexible, creative thinking about numbers and operations. Your goal is to move a from a starting number to a target number, but there are many ways to do this! Adjust the sliders to control the bounds of the numbers involved. ## Moving Dots

How many dots are there? How do you see it? This number talk resource is designed to give students lots of different ways of seeing and describing a number of dots, but with the added advantage of seeing the dots move from one arrangement to another. Use this with the goal of students flexibly describing many ways of composing/decomposing a number. ## Number Balance

Explore ideas around equality, decomposition, missing addends, and more! Up the ante by finding the mystery number. ## Number Path

An exploration of +/- 1 or 10 on the hundreds chart. Make a "path" (of up to 50 squares). Your job is to figure out the numbers. By clicking on the square, the number is revealed. ## Part-Part-Whole Estimation

Adjust the slider to control the size of the numbers. One of the pieces (a part or the whole) is randomly provided. Use estimation to fill in the rest. Feedback provided. ## Piggy Bank

Drag coins or \$1 bills into the piggy bank. Click to show the total amount. ## Place Value Bars

Enter a whole number (under 1 million) and it will be shown as a bar partitioned along base-10 values. Use this for a visual demonstration of, for example, why 543 > 345, beyond "because 5 is bigger than 3". ## Placing Numbers (up to 30 or up to 50)

An unmarked number line is provided, with 0 on the left. Students are given a random number (either 1-10 or 11-30/50) to place on the number line (repeated up to 20 times). The goal is not only to place numbers in the right order, but also in the correct relative position (e.g. 2, 3, 8, but the 3 should be closer to the 2 than the 8). Feedback is provided by displaying the correct locations based upon the location of the largest number. ## Placing Whole Numbers on the Number Line

Drag whole numbers to the correct locations on a (mostly) blank number line. Feedback provided. Adjust the upper limit for the size of the number and how many are placed on the line. ## Random Places

The purpose of this tool is to help students see the connection between (a modeled representation of ) expanded form and the digits that make up a number. Use the slider to select which places to use (ones and tens are required, but hundreds - for 2nd grade - and thousands - for 3rd grade - are optional). This program will then make a number by randomly choosing one base-ten block for each place (up to 9) that you choose. Once you click start, the number gets covered up by a purple rectangle that you reveal once you've had a chance to discuss what might be under it. Consider the following questions:

• What's a number that might be under here?

• What's a number that couldn't possibly be under here?

• What's the smallest number that might be under here?

• What's the biggest number that might be under here?

• What's something that ALL possible numbers have in common? ## Separable Clock

A simple tool that allows you to separate the hour and minute hands of an analog clock in order to analyze them independently. ## Showing Numbers

Intended for students to get a sense for "bigness" of numbers. Type in a number to see it displayed in an array. If you wish, enter another number to see a visual comparison. ## Showing Numbers with Place Value

Enter a number (up to 1000), then regroup it into ones, tens, and hundreds. See also "Making Tens." Designed to allow students to see lots of equivalent representations of numbers. ## Splitting 100

This is meant to help students see the relationship between coins and numbers. Begin the discussion by asking them what they notice as you cycle through the different versions of splitting up the 100 (controlled by the "Switcher" slider). The work to make connections between the bundles/groups and various coins. See below for a potential prompt.  ## Ten Frames

One or more ten frames appears on the screen (you can adjust this). A randomly generated number of dots flashed, (partially) filling in the ten frame(s). Your job is to say how many dots you saw and how you saw it. ## Tens and Ones Estimation

This activity is meant to get students using place value flexibly as they estimate a quantity (randomly generated between 20 and 99). Enter a number of tens and ones to match the given (grey) amount. Once you've matched it, try to think of other ways of making the same amount. ## Two Piggy Banks

Drag coins onto both banks (or Fill Randomly on both)

• Which bank has more? (I like that there'd be lots of ways to answer this)

• What coins would we add to make the banks equal?

Drag some coins onto one piggy bank (or Fill Randomly)

• Students tell you the value. Click to show total.

• Students tell you another way to reach the same total. Drag that onto the other piggy bank. Click show totals for both. Do they match? ## What Shapes?

Use this activity to develop definitions of simple polygons by noticing patterns. Build math language from informal to formal. ## What's the Number?

A random number (upper limit is adjustable) is generated and placed on a blank number line. Your job is to guess where it landed. Click "more info" to zoom in and refine your guess. ## Year Zoom

Start by looking at a year, then gradually zoom in through the month/day/hour/minute. 