The Counting Section features a Multiples Table showing Digits 1 - 12, up to 120. Use this as a reference throughout Level/1 as students are learning Unit Operations.

Counting Groups contains 6 tools:
• Dots and Digits where in Dots mode students learn about precision by highlighting an exact number of Dots and in Digits mode realize benefits counting by groups of 10s instead of 1s.
• Group Similar Shapes has students sort 10 shapes into 3 groups, Circles Squares and Triangles, in Hard Mode 20 Shapes are sorted into 4 Groups, including an Other Group.
• Doubles and Halves generates a number less than 500 and requires no carry 10 in easy mode.
•Counting money presents up to 3 units (easy) or 9 units (hard) of: Dollar Quarter Dime Nickel Penny, Student must total the amount and answer with a dollar sign and 2 Decimals
•Mean Median Mode generates sets of 10 digits, students may use a pencil, paper and calculator to complete this skill.

The Add and Subtract to 100 tool helps students improve their base10 acumen by adding up to and over the next group of 10 faster. The tool is timed and intended to be used regulaurly, as students improve skills by getting faster in all 4 operating modes.

The Numeration section features 4 tools:
• Counting to/from 1 Any Number to a Thousand, Million and Billion. Students learn to work right to left starting with the least significant digit first then moving left.
• Name Numbers to a Thousand Million and Billion offers a word bank to build the numbers by clicking on the words.
• Rounding Numbers up to 10,000 generates 5 numbers to be rounded to the nearest 10 100 and 1000.
• Scientific Notation generates 2 numbers not more than 4 powers apart and has students Add Subtract Multiply Divide them.

Each tool in the Numeration Section has a tutorial showing How-To-Do the skill.

Counting Section Video

The Multiples Table

•Dots and Digits

•Doubles and Halves

•Counting Money

•Mean Median Mode

•Group Similar Shapes  

•Sums from 10 to 20

•Periods of Tens

•Print Multiples

Mean: is the average of all the numbers in the set. Simply add the numbers to get a total sum then divide by the number of digits to get Mean.

Median: is the number in the middle of the sorted set. First rewrite the numbers sorted Low to Hi.

• For sets with an odd number of digits the digit in the middle is the Median.

• If the set has an even number of digits the mean of the two middle digits is the Median.

Mode: is the digit which occurs most often. If a tie then there is No Mode.

Attempt / Correct
Mean:0/0   Median:0/0   Mode:0/0
hidereset  

NewAnswer

Mean Median Mode Calculations

  Mean

Median

  Mode

In EASY mode each digit will half or double without any carry or borrow, across the next group of 10

In HARD mode there may be carry or borrow across groups of 10

The answers in either mode will always be a whole number

Attempt / Correct
Easy   Hard
Halves: 0/0   0/0
Doubles: 0/0   0/0
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 HALF

DOUBLE

  0 Groups Made

New Numbers

Enter a target number between 10 and 20
then click New Numbers

In Easier mode there may be up to 3 of each
In Harder mode, there may be up to 9 of each.

Students learn to add (or count) the money in their heads, keeping track of the totals as they go.

Attempt / Correct
Up to 3 Coins:0/0
Up to 9 Coins:0/0
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3 Coins   9 Coins
NewAnswer

Enter Dollars and Cents as Shown

1 Dollar = 100¢

1 Quarter = 25¢

1 Dime = 10¢

1 Nickel = 5¢

1 Penny = 1¢

Attempt / Correct
Fwd: 0/0   0/0   0/0
Bwd: 0/0   0/0   0/0
resethide

ForwardBackward
Thousand Million Billion
New Numbers

Periods of Tens

From: 00     To: 00

 

If you can Name 3 digit numbers - you can Name Any Number because large numbers are made of 3 digit names followed by the Period of 10s Name.

Try to name this number then click here to see if you are correct.

The tool operates in 3 modes requiring numbers to be named up to A Thousand, Million or Billion.

What is Scientific Notation

Scientific notation is a way to write very large or small numbers in a consistent format. There are two parts to the number:

First: The number which must have only one non-zero digit to the left of the decimal:   #.###...

Remember after an Add Subtract Multiply or Divide Operation, the digit may not have exactly One Digit to the left of the decimal, in this case the number must be formatted.

Second: The power of ten to multiply by.

Scientific Notation → Regular Number

1.2345 x 10¹ →12.345

1.2345 x 10^-1→.12345

1.2345 x 10⁰ →1.2345

Print Worksheet / Key

WhyHow

Why use Scientific Notation

Some numbers are so big they don't have a name

602,000,000,000,000,000,000,000

Number of Atoms in a Mole used in High School Chemistry

6.02 x 10²³

Some numbers are so small they don't have a name

0.000000000675

The Wave Length of Red Light in Meters used in Physics

6.75 • 10^-10

Scientific Notation is a way to communicate exact quantities all over the world.  Every country in every continent reads and processes scientific notation the same way.

What

How

Operations Worksheet / Key

WhatWhy

How to Add Subtract Multiply Divide

Addition and Subtraction require Exponents to be the same

Adding (1.1 x 10¹⁹) + (2.2 x 10¹⁹) is easy

The Answer is (3.3 x 10¹⁹)

Look at the same problem written in expanded form

 11000000000000000000

+22000000000000000000

 33000000000000000000

If the exponents do not match we must convert one

1.1•10¹⁹ + 2.2•10¹⁴

To make exponents match we move the decimal points
and change the exponents - see below:

2.2•10¹⁴ = .22•10¹⁵ = .022•10¹⁶ = .... = .000022•10¹⁹

Look at the same problem written in expanded form

 11000000000000000000

+     220000000000000

 11000220000000000000

Answer: 1.100022•10¹⁹

If we are rounding to 2 decimals, the second number is too small to matter and the answer is the bigger number.

Multiplication is easier. First multiply the digits then add the exponents.

(2.2•10¹⁹) • (2.0•10¹⁴)

2.2 • 2.0 = 4.4

10¹⁹ • 10¹⁴ = 10^{(19 + 14)} = 10³³

Answer = 4.4 • 10³³

Division is also easier. First divide the digits then subtract the exponents.

(2.2•10¹⁹) / (2.0•10¹⁴)

2.2 / 2.0 = 1.1

10¹⁹ / 10¹⁴ = 10^{(19 - 14)} = 10⁵

Answer = 1.1 • 10⁵

This tool generates two numbers in scientific notation, each with two significant digits and no more than 4 powers apart, presenting them in: Add Subtract Multiply Divide operations.

attempt/correct
add   subtract   multiply   divide
0/0   0/0   0/0   0/0
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New   Answer

WhatWhyHow

= • 10


= • 10


= • 10


= • 10

Doubles and Halves

Attempt / Correct
Easy: 0/0   Hard: 0/0
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Double:     Half:

Level/1 Forward, 9,10,11, Under 30 Seconds

Use this tool in Level/1 with, 9,10,11, fwd intervals, scoring under 30 seconds. Level/2 continues with subtraction and intervals from 6-14, all modes in under 30 seconds.

Instructors may challenge students to get faster as they develop base10 add and subtract skills. Perhaps posting a chart in a classroom with each student's fastest times on it. Students try to improve their times?

Sums Between 10 and 20

Attempt / Correct
10:0/0     20:0/0
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10 Shapes   20 Shapes
NewAnswer

  Square 

  Circle  

Triangle  

  Other  

Matching Digits and Dots

Dots mode:

Hovering each dot allows students to make cognitive associations between physical quantities and abstract digits.

Digits mode:

A random number of consecutive dots are highlighted and students are asked to count them. Dots are grouped in rows of ten so the student learns counting by tens is faster than counting by ones.

Students learn about precision and magnitude when matching the exact amounts. Many students will complete these assignments the first time they try them.

Rounding to a Place → Two Things

1: All Digits to the Right of the Place become 0.

2: The Place Stays the Same or Increases by +1 → if the Digit to the Right is 5 or Greater.

Round 7483 to the nearest

10100 1000

3 Examples

Print Worksheet/Key

Round to Nearest 10 100 1000

Reset

Back to Rounding

This tool generates 5 numbers and students round each to the nearest 10 100 and 1000.

A How to Round tutorial animation may be helpful to students and useful to teachers.