# Abacus Variations

This easily created version of an abacus can teach place value and show how different cultures calculate. Abaci can even be based on math systems other than base 10!

**Grades covered:**1 through 8

**Curriculum Topics:**Math, Place Value, Historical Math Tools, Addition

### Standards

Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.

1.NBT.2. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:||Common Core Mathematics||Grade 1||Number And Operations In Base Ten||Understand Place Value|||1.NBT.4. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.||Common Core Mathematics||Grade 1||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||1.NBT.6. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.||Common Core Mathematics||Grade 1||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||1.OA.6. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 ? 4 = 13 ? 3 ? 1 = 10 ? 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 ? 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).||Common Core Mathematics||Grade 1||Operations And Algebraic Thinking||Add And Subtract Within 20|||2.NBT.1. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Understand Place Value|||2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.||Common Core Mathematics||Grade 2||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Add And Subtract|||3.NBT.2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.||Common Core Mathematics||Grade 3||Number And Operations In Base Ten||Use Place Value Understanding And Properties Of Operations To Perform Multi-Digit Arithmetic.4

1.4 Count and group objects in ones and tens (e.g., three groups of 10 and 4 equals 34 or 30 + 4).||CA Mathematics||Grade 1||01. Number Sense||1.0 Students understand and use numbers up to 100.|||2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference).||CA Mathematics||Grade 1||01. Number Sense||2.0 Students demonstrate the meaning of addition and subtraction and use these operations to solve problems.|||1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit.||CA Mathematics||Grade 2||01. Number Sense||1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.|||1.2 Use words, models, and expanded form (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).||CA Mathematics||Grade 2||01. Number Sense||1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000.|||2.2 Find the sum or difference of two whole numbers up to three digits long.||CA Mathematics||Grade 2||01. Number Sense||2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two- and three-digit numbers.|||1.3 Identify the place value for each digit in numbers to 10,000.||CA Mathematics||Grade 3||01. Number Sense||1.0 Students understand place value of whole numbers.|||1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 +6).||CA Mathematics||Grade 3||01. Number Sense||1.0 Students understand place value of whole numbers.

**Categories include:**

- Grades K-2
- Grades 3-5
- Grades 6-8
- Math

**Tags:**Addition & Subtraction, Place Value

**Subjects covered:**["Math"]