# Abacus Primer

The abacus is an ancient tool for doing calculations. This activity uses a simplified abacus to teach place value. Each bead represents 1 in the given place, and students can use it to get a visual understanding that 10 beads in a given place (1s, 10s, 100s) can be represented by a single bead in the place to its left (10s, 100s, 1000s).

**Grades covered:**through 3

**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
- Math

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

**Subjects covered:**["Math","Social Studies"]