Operations and Algebraic Thinking

  • Represent and solve problems involving multiplication and division.
  • Understand properties of multiplication and the relationship between multiplication and division.
  • Multiply and divide within 100.
  • Solve problems involving the four operations, and identify and explain patterns in arithmetic.


Number and Operations in Base Ten

  • Use place value understanding and properties of operations to perform multi-digit arithmetic.


Base Ten Number Blocks
This simple app allows you to use base ten blocks in the form of ones, tens, and hundreds to aid in solving addition and/or subtraction problems.
This app works great for preschool students through elementary school.

Base Ten Fun
Base Ten Fun utilizes base ten blocks as virtual manipulatives to help children with place value, number sense, counting, addition and subtraction. This app focuses on the one’s, ten’s and hundred’s place using cubes, rods and flats as manipulatives. The app is appropriate for children in elementary school grades Kindergarten and up.

Base Ten Fun includes three practice modes and a fun BINGO game. The practice modes and the BINGO game are highly customizable to meed the needs of a variety of learners.

Practice Modes Overview
Practice modes present players with target numbers which they must represent by arranging manipulatives or entering digits. For perceptual variability the practice mode displays the numbers students have created using two different representations: a dynamic number line and labeled place value boxes. When a player gets ten correct they can select a new color set of base ten blocks!

Three Practice Modes Overview
1. Look and Make: Numbers are presented visually as digits and and players must represent them by arranging manipulatives.
2. Listen and Make: Numbers are presented auditorily by voice and players must represent them by arranging manipulatives.
3. Count and Write: Numbers are presented as manipulatives and players must represent them by entering digits.

Base Ten Fun BINGO
Base Ten Fun BINGO is highly customizable to meet the needs of a variety of players. The game challenges players to count manipulatives and tap the corresponding number in a BINGO grid. The goal is to get BINGO as quickly as possible without making mistakes. Players can collect BINGO Bugs by earning high scores.

Overview of Features:

-30 player profiles
-Create custom characters
-Practice modes
-My BINGO Bugs
-Highly customizable

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Hands-On Math Base Ten Blocks
Hands-On Math: Base Ten Blocks is a virtual math manipulative playground where students explore and discover place value concepts and also learn addition and subtraction with regrouping. Our Base Ten Blocks allow students to experience and develop math concepts through interaction and discovery.

When first learning place value, blocks can be set to represent ones, tens and hundreds. Later, to introduce decimals, blocks can be set to ones, tenths and hundredths.


Whole Numbers
Reading and Writing Numbers
Addition and Subtraction

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Base Ten Blocks
Practice place value with Base Ten Blocks.

This app has two modes; an explore mode where you can see the relationship between place value and base ten blocks and a test mode where you are given a number and you have to fill in the places with the correct number of blocks.

Thousands, hundreds, tens and ones are used in the app but you can change the test mode to which place value suits the needs of your learner.

As you drag the blocks into place it will automatically update them when you hit ten. So ten ones will become a ten block and shift into the correct position.

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Number Pieces, by the Math Learning Center


Base Ten Blocks English and Spanish
Hands-On Math Base Ten Blocks supports both English and Spanish languages. Hands-On Math Base Ten Blocks simulates the use of a popular math manipulative used to teach place value and addition and subtraction with regrouping.

Base Ten Blocks are one of the best ways to help students learn about place value. While using the app students place Base Ten Blocks on an interactive Playground to represent numbers. Blocks can be regrouped or exchanged by dragging a virtual manipulative from one column to the next.

Using Hands-On Math Base Ten Blocks students can develop the following important mathematical concepts:

  • Place value concepts
  • Regrouping in the ones, tens and hundreds places
  • Basic operations: addition and subtraction
  • Naming numbers
  • Expanded notation
  • Reading and writing numbers

Base Ten Blocks are a very useful way for student visualize numbers, intuitively understand place value and deepen their understanding of addition and subtraction. Use Base Ten Blocks to have students represent numbers, as well as read and write the numbers. Rules for regrouping can be difficult for children. Use Base Ten Blocks to illustrate regrouping by dragging and dropping blocks from one column to another.

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Number and Operations -- Fraction

  • Develop understanding of fractions as numbers.


Numbers - Operations (2) - Fractions/Decimals/Percents/Ratios from Elevated Math
Twenty-five lessons provide initial instruction or intervention to help students with concepts involving fractions, decimals, exponents and powers, and percents.

Five of these lessons develop and deepen an understanding of mathematical concepts and relationships. Lessons include diagrams and illustrations of fraction strips, hundredths squares, number lines, grids, Venn diagrams, factor trees, symbols, drawings, and blocks. Problem solving is an integral part of each lesson.
M4.1 Concepts of Fractions, Ratios and Percents
M4.2 Concepts of Decimal Place Value and Fraction and Percent Equivalents
M4.3 Factors and Prime Factorization
M4.4 Prime Factorization, GCF, and LCM
M4.5 Simplifying and Converting Fractions

The next seven lessons present instruction in decimal operations, exponents and powers. When working with decimal numbers, student success depends on an understanding of whole numbers and place value. Students are hindered if a solid conceptual foundation is not built. In lessons 5.1 and 5.2 students use number lines to establish an understanding of relative location while converting, comparing, and ordering fractions and decimals. Lessons 5.3, 5.4, and 5.5 apply the four basic operations of adding, subtracting, multiplying and dividing. These lessons utilize models, illustrations, and/or diagrams to reinforce conceptual understanding of the content and development of algorithms. Lessons 5.6 and 5.7 help students develop a solid understanding of these unique numbers in contexts encountered outside the classroom in everyday life or in other subject areas. Estimation strategies and “reasonableness of answer” thinking are stressed throughout these lessons to develop the student’s number sense and flexibility of thought.
M5.1 Rounding and Comparing Decimals
M5.2 Converting, Comparing, and Ordering
M5.3 Adding and Subtracting Decimals
M5.4 Multiplying Decimals
M5.5 Dividing Decimals
M5.6 Exponents and Powers
M5.7 Scientific Notation

The next six lessons integrate diagrams, models, and illustrations of egg cartons, fraction strips, and fraction circles to help students develop conceptual understanding of what takes places when fractions are added, subtracted, multiplied and divided. Estimation strategies and “reasonableness of answer” thinking are stressed.
M6.1 Adding and Subtracting Fractions with Like Denominators
M6.2 Adding Fractions with Unlike Denominators
M6.3 Subtracting Fractions with Unlike Denominators
M6.4 Adding and Subtracting Mixed Numbers
M6.5 Multiplying Fractions
M6.6 Dividing Fractions

The last seven lessons focus on ratio, proportion, percent, and problem solving with percents. Models are used to differentiate between perfect squares up to 100 and other numbers, students recognize and identify perfect squares and their square roots, and students solve problem situations involving square roots and perfect squares in lesson 7.1. The lessons include:
M7.1 Square Roots
M7.2 Finding Percents
M7.3 Decimal and Percent Equivalents
M7.4 Ratios, Rates, and Proportional Reasoning
M7.5 Percent Proportions
M7.6 Using Percent Equations
M7.7 Problem Solving with Percents

Student print materials and Teachers' notes are available for download at www.elevatedmath.com.

Pizza Fractions: Beginning with Simple Fractions


Fraction Basics

Measurement and Data

  • Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
  • Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
  • Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Reason with shapes and their attributes.

  • Reason with shapes and their attributes.