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Guideline to helping students with math problems.

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I have many, many parents tell me they don't understand the math their child is doing, and they don't want to confuse them by showing them a different way to solve the problem. There are obviously different opinions revolving the Common Core State Standards (CCSS) but no matter what, we still want to be able to help our children with their homework and feel connected to what they are learning. I thought it would be helpful to explain some of the ways children are learning to add and subtract so we can better connect to the work they are doing in the classroom.

There are different models that are used to help children understand the relationship between addition and subtraction. I like to think of these two operations as always connected. I try not to teach one of these concepts without the other one. So in essence, as students are learning to add, they should also be learning to subtract.

Below are some of the models that students are using to help them understand the relationship between addition and subtraction. Hopefully seeing these models and understanding how to use them will help you when you see your child using them.
MORE: 5 Resources for Parents Who Are Stumped By Math Homework
Ten Frames: A ten frame is a 2 x 5 array that is filled with counters to teach children subitizing (seeing a number), combinations of 10, patterns and adding/subtracting. As the child fills the 10 frame they start to "see" the value of different numbers, and can begin to add and subtract numbers less than, equal to and greater than 10. One of the most important concepts of a ten frame is for a child to "know" that when the frame is filled it is equal to 10. They don't need to go back and count all the counters starting at 1. This also reinforces the concept of place value and our Base Ten System. Practice using ten frames with your child with this handy ten frame printable.

Image: GreatMinds.net

Base Ten Blocks: Base Ten Blocks are manipulatives used to represent place value and assist students in understanding the Base 10 System. Below is an example of using tens and ones to add with regrouping. Students use these blocks as a way to visualize the regrouping process so that when they learn the traditional algorithm they truly understand what they are doing. These really are helpful as the numbers get larger and students make careless mistakes - the base ten blocks help them to see their mistake and how to correct it.

Image: mason.gmu.edu

Part-Part-Wholes: A part-part-whole diagram is essentially a bar model that represents the different parts and wholes in a number equation. This model is an excellent way for young students to see the connection between addition and subtraction. I really like to use part-part-wholes when solving word problems. Students can identify the unknown number with a blank space or question mark, then decide whether they are going to add or subtract to solve.

Image 1: LangfordMath.com / Image 2: Hereford Elementary First Grade

Number Lines: Number lines are an excellent model for students to show or represent their mathematical thinking. They help students to move from the concrete/pictorial stage to a more abstract understanding of addition and subtraction. A great way for students to show understanding of both operations is to show addition above the number line and subtraction below, like in the visual below:

Image: SoftSchools.com

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Addition and Subtraction Models and Strategies

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I have many, many parents tell me they don't understand the math their child is doing, and they don't want to confuse them by showing them a different way to solve the problem.

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This game will help students learn to count by 2.

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Practice addition and subtraction with our popular math games. Discover fun and engaging learning games for children in grades 1 to 6.

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These catchy songs will help your child to remember how to add and subtract.

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These addition songs and subtraction songs are available from a variety of albums. Use them for teaching skip counting, place value, word problems, buying and selling.

Songs for Teaching Addition (Including Skip-Counting Songs)
4 Plus Song - Alan Stern
7 Plus Song - Alan Stern Zero the Hero Exercise and Count - Jack Hartmann
The 9 Rule - Jeff Schroeder
10 Silly Monkeys - Jack Hartmann
Add and Step On Ones Rap - Music with Mar.
The Add and Subtract Body Part Dance - Jack Hartmann
Add At a Circus - Music with Mar.
Add It On - Jennifer Fixman
Add One More - Ron Brown
Adding Doubles - Music, Movement & Magination
Addition and Subtraction - MindMuzic
Addition/Subtraction Word Clues Song - Tim Pacific
Alligator 10 More (Adding 10 to Any Number) - Jennifer Fixman
Bouncing Kangaroos Adding with Six - Music with Mar.
Climbing Ladybugs Adding with Nine - Music with Mar.
Columns - Arnold Rosenthal
Count-Ons - Jeff Schroeder
Counting 2's to 20 - Ron Brown
Counting by 1, 2, 5 and 10 - Jennifer Fixman
Double It Up - Jennifer Fixman
Doubles Plus One - Jeff Schroeder
Eight Jumping Adding Puppies - Music with Mar.
Fact Family - Music with Mar.
If You Know How to Count, You Can Add by One! - Marla Lewis
It's A Party (Addition) - MindMuzic
Know Those 10's - Jennifer Fixman
Numbers With a 1 - Listen & Learn
One More Please - Music, Movement & Magination
The Pizza Eating Alligator - Jennifer Fixman
Random Addition Quiz - Alan Stern
Round it Off - Arnold Rosenthal
Solving "Real Life" Problems - Jeff Schroeder
Ten Adding, Swinging Monkeys - Music with Mar.
When You're Adding Boxes - Kathleen Wiley
You Carry Over - Arnold Rosenthal

Songs for Teaching Subtraction
13 Minus Song - Alan Stern
Addition and Subtraction - MindMuzic Random Subtraction Quiz - Alan Stern
Step Back: Counting Back to Subtract - Carl M. Sherrill
Twelve Flying Subtracting Bees - Music with Mar. Subtract and Step On Ones Rap - Music with Mar. Two Subtracting Marching Ants - Music with Mar.
When the Box is in the Front - Kathleen Wiley Subtract with an Addition Fact - Jennifer Fixman
Subtracting by One: One Less Penny - It All Adds Up
Subtraction - Jeff Schroeder Bluesy Subtraction - Music with Mar.
Fact Family - Music with Mar.
Five Fish (Subtraction) - Ron Brown
Five Hopping Subtracting Frogs - Music with Mar.
It's A Party (Subtraction) - MindMuzic
Long Subtraction - Learning By Song/Barbara Speicher
The One-Less-Penny Blues (Subtraction) -Music, Movement & Magination
The Pizza Eating Alligator - Jennifer Fixman

When You Are Subtracting - Learning Math by Song

Money and Coin Songs that Teach Addition and Subtraction Facts
and Concepts
15 Cents - Music, Math and Money
It Starts with a Penny - Music with Mar.
Money Counts - It All Adds Up
Subtracting by One: One Less Penny - It All Adds Up
The U.S. Money Song - Tim Pacific

Teaching the Concept of Place Value in Addition and Subtraction
Columns - Arnold Rosenthal
What Place? - Learning Math by Song

Teaching How to Solve Word Problems
Adding and Subtracting Vocabulary - Jim Thompson
Solving "Real Life" Problems - Jeff Schroeder
Solving Word Problems - Learning Math by Song

Math Books & Musical Plays
Mastering Math: A Sherlock Holmes Problem Solving Mystery - Bad Wolf Press
Math Facts to the MAX! - Carl Sherrill
MatheMagical Showtime! - Carl Sherrill
RiddleMath - Carl Sherrill

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These addition songs and subtraction songs are available from a variety of albums. Use them for teaching skip counting, place value, word problems, buying and selling.

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If your child is having any trouble, this is a great reminder for them.

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National Center on Intensive Intervention

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Using Manipulatives to Illustrate Addition Problem Structures

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If your child is having any trouble, this is a great reminder for them.

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National Center on Intensive Intervention

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Using Manipulatives to Illustrate Subtraction Problem Structures

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After completing the addition worksheet, students will work on this subtraction worksheet. Students are expected to use manipulatives to help them solve the problems.

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I will begin my lesson using this simple addition worksheet. Students will need to use manipulatives to solve problems.

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This addition and subtraction game will be homework for students. I want students to work for 10 minutes every night to enhancing adding and subtracting skills.

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AdaptedMind is a customized online math curriculum, problems, and worksheets that will significantly improve your child's math performance, guaranteed. We make learning fun, game-oriented, and give you ways to get involved.