Teaching Why (not just How): Column Addition and Subtraction

With enough rote practice, most students can learn to “carry the one” or “exchange/trade ten” to solve multi-digit addition and subtraction problems. But to truly understand the process and become fluent with it, students need to take a look under the hood and see the place value principles at work behind the operations. That’s why at Happy Numbers we focus on why the standard algorithm works, rather than how it works. We believe that by building understanding first, fluency will follow (and not vice versa). As a result, students are better able to find and correct errors and they are better-equipped to work with larger numbers and even decimals.
This post will share some of the activities we suggest for building deep conceptual understanding of column addition and subtraction. We’ll also explain how we scaffold instruction to help students create meaning, rather than just memorize steps. All of the activities shown are available at Happy Numbers, but you can re-create them in your classroom offline as well…

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K-2 Students Be Shoppin’!!!!

Two great reasons to use shopping-based exercises throughout your math instruction: students investigate concepts thoroughly by applying skills to a new situation, and the math itself is what piques student interest (rather than a separate, unrelated reward). We’ll show you how we scaffold this approach across a range of skill levels and how your students can benefit from shopping activities online or off!

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How the Hundred Chart Helps Students Add & Subtract

Students learning to add and subtract 2-digit numbers must rely on a solid foundation of place value understanding. Few resources emphasize place value as well as the hundred chart. It allows for more advanced 2-digit operations, which can become cumbersome with manipulatives such as base-10 blocks. Adding this tool to your shed will give you one more way to reach learners in your class — we’ll show you how…

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Number Sense with the Hundred Chart

Research shows that using multiple representations of an idea is a powerful approach to promote deeper mathematical thinking and conceptual understanding for your students. We recently blogged about the teaching potential of base-10 blocks and of the number line. Now, we would like to share with you the power of the hundred chart and how you can use it to create meaning with your students…

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The Pan Balance: Hands-On Approach to Equations

In an effort to meet our goals of building conceptual understanding, we at Happy Numbers look for ways to provide students with multiple representations of mathematical ideas. One often-overlooked representation of equations is the pan balance. Like other tools we’ve written about in our blog – real objects, base-10 blocks, number line – the pan balance is a great concrete visual that helps primary students “see behind the veil” of complex math problems.
Wondering how? Then keep reading!

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Do You Dread Teaching Regrouping and Exchanging? Let Us Help

A common misconception about math, held by children and adults alike, is that it’s about knowing formulas, methods, and procedures. Indeed, these aspects of math are important, but what’s much more important – even essential – is an understanding of the meaning behind those formulas, methods, and procedures. Regrouping and exchanging in two-digit addition and subtraction is one such procedure that is often used without understanding the underlying concepts. At Happy Numbers, we aim to resolve this misconception by designing activities that are visual, concrete, and coherent. Here, we would like to share with you some ideas we use to approach this challenging topic…

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2-Digit Addition and Subtraction (with Purpose and Meaning)

According to the Grade 1 Common Core State Standards, math instruction should focus on four critical areas, one of which is developing understanding of whole number relationships and place value, including grouping in tens and ones. Getting there doesn’t happen by accident: it starts with building a solid understanding of 2-digit numbers (which is the 1.NBT.B cluster) together with the ability to use place value understanding and properties of operations to add and subtract (1.NBT.C cluster). It’s an extremely important goal (and not the easiest one) as fluency with multi-digit numbers will build upon this knowledge.

Some time ago, we released our Numeration 21-100 topic, which is aligned with goals of the 1.NBT.B cluster. It is a sequence of 22 exercises covering how 2-digit numbers are composed, how to compare them, place value, and round numbers. These skills prepare students to successfully begin adding and subtracting 2-digit numbers, which is what our latest topic, Plus & Minus 1-100 (part 1) designed for.

In this post, we’ll walk you through the sequence of 16 exercises that comprise Plus & Minus 1-100 (part 1) to give you an in-depth view of the learning behind it…

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