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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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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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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(This is a guest post from our friend Brandi, an elementary teacher who will share a fun classroom activity for promoting awareness of large numbers.) A Guessing Jar is one of my favorite activities for promoting number sense and an awareness of how large a number is. I love that it can be filled with anything small or large and right away we have a number activity that is unique every time. n order to allow everyone a chance to bring in something for the jar, I have each student bring in an item for the jar during their birthday week. Candy is always a favorite but it’s up to each child. I have had everything from candy to cotton balls to Legos. The first thing my students do is make their individual estimates. At the beginning of the year their guesses fall into a wide range of way too small to way too large, but by mid-year or end of the year the guesses are becoming more and more accurate.

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Difficulty in reading can spill over into other subjects, affecting student performance. Our mission is to make math accessible and enjoyable for all students, while helping teachers run effective, independent centers. For some time now, Happy Numbers has been working to add auditory directions to our online math exercises. This new sound feature allows students to click on the directions within any exercise to hear them read aloud. Now, your primary students can strengthen their math skills without being hindered by reading ability!

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Every year when I start things rolling in my third grade classroom, I am amazed at the levels of abilities of my students. There are always a handful of students who, for whatever reason, are lacking number sense in big ways. This handful of students typically struggles with making combinations to 10. So I do what any teacher would do best, I re-teach, and re-teach, and re-teach. I always start with a concrete approach first. For example …

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How can you help your primary students make the leap from working with small numbers to becoming fluent with larger ones? One way they can start thinking in larger ‘chunks’ is by counting by tens. More than just an oral exercise, counting by tens is an essential skill that builds number sense, encourages thinking about number structures, and economizes counting and operations. Students with a strong conceptual understanding of round numbers, a ‘ten’, and ‘the tens place’ are better prepared to work with two-digit numbers and beyond. In this post, we will share the ideas behind our exercises in the topic Counting by Tens and some additional tips on reinforcing counting skills using Unifix cubes…

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