## Grade 2 Overview: Fluency with Addition and Subtraction

The world of numbers is extremely vast, and that is the main idea students explore in Grade 2. They extend their knowledge of numbers from 100 to 1000 and review operations they learned in Grade 1 with larger numbers. The fluency with addition and subtraction students grasp within this school year creates a firm foundation for the multiplication and division they will encounter in Grade 3.

In the Happy Numbers Grade 2 curriculum, students work extensively with place value, as they need to understand number positions to master operations with three-digit numbers. They study new instruments for math operations, such as Place Value Disks and the Place Value Chart, and expand their knowledge of procedural fluency by learning the standard algorithm of Column Addition and Subtraction and Mental Strategies. Students practice these skills using tangible and vivid visual models given in multiple representations to build a solid and powerful foundation for future math achievements.

Explore below many of the tasks and learning scenarios for Grade 2!

All exercises mentioned below are part of the Happy Numbers course for Grade 2. Visit HappyNumbers.com to explore our full curriculum and sign up for a free trial.

## Foundation for Fluency

Happy Numbers leads students to fluency development in several steps. First, they practice making ten.

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Then they progress to adding ones to ten or subtracting ones from a two-digit number to get ten.

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Also, students add and subtract a one-digit number and a two-digit number without passing through ten.

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And finally do this across a ten.

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In Module 1, students work with numbers up to 100.

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## Length Measurement

In Grade 1, students became familiar with the concept of a unit for length measurement. They review it first through a real-world scenario with sneakers.

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Then Happy Numbers reminds them about using centimeters…

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…and introduces the ruler.

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With the ruler, students learn the concept of a millimeter and its relation to a centimeter.

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Finally, they use both units of measurement to determine sums and differences of lengths.

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## Three-Digit Numbers & Place Value

Students begin to practice with three-digit numbers on the familiar model of objects in ten-frames.

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They develop fluency in number sequencing beyond 100 by solving exercises with the Number Line.

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Students learn to build a three-digit number using the Base-10 Block representation. Obviously, this model becomes limited with larger numbers, so Happy Numbers also includes place value cards in this exercise. These reinforce the representation and help to develop place value determination.

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Then students practice decomposition of a number into hundreds, tens, and ones using only place value cards.

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In addition, they learn unit, standard, expanded, and word forms of numbers on memorable visual scenarios like this one with cute octopuses. In Happy Numbers, all exercises are voiced in English and Spanish, so students can read and listen to instructions in the language of their choice.

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Students become familiar with the Place Value Chart. It’s very useful when working with compound numbers. The representation is more abstract than previous ones, and is handy, as students can drag disks through the chart as manipulatives. First, they learn to use it for two-digit numbers.

To see the full exercise, follow this link.

Then they start practicing with three-digit numbers.

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Through a variety of exercises and visual representations, Happy Numbers helps students learn the equivalence between ones, tens, hundreds, and thousands. They reinforce knowledge through dialogue with funny bigheads.

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To develop place value determination skills, Happy Numbers leads students to solve “more or less” tasks. They add and subtract 1, 10, or 100 to or from different three-digit numbers.

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Game-like scenarios make math engaging and help to work new skills out!

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Finally, students can identify counting patterns and complete a number series according to it.

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## Comparing Three-Digit Numbers

To strengthen students’ fluency with numbers to 1000 and their place value, Happy Numbers underpins the curriculum with exercises on number sequencing and comparing. First, students grasp the difference between two-digit and three-digit numbers with visual scaffolding.

To see the full exercise, follow this link.

Then they learn to compare two three-digit numbers. Place value cards help to determine the difference whether numbers vary in hundreds, tens, or ones.

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In addition, students practice on complex tasks where they need to first build numbers based on visual representations and then arrange them in ascending and descending order.

To see the full exercise, follow this link.

## Column Addition and Subtraction

In Grade 2, students also explore the standard algorithms of Column Addition and Subtraction to build procedural fluency in light of place value. It’s an amazingly powerful foundation for developing math mindset! We start to use it in conjunction with Place Value Cards to help students understand that here they need to apply knowledge of place value that they already have.

To see the full exercise, follow this link.

Only then do they transfer to using columns alone for addition of two-digit numbers without regrouping.

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In addition, they practice on a disk model. Happy Numbers uses these representations alone or together to show the scalability of the mathematical operation and build a complex concept understanding.

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For example, this is how it looks when students learn to add with exchanging into the hundreds.

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Happy Numbers provides step-by-step guidance to explain each new concept. Watch how students learn to subtract with exchanging through step-by-step prompting.

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Later, students use the skill to solve two- and three-digit column subtraction.

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Finally, they work through the standard algorithm with two three-digit numbers.

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Columns will be used later for multiplication, so it’s very important to study this procedure qualitatively. Happy Numbers provides students with a large number and variety of tasks for practicing and developing its usage.

## Mental Strategies

Module 5 of Happy Numbers’ Grade 2 curriculum is concentrated on developing Mental Strategies for addition and subtraction within 1000. Mental Strategies are also built upon place value, and Happy Numbers first explains this connection with the help of unit form and Place Value Disks. Students see that addition of round numbers is as easy as addition of single-digit numbers.

To see the full exercise, follow this link.

To see the full exercise, follow this link.

Step by step, Happy Numbers gives students fewer hints and more freedom to solve in a way that is comfortable for them.

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Nevertheless, we don’t want students to forget about making 10 or 100 first…

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…a skill that also applies to subtraction, the flip side of addition.

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After this practice with three- and two-digit numbers, students solve tasks with only three-digit numerals. They are ready!

To see the full exercise, follow this link.

## Preparation for Grade 3

After substantial addition and subtraction practice, students move on to the basics of multiplication and division. In Grade 2, they won’t yet be directly involved in these mathematical operations, but they will become familiar with the basic concepts of equal groups, repeated addition, and an array.

Because it’s the very beginning, we start with manipulatives that look the same as real objects.

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Students fluently drag the numbers and signs on the screen, creating a deep, tangible experience.

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Next comes repeated addition sentences based on an array.

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This is doubly powerful because arrays will be used not only in the forming of multiplication, but also in the measurement of area that they will study in Grade 3. Students complete tasks that build this foundation in Topic C of Module 6.

To see the full exercise, follow this link.

Colored squares look the same as area units and are used here as manipulatives for building simple geometric figures students will learn to measure in Grade 3.

## Practice Makes Perfect

When a teacher can’t stand behind students’ backs each minute, it’s very important to choose an instrument that will grab attention and adapt to the needs of each student. That is what we thought about when creating exercises for your class. After all, to master anything in math, it’s necessary to try, try, and try again. That’s why Happy Numbers prepared a great number of exercises with vivid and understandable visual models, voiceover support, and engaging scenarios. The friendly and responsive program will immerse students in math and help them to master Grade 2 standards with pleasure. Explore the Grade 2 curriculum, and develop fluency in your class!

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