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 greater 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 embraces the idea that if students understand composition of ten they will easily cope with addition and subtraction of any two- or three-digit numbers. That’s why Grade 2 starts with developing fluency with composing ten in familiar scenarios such as cubes, a berry truck, a UFO, and the number line.

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(see Grade 2 Module 1 — Topic A: exercise c)

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(see Grade 2 Module 1 — Topic A: exercise b)

Once this foundation is laid, students grasp the principle of two-digit number composition based on the addition of ten and ones. Modeling with and without manipulatives allows students to compose and decompose numbers into tens and ones and effectively master work with two-digit numbers.

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(see Grade 2 Module 1 — Topic A: exercise d)

The next step in building fluency within 100 is addition of a two-digit number and a single-digit number with and without moving across a ten. Happy Numbers provides students with visual models differing in the level of abstraction as they gradually build conceptual understanding.

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(see Grade 2 Module 1 — Topic B: exercise a)

When it comes to addition across a ten, Happy Numbers thoroughly and systematically explains the transition. The persuasive model of Base-10 Blocks clearly clearly presents each step of this math operation.

Dive into Three-Digit Numbers

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

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(see Grade 2 Module 3 — Topic A: exercise b)

They develop fluency in number sequencing beyond 100 by solving exercises with the Number Path: from quite simple to more complicated.

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(see Grade 2 Module 3 — Topic B: exercise i)

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(see Grade 2 Module 3 — Topic B: exercise n)

No less important, students 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 study proper pronunciation together with all written forms.

Topic E starts with exercises aimed at the recognition of three-digit numbers on the Base-10 Block model. Obviously, this model becomes limited with larger numbers, so we use it at the beginning for the sake of explaining new material with a familiar scenario and gradually introduce a new instrument — the Place Value Chart.

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(see Grade 2 Module 3 — Topic E: exercise b)

This model comes in handy when forming an understanding of compound numbers. At the same time, this model is more abstract and more practical. By moving Place Value Disks within the chart, students grasp the composition of two- and three-digit numbers and build meaning behind each digit in the number. Moreover, they will have so much fun working with it, as Place Value Disks are used as manipulatives!

Because students have already mastered the skill of number sequencing beyond 100, they are now ready to compare numbers. For that skill, Happy Numbers offers Place Value Cards, which clearly demonstrate digits’ places.

 

At the end of Module 3, Happy Numbers offers practice with 1, 10, or 100 more or less on the model of the Place Value Chart.

 

Here, students also build the skill of counting by tens, which will hereafter help them to work with round numbers. It’s a useful skill for everyday math, helpful in many common situations, for example, payment in a store!

Column Addition and Subtraction

In Grade 2, students also explore the standard algorithm 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.

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(see Grade 2 Module 4 — Topic B: exercise b)

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

 

Next, students learn to add across tens and do the same with subtraction.

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(see Grade 2 Module 4 — Topic C: exercise h)

Then comes the important skill of adding two-digit numbers with exchanging into the hundreds. In Happy Numbers, these exercises include Place Value Disks, in which the addends are specially color-coded  to help differentiate numbers in an equation.

In Module 5, tasks include all three-digit numbers to add or subtract using the standard algorithm (Column Addition and Subtraction). Students solve equations with and without multiple exchanges, using both the model of Place Value Disks and Column Addition. First, they solve an equation with the help of Place Value Disks.

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(see Grade 2 Module 5 — Topic B: exercise a)

 

And then just with Column Addition.

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(see Grade 2 Module 5 — Topic B: exercise c)

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(see Grade 2 Module 5 — Topic C: exercise e)

 

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 of 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.

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(see Grade 2 Module 5 — Topic A: exercise a)

 

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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(see Grade 2 Module 5 — Topic A: exercise d)

 

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

 

image16(see Grade 2 Module 5 — Topic A: exercise f)

 

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

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(see Grade 2 Module 5 — Topic A: exercise j)

 

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

 

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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(see Grade 2 Module 6 — Topic A: exercise a)

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

Next comes repeated addition sentences based on an array.

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.

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(see Grade 2 Module 6 — Topic C: exercise c)

 

Colored squares look the same as area units and are used here as manipulatives for building simple geometric figures students will learn 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 exercise 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.

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