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 in addition and subtraction students attain this 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 use new tools 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 provided in multiple representations to build a solid and powerful foundation for future math achievements.

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

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.

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

Also, students add and subtract a one-digit number and a two-digit number without regrouping.

And finally, students do this regrouping.

In Module 1 students practice working with numbers up to 100 with the help of multiple visual exercises like, for example, this one:

## Length Measurement

In Grade 1, students became familiar with the concept of a length measurement unit and now they review the topic in a familiar scenario. They try to measure the length of a skateboard in sneakers!

Soon students quickly discover that measuring skateboard in sneakers might not give us an exact and common result for all. How do we measure if we all have different-sized sneakers?
Once they realize that and get a clear understanding of the idea, we can introduce measurement units for length.

Explaining this concept thoughtfully, by referring to visual images of familiar objects, will strengthen conceptual understanding. Consider this example, in which Happy Numbers measures the length of a penny in centimeters, which are represented by cubes.

Moving further, students measure longer objects, like keys, still referring to the same cube representation of centimeters.

Now students are ready to start learning how to use a centimeter ruler and measure objects with it.

Slowly they practice identifying the measurement on the ruler that’s closest to the endpoint of the object. Happy Numbers makes sure that students polish their new skill and shows a video that explains how to use a ruler to measure the length.

Once students master the skill of measuring lengths with a centimeter ruler, they move to bigger and taller objects. In this process, they realize that they need other measurement tools. How can anyone measure the length of a bridge using a centimeter ruler? This is a good chance to introduce another measurement unit, the meter, and reveal its connection to the centimeter.

Finally, they use both units of measurement to determine sums and differences of lengths. Like in this example, where students need to measure the length of an ice cream before and after it starts melting. Again, Happy Numbers refers here to some familiar and yummy objects, in order to make it easier for students to practice a new skill!

Students are now ready to use tape diagrams to represent and solve addition and subtraction word problems involving length. That is how Happy Numbers scaffolds the way to some crucial math concepts in the easiest and most comprehensive way.

Having taught the students how to use centimeters and meters, we cannot move from this topic without giving a clear explanation of what inches are. It’s high time for Happy Numbers to show the difference between centimeters and inches with the help of Dino and his friends!

Understanding the concept of centimeters and inches may be confusing for students at first. That is why we demonstrate it with many visual examples where the same objects are measured both ways.

## Three-Digit Numbers & Place Value

In this Module, students begin manipulating three-digit numbers on the familiar model of objects in ten-frames. Moving boxes of apples into the truck helps them visualize the number of objects manipulated.

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

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 which reinforces the representation and helps to develop place value determination.

After that, students practice decomposition of a number into hundreds, tens, and ones using only place value cards. This one, for example, practically lets students break the number into its parts with the help of some tools.

In addition, they learn unit, standard, expanded, and word forms of numbers during memorable visual scenarios like helping the police investigate a spy case. 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.

Joining favorite characters in their investigation, students start practicing each number form, moving step by step. Captain Pterlock and Detective Lizzard won’t take aboard those who’re not ready for challenges!

Missions get more exciting when students are given limited chances for mistakes. Now they have to try and save their lives (hearts at the top right corner of the screen) while practicing standard forms of numbers.

Students even get a chance to be secret agents for a while and tune all their spy gadgets like listening devices, for example,  before they go on a mission. But first, they need to figure out how to work with this cool device by showing the expanded form of a given number.

Now it’s time to get 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.

Then they start practicing with three-digit numbers.

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.

To develop place value determination skills, Happy Numbers leads students to solve “more or less” tasks. They begin with the support of a disk model using a place value chart.

They add and subtract 1, 10, or 100 to or from different three-digit numbers.

Finally, students can identify counting patterns and complete a number series according to it. Game-like scenarios make math engaging and help students work new skills out with a minimal amount of anxiety.

## 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 master the difference between two-digit and three-digit numbers with visual scaffolding.

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

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

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 a math mindset! We start to use it in conjunction with Place Value Disks to help students understand that they need to apply previously gained knowledge of place value.

Then they transfer to using columns for addition of two-digit numbers without regrouping with scaffolding by disk model. Watch how Happy Numbers moves from familiar real-life objects, columns, to column addition.

Happy Numbers uses these representations alone or together to show the scalability of the mathematical operation and build deep conceptual understanding.

When students have finally grasped the idea of Column Addition, they are ready to move from Place Value Disks to some more exciting training activities. Again, giving a limited amount of chances for mistakes spices it up a little and brings in added challenge.

Now when the students know everything about two-digit addition without regrouping, Happy Numbers introduces exchanging ones for tens with the help of place value disk because students are now ready to conquer new math heights.

They start practicing on Place Value Disks with step- by- step instructions and hints from their favorite characters.

And slowly move from the addition of two-digit numbers with the help of the model…

….to the addition of two-digit numbers without it.

Now when students build on their understanding of column addition and exchanging to move into the tens place they can move to learning addition with exchanging into the hundreds. Still, with the help of Place Value Disk exercises Happy Numbers guides students through the transition.

Like always, step-by-step prompting helps ensure conceptual understanding and procedural fluency. The next stage is a familiar transition to a gradual release model which helps students become independent with these multi-step problems.

Happy Numbers provides play-by-play guidance to explain each new concept and walks students through each step. Watch how they learn to subtract with exchanging using familiar tactics.

Later, students use the same skills to solve two and three-digit column subtraction. Now it seems much easier to perform the same steps that they went through while mastering addition!

Finally, students work through the standard algorithm with two three-digit numbers and this is how we create careful stepwise instructions to promote students’ understanding of Column Addition and Subtraction.

Columns will be used later for multiplication, so it’s very important to study this procedure qualitatively and Happy Numbers will make sure of it by providing 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.

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

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

…a skill that also applies to subtraction, the flip side of addition.  That’s why we provide them with relevant exercises on that as well.

After this practice with two and three-digit numbers, students begin solving tasks with only three-digit numerals. Now they are ready to move on!

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

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

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

Next come repeated addition sentences based on an array.

This is doubly powerful because arrays will be used not only in 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.

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.

## Even and Odd Numbers

Students explore the concept of even and odd in multiple ways. Firstly, students pair the objects as this idea seems to be essential for understanding the whole phenomenon.

Classically, Happy Numbers refers to familiar objects in order to root the idea. Here, for example, where we ask them to pair yummy cupcakes!

Students use pairing, addition patterns, and number line patterns to determine the main principles of even and odd. Dino will help them see what numbers even and odd numbers end with and will help them understand how to differentiate between them.

Here’s an example of a number line pattern with a word sentence which may help to practice the skill at a new level.

Students also use ending digits to determine even or odd in numbers up to three digits by helping Dino around the factory.

Being able to differentiate between even and odd is one of  multiple essential math skills. In order for students to practice it and master it on another level, Happy Numbers created lots of interactive exercises!

## Problem Solving with Data

Besides helping students learn new math skills, Happy Numbers makes sure they can use them in practice for different purposes, including problem solving and data reading. That is why we created a set of exercises for students to practice analyzing data in line plots. Here, for example, they can experiment on measuring lengths of animals.

Students learn to create line plots based on measurements, compare the results and answer the questions to analyze the data. This is how we lay a groundwork for future development of data reading skills.

## Fractions as Equal Parts of Shapes

In 2nd Grade, students prepare for work with Fractions by building upon their knowledge of halves, thirds, and fourths to answer more complex questions about fractional parts of shapes. They split shapes into given fractions, identify the size of fractional parts, and tell how many parts make a whole.

As always, Happy Numbers provides some good exercise to review skills and prepare students for the next step. Joining Dino in one of his journeys will help them to refresh their memory in the most exciting way!