Grade 4 Overview: Working with Number Positions

All the knowledge students have accumulated about the place value over the previous grades will be used and expanded in Grade 4. This year, they will learn numbers within one million, study rounding, multiply and divide multi-digit numbers, learn the concept and properties of divisibility, and work with fractions in unit, fraction, and decimal forms. Happy Numbers offers such a curriculum for K-4 that will help teachers build meaning behind algorithms of multiplication and division and lay the foundation for developing fluency with fractions in Grade 5.

This math year is much more serious and analytical than previous years. Students already learned a number of strategies for different math operations, and in Grade 4 they will need to first select the necessary written or mental method and then accurately apply it. They begin to manage their math ‘baggage’, and that is what we call math mindset! Grade 4 is a very important year in mathematics, when students have laid out patterns of solving certain mathematical situations. Happy Numbers is very glad to be your partner when students really need wise guidance!

Let’s take a sneak peek at the Happy Numbers Grade 4 pedagogy!

All exercises mentioned below are part of the Happy Numbers course for Grade 4. Visit to explore our full curriculum and sign up for a free trial.

Multi-Digit Numbers and Rounding

Students start to work with multi-digit whole numbers by relating tens to hundreds to thousands in the base-10 system. By using manipulatives, word form, and numerical form, Happy Numbers reminds them about the ratio of ones, tens, and larger numbers.


Already in exercise C of Topic A, students form 1 million by repeated multiplication by ten. Happy Numbers shows the process on the Place Value Chart, which was first introduced in Grade 2.

Students progress the whole way to 1 million step-by-step to strengthen understanding.


Students review units and place value within 1 million. Practice makes perfect, doesn’t it?


Topic B starts the comparing of multi-digit whole numbers within 1 million. Students learn comparing based on number positions with the help of Place Value Cards and Chart.


(see Grade 4 Module 1 — Topic B: exercise b)

Happy Numbers always builds understanding on a concrete visual model and then gradually transitions to abstract. So if there is a mistake in a numerical task, the software will rapidly give instant feedback on a visual model. Our students learn from their mistakes, forcing their math mindset to grow!

Simultaneously with comparison, students practice number sequencing within 1 million…


(see Grade 4 Module 1 — Topic B: exercise e)

…and determine 1,000/10,000/100,000 more or less on the Place Value Chart with color-coding.


Students explore rounding of multi-digit whole numbers in exercises with vivid cosmic style! Happy Numbers combines the Number Path and familiar scenarios with UFOs to engage students and boost their inspiration. Because what can motivate more than the goal of building a spaceship?

Students then come to the addition of multi-digit whole numbers. First, they try it with visual help of the Place Value Chart and Column Addition with and without color- coding.


(see Grade 4 Module 1 — Topic D: exercise c)

In the last Topic of Module 1 they do the same, but with subtraction. See how it looks with Place Value Disks.

By applying colored manipulatives for each number position, Happy Numbers builds conceptual understanding of place value principles. Students will grasp the knowledge through bright visual models and easily transfer it to abstract equations.

Area and Perimeter Formulas

Before Happy Numbers begins the dive into the most important and challenging part of the Grade 4 curriculum — multi-digit multiplication and division — students encounter the formula for rectangle area measurement and its notation. In several exercises of Topic A in Module 3, they learn and practice it, solving for different parts of the formula.


(see Grade 4 Module 3 — Topic A: exercise b)

(see Grade 4 Module 3 — Topic A: exercise d)

Together with the formula of area in this topic, Happy Numbers introduces a perimeter formula and its variations.


(see Grade 4 Module 3 — Topic A: exercise e)

Multi-Digit Multiplication

Beginning with multiplication by 10, 100, and 1000, our trip into multiplication relies heavily on the Place Value Chart. Students drag colored manipulatives, multiply them, and then write multiplication sentences. Step-by-step instruction draw a full and comprehensive picture of the procedure, so students will grasp its application, including the place value transformation.

How to get students excited about math? Give them a challenge! Attempting to navigate on-screen obstacles will force students to optimize the counting process and quickly propose the correct answer.


Working with the Place Value Chart allows students to develop more advanced multiplication skills. They’ll learn to make a trade while multiplying and combine factors in equations.

In Topic C, Happy Numbers introduces Column Multiplication with partial products. Students use a numerical equation, a Place Value Chart, and the Column record to find an answer. Dino guides them step-by-step through the process.

Here, students practice multiplying numbers up to four digits by single-digit numbers. They work extensively with place value understanding using manipulatives they can move while solving tasks.


Next, students learn the standard algorithm for solving multiplication equations. They begin using it in conjunction with a Place Value Chart. And it works! With each exercise, Happy Numbers provides fewer hints, and finally students can multiply up to four digits by a single-digit number without the help of the software.

At the end of the topic, students review the partial products method, standard algorithm, and distributive property of multiplication on tasks with area of a rectangle.


(see Grade 4 Module 3 — Topic C: exercise n)

Multi-digit multiplication continuous in Topic H, where students will learn multiplication of two-digit by two-digit numbers. They start with multiplication with a round number, which they need to split into a multiple of 10.


Next, they apply the method of splitting an area measurement by using the distributive property.


(see Grade 4 Module 3 — Topic H: exercise h)

Students review usage of partial products and the standard algorithm first on equations with round numbers and then on equations with any two-digit numbers.

Multi-Digit Division

Students start to expand their knowledge about division by reviewing the concept of equal groups in a familiar scenario with real objects.


(see Grade 4 Module 3 — Topic E: exercise b)

They learn the definitions of quotient and remainder on a visual model with tennis balls and an array model.


(see Grade 4 Module 3 — Topic E: exercise e)

Then students transition to studying multiples. It’s no problem for those who learned the Multiplication Table in Grade 3!


(see Grade 4 Module 3 — Topic E: exercise h)

Happy Numbers adds Tape Diagrams when necessary to visually explain new concepts.


(see Grade 4 Module 3 — Topic E: exercise k)

And students will apply it in tasks with engaging real-world scenarios.


(see Grade 4 Module 3 — Topic E: exercise n)

Then students learn the definition of divisor. Dino helps students to visually represent the equation.


(see Grade 4 Module 3 — Topic E: exercise q)

After that, Happy Numbers introduces long division with single- and two-digit numbers. It comes with plenty of support from Dino  and the Place Value Chart.


(see Grade 4 Module 3 — Topic E: exercise r)

With the same algorithm, students solve division problems that involve regrouping or require recording of partial quotients.


(see Grade 4 Module 3 — Topic E: exercise x)

Finally, students try to solve division equations by long division without additional visual models. Will they succeed with such a hard task? If students make a mistake, Happy Numbers reminds them of the steps they just learned.


(see Grade 4 Module 3 — Topic E: exercise y)

Now it’s time for a break to review some familiar topics. Students join Dino in his balloon flight revisiting the Multiplication Table, completing number sentences, and finding all factors on array model.

Next, Happy Numbers introduces the concept of divisibility and its properties and builds the connection between factors, multiples, and divisibility. Happy Numbers also remind students of properties of multiplication, which are necessary here.

They become familiar with the concepts of prime and composite numbers and begin to decompose numbers into all possible pairs of factors to find all prime numbers up to 100.

In Topic G, students polish their knowledge of notation of division equations. They use unit and standard notation as well as a disk model for building fluency within abstract modeling.


(see Grade 4 Module 3 — Topic G: exercise b)

Then Happy Numbers offers several tasks on practicing long division of three- and four-digit number by a single-digit number. These problems are presented with and without the visual model of a Place Value Chart or Tape Diagram, regrouping, partial quotients, and a reminder. There are equations on division across zero or with zero in the quotient. This variety of exercises helps build fluency with the method!


(see Grade 4 Module 3 — Topic G: exercise y)

Operations with Fractions

Module 5 of the Grade 4 curriculum is a key component of the study of fractions in elementary school. Here, Happy Numbers offers a comprehensive system of exercises designed to foster students’ knowledge of fractions and operations with them. They explore notations, comparison, equivalence, addition, subtraction, and  multiplication of a fraction and a whole number. They also perform operations with mixed numbers and improper fractions. But first, they review Grade 3 exercises to reinforce fraction notation on visual models with a shaded figure.


(see Grade 4 Module 5 — Topic A: exercise a)

As always, students smoothly transition from learning rules based on step-by-step instructions and visual models to numerical and abstract thinking.


(see Grade 4 Module 5 — Topic A: exercise e)

Students grasp the concept of fraction equivalence and its notation by multiplication and division in Topic B of Module 5.


(see Grade 4 Module 5 — Topic B: exercise c)


(see Grade 4 Module 5 — Topic B: exercise f)

Happy Numbers helps students to study comparison of fractions on Diagrams, the Number Line, and tasks based on real-world scenarios. They will learn several important methods for comparing fractions: comparing fractions with like numerators or denominators, using benchmark fractions such as 1/2 and 1, and renaming fractions with a common denominator (an important cornerstone of the Grade 5 curriculum).


(see Grade 4 Module 5 — Topic C: exercise j)


(see Grade 4 Module 5 — Topic C: exercise k)

Here are some sweet exercises to increase students’ appetite for fraction addition and subtraction!


(see Grade 4 Module 5 — Topic D: exercise a)

Get ready for quick thinking! Students help a skateboarding cat pass all obstacles. A right answer = a swerve to safety.. Don’t worry, no cats are harmed in the mastering of this math skill.


Happy Numbers illustrates subtraction of fractions on the Number Line and then asks students to complete the rule. By filling gaps in the rule, they can better understand and analyze the math operation they just performed.


(see Grade 4 Module 5 — Topic D: exercise f)

…and then practice it in a fun task with the cute character!


(see Grade 4 Module 5 — Topic D: exercise f)

Mixed Numbers

After students find that the same numerator and denominator form 1, they study the concept of mixed numbers. As always, the idea is introduced with an easy-to-understand visual model, then they are ready for a numerical approach.


(see Grade 4 Module 5 — Topic E: exercise b)

Students practice renaming mixed numbers as repeated addition. This helps them rewrite mixed numbers as improper fractions and vice versa.


(see Grade 4 Module 5 — Topic E: exercise f)

Students will feel like inventors in these Happy Numbers lessons! See how cool it is to practice mixed numbers with creative exercises:

Now it’s time to extend and apply students’ previous knowledge. They need to use algorithms they learned for fractions to compare mixed numbers. Happy Numbers exercises are designed to relate to the students’ experiences and interests. For example, the rule here is presented in the form of an online chat.


(see Grade 4 Module 5 — Topic E: exercise l)

They will apply this skill in different engaging tasks like this one. Who doesn’t want to feed a cute kitten?

Finally, Happy Numbers offers a review task in which students need to be especially focused to preserve all their hearts.

Now students are ready for an extensive practice of addition, subtraction, and comparison of mixed numbers with like denominators.


(see Grade 4 Module 5 — Topic F: exercise l)


(see Grade 4 Module 5 — Topic F: exercise o)


(see Grade 4 Module 5 — Topic E: exercise m)

At the same time, they continue to develop their number sense by estimating the sums of mixed numbers.


(see Grade 4 Module 5 — Topic F: exercise a)


(see Grade 4 Module 5 — Topic F: exercise b)

We finish the Module with multiplication of a fraction by a whole number. Happy Numbers introduces it as repeated addition on a visual model such as a Tape Diagram, and later as a numerical equation. The culmination of the topic is multiplication of a whole number by a mixed number.


(see Grade 4 Module 5 — Topic G: exercise f)

Finally, students will practice repeated addition of fractions as multiplication on cosmic visual models. The conquest of the universe is available only to those who have mastered the fraction, isn’t it?

Decimal Fractions

In Module 6 of Grade 4, students dive deeper into the world of fractions and become familiar with the decimal form. They learn the meaning behind decimals and equivalence between different number notations, which will help them compare and perform operations with decimals.

In this Module, Happy Numbers uses two types of tasks. The first includes a decimal fraction and its visual representation, which reminds students of the correspondence between different types of numerical notation and grasp it visually. The second is where students need to fill the gaps in fraction notation and finally record them by themselves.

In Topics A and B, Happy Numbers mainly work with notation of decimal fractions with tenths and hundredths. Students already have a direct understanding of fraction meaning from the end of the Grade 3…


(see Grade 4 Module 6 — Topic A: exercise a)


(see Grade 4 Module 6 — Topic B: exercise b)

…so they only need to grasp that it is the same entity in a different representation. Building meaning behind fraction notation can be done step-by-step as a puzzle!


(see Grade 4 Module 6 — Topic A: exercise c)


(see Grade 4 Module 6 — Topic B: exercise e)

Students also learn the algorithm for forming for mixed numbers as decimals. Dino and the grasshopper are a strong team to study with!


(see Grade 4 Module 6 — Topic A: exercise f)


Happy Numbers uses the Place Value Chart to build understanding of place value in decimal numbers. Students fill all the gaps including the one for the decimal to consolidate knowledge about decimal notation.


(see Grade 4 Module 6 — Topic A: exercise m)

For decimals with hundredths, Happy Numbers presents an area model separated into 100 parts. It’s convenient and easy to work with on the screen!


(see Grade 4 Module 6 — Topic B: exercise f)

Students will also study decimal equivalence when there is a zero at the end of a number…


(see Grade 4 Module 6 — Topic B: exercise h)

… and match the notation of mixed numbers in fraction and decimal forms.

image16(see Grade 4 Module 6 — Topic B: exercise r)


When it comes to comparing, Happy Numbers presents 8 exercises on comparing number pairs and 8 exercises on number ordering. Practice makes perfect!


Students apply their knowledge on tasks with visual models, which become more abstract with each new step. They begin with a model of real objects, then transition to an Area Model and the Number Line. Then comes the Place Value Chart and finally numerical notation.

In Grade 4, learning about decimals ends with the addition of decimal numbers using their fraction form. Happy Numbers presents an addition equation in which numbers are written in decimal form, then students translate it into fraction form, perform the math operation, and translate the result back into decimal form.

image3(see Grade 4 Module 6 — Topic D: exercise e)

If a student makes a mistake, Happy Numbers provides prompts to add fractions with different denominators. Then the fraction can be multiplied as was learned in the previous Module.


Keep It up!

As you can see, Grade 4 math is becoming more complex, deep, analytical. Students start to use the conceptual understanding they have accumulated over previous grades and expand it comprehensively with the help of detailed tasks. They learn rules and build bridges between different mathematical topics, between geometry and fractions, between the number positions, and between addition and subtraction. It is extremely important to have the right guidance and use actual pedagogy to help them stay on the right track! Happy Numbers developed such a  curriculum for Grade 4 students that will both help to review themes they’ve mastered and build new knowledge on this foundation. If you want to discuss our approach or have any questions and suggestions which will help to strengthen your work, please write a comment or contact the Happy Numbers Support Team. We’re always open to feedback!

How can you enhance your instruction with Happy Numbers?

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