# Grade 4 Overview: Working with Number Positions

All the knowledge students have accumulated about place value in previous grades will be used and expanded upon 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. The Happy Numbers K-4 curriculum helps teachers build meaning behind the algorithms of multiplication and division and lay the foundations necessary for developing fluency with fractions in Grade 5.

This math year is much more serious and analytical than previous years. By now, students have already learned a number of strategies for different math operations. In  Grade 4 they will need to select the necessary written or mental strategy and then apply it correctly. Students also begin to manage their math ‘baggage’, which we call math mindset!
Grade 4 is a very important year in mathematics in which students lay out patterns of solving certain mathematical situations. Happy Numbers is very glad to be your partner when students really need experienced 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 HappyNumbers.com 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. Using manipulatives, word form, and numerical form, Happy Numbers reminds them about the ratio of ones, tens, and larger numbers.

They build up multiplication sentences using a mix of unit form and number form, then express them visually on a Place Value Chart. Multiple representations help combine math skills and boost comprehensive conceptual understanding

In Topic B, students begin comparing multi-digit whole numbers within 1 million. They learn to compare based on number positions with the help of Place Value Cards and Chart. In the next step, Happy Numbers makes sure that students practice comparing multi-digit numbers by trial and error. So if there is a mistake in a numerical task, the software will rapidly give instant feedback. Our students learn from their mistakes, forcing their math mindset to grow!

Simultaneously with comparison, students practice number sequencing… …and determine 1,000/10,000/100,000 more or less on the Place Value Chart with color-coding.

Students explore rounding multi-digit whole numbers in exercises with vivid cosmic style! Happy Numbers creates engaging scenarios with basketball games to boost students’ motivation. They are presented with Number Line scaffolding if something goes wrong.

Students then come to the addition of multi-digit whole numbers. First, they try it with the visual support of the Place Value Chart and Column Addition with and without color-coding. In the last Topic of Module 1 they did 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 dives 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, Module 2, they learn and practice it, solving for different parts of the formula.  Along with the formula for area, Happy Numbers introduces a perimeter formula and its variations. ## Multi-Digit Multiplication

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

Wondering 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.

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 with up to four digits by single-digit numbers. They work extensively with place value understanding, using manipulatives while solving problems

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 in tasks focused on the area of a rectangle. Multi-digit multiplication continues in Topic G, where students learn to multiply two-digit by two-digit numbers. They start 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. 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 of division by learning the definitions of quotient and remainder on a visual model with tennis balls and an array model. Then students move to multiples and it’s no problem for those who learned the Multiplication Table in Grade 3! Happy Numbers provides Tape Diagrams when necessary to help explain new concepts visually.. Then students learn the definition of divisor. Dino helps students to visually represent the equation. 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. With the same algorithm, students solve division problems that involve regrouping or require recording of partial quotients 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. Now it’s time for a break to review some familiar topics. Students join Dino in his balloon flight, completing number sentences by finding their missing factors. Thus, they  review multiplication and get ready for the next learning step.

Next, Happy Numbers introduces the concept of divisibility and its properties and builds the connection between factors, multiples, and divisibility. Happy Numbers also reminds students of the 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.

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

Module 3 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 based on visual models with a shaded figure. As always, students smoothly transition from learning rules based on step-by-step instructions and visual models to numerical and abstract thinking. Students learn the concept of fraction equivalence and its notation by multiplication and division.  Happy Numbers helps students compare fractions using Diagrams, the Number Line, and tasks based on real-world scenarios. They 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)..  Here are some sweet exercises to increase students’ appetite for fraction addition and subtraction! 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. ## 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. Students practice renaming mixed numbers as repeated addition. This helps them rewrite mixed numbers as improper fractions and vice versa. Students 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. 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 focus intently to preserve all their hearts.

Now students are ready for extensive practice of addition, subtraction, and the comparison of mixed numbers with like denominators.  At the same time, they continue to develop their number sense by estimating the sums of mixed numbers.  We finish the Module with multiplying a fraction by a whole number. Happy Numbers introduces it as a 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. Finally, students will practice repeated addition of fractions as multiplication on cosmic visual models. Conquering the universe is only possible for those who have mastered the fraction, isn’t it?

## Decimal Fractions

In Module 4 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 the real world. The second is where students need to fill the gaps in fraction notation and finally record fractions by themselves.

In Topics A and B, Happy Numbers mainly works with notation of decimal fractions with tenths and hundredths. Students already have a direct understanding of the concept of fraction from the end of the Grade 3… …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, just like a puzzle! In addition, students learn equivalence between tenths and hundredths. They practice both unit, fraction, and decimal forms by completing the table. It’s a good base for future work with data analysis! Happy Numbers introduces the algorithm for forming mixed numbers as decimals. Dino and the grasshopper are a strong study team! When it comes to comparing, Happy Numbers presents several exercises on comparing number pairs and several exercises on number ordering. Practice makes perfect!

Students apply their knowledge in 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. 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.  