## Grade 5 Overview: Fractions, Rounding and Data Analysis

In Grade 5, students start to combine familiar and new math skills for problem-solving. Happy Numbers includes many exercises with interconnection of different skills so that students learn to fluently operate their knowledge. You’ll also find tasks in which they can choose the next step in problem-solving, which reinforces their independence in math.

The curriculum covers general skills of working with fractions and decimals: addition and comparison of fractions with different denominators, solving word problems, long multiplication and division, finding a fraction of a number, extraction of the whole part and fractional part by long division, and a lot more. Students expand their skills of rounding (started in Grade 3) to decimal fractions. They discover fractions as division and master fraction reduction. This leads to expanding their knowledge with fraction division and grasping the connection between division by a fraction and multiplication by its denominator. In the meantime, they have much work to do with place value, including working to the thousandths place.

Moreover, students develop the skill of translating word problems into mathematical notation. They advance to more complex composition and analysis of data including engaging tasks with line plots, which is perfect practice for data analysis. In addition, they become familiar with the concept of an exponent and build fluency with powers of 10.

Sounds heavy? Not at all, if there is a teacher and a good digital assistant! Explore the Happy Numbers Grade 5 curriculum with this overview and its concrete examples and pedagogy notes. Use of multiple representations, manipulatives, and interactive exercises with an opportunity to choose the next steps can make your lessons more interesting and effective!

## Decimal Fractions

#### Introduction of Thousandths

Happy Numbers introduces thousandths by the familiar model of the Place Value Chart. Students can drag disks through the chart and get a tangible experience of the number composition. In addition, they complete patterns in the word form to build a complex understanding of this new concept. #### Comparison of Decimals

Since students have mastered the place value of decimal fractions, they can now compare them. Happy Numbers supports these exercises with the Place Value Chart. Here, students won’t have the ability to move disks, so they can concentrate their attention on the comparison of each digit. To strengthen understanding and develop fluency, students arrange decimals according to given conditions. Тo see the full exercise, follow this link.

#### Rounding Decimals

Students began to study rounding in Grade 3. In the Grade 5 curriculum, they expand their knowledge and learn rounding of decimal fractions to hundredths, tenths, ones, and tens. They compose rounding rules with the visual support of the Number Line. Happy Numbers provides engaging tasks to help students develop fluency. Determine the right rounding direction and make a basket!

Also, students work out the skill qualitatively. Here, they round a given number step-by-step to learn that the pattern works for any digit. This rounding strategy can be not-so-obvious. Using comparison, students first determine which way to round the number and then get down to solving. Estimation is a strong theme, as it’s important for real-life situations. Even when buying products, it’s convenient to evaluate the approximate result without performing a direct math operation. By giving text tips, Happy Numbers leads students to grasp the concept.

Work with decimals is based on place value understanding, so Happy Numbers continues to support its pursuit with the Place Value Chart. At the same time, students use Column Addition and Subtraction to smoothly transfer to a more abstract level. Later, the software reduces the scaffolding to check if students can solve a task using the abstract approach. To make this transition more comfortable, Happy Numbers includes unobtrusive tips. Students can follow them to help acquire the procedure. #### Multiplying Decimals

Multiplication of decimals won’t be hard if a student has already mastered the pattern for whole numbers. Happy Numbers gives them visual support, provides text tips, and uses equations with simple numbers to start building understanding of the process from the easiest level.

Students learn methods for solving more complex math problems. Practicing the conversion of decimals into whole numbers with subsequent conversion of the product back helps them explore the importance of correct decimal point placement.

Conceptual understanding in math is built on the fluent use of methods that help to optimize the process. One of the methods Happy Numbers suggests is simplifying multiplication of a 2-digit decimal number by a 2-digit whole number by using partial products. The approach is visually represented by an area model. Students then progress to multiplication without step-by-step guidance. They also apply their knowledge of decimal point placement. In Module 4, students learn to multiply decimals. They begin with multiplying by 0.1 and 0.01 using the Place Value Chart…

… and quickly advance to more abstract Column Multiplication of various decimals. #### Dividing Decimals

The division of decimals starts traditionally with Place Value Chart support. Happy Numbers proposes that students manage the solution through answers to step-by-step questions. The consistent guidance helps each student to smoothly progress through his or her zone of proximal development. See how Happy Numbers leads them through the division of decimals represented as long division. Each step is entitled above the page, and numbers become manipulatives when needed.

Decimals may appear in the quotient even if there weren’t any in the equation. In addition, here students use their skills of rounding to first estimate the quotient and test it.

Happy Numbers models situations in which the preliminary quotient can be over- or underestimated. Students apply their version of the quotient and change it if necessary. When the skill is mastered, students can choose whether they need to estimate the quotient or they are ready to fill it in. The opportunity to choose the next step builds confidence inmanipulating math operations.

#### Multiples of 10

Happy Numbers shows how multiples of 10 work with decimals using concrete examples. Then students need to fill the gaps in the rule. Thus, students learn to independently draw conclusions based on specific situations and convert them into patterns for use in similar cases. Distinguishing of a ten from a multiple of ten simplifies the solving process, so students learn to apply this method following the Happy Numbers instructions.

#### Renaming Decimal Numbers in Unit Form

This skill is helpful for a better understanding of number value and for development of oral math skills. Students practice renaming both sides and build fluency with it.  ## The Concept of an Exponent

The concept of an exponent is introduced through repeated multiplication. Students analyze given expressions and complete the table. Then, Dino helps them to sum up the results and compose rules. Happy Numbers then gives them an exercise to consolidate the skill. ## Powers of 10

In Grade 5, students become familiar with powers of 10. Its application is useful to simplify complex expressions, quickly estimate a product, or employ mental strategies. In addition, students practice factoring out and rearranging factors according to multiplication properties. Students explore multiplicative patterns connected to powers of 10 with the visual support of the Place Value Chart. If there are no mistakes, Happy Numbers reduces the scaffolding to reinforce skill development.

Moreover, they discover the pattern of zero addition when multiplying by 10, its powers, or its multiples. For expressions with decimals, Happy Numbers provides special tasks in which students practice decimal point placement. Exercises including the interconnection of different skills help students grasp the logic of applying various mathematical skills and form conceptual understanding. Look at this task, where they apply knowledge of the associative property along with practicing factoring out and powers of 10.

## Multi-Digit Whole Numbers

#### Composing the Expression

Speaking math is really important, as it’s a part of a complex understanding. How can a student develop math mindset without verbal skills?

#### Rounding and Estimation Strategies

Happy Numbers shows how estination of the product by rounding can make mental multiplication easier. Real-life scenarios help to engage students in the given problem. They build equations according to a word problem and estimate the product.

In addition, they develop fluency with rounding of whole numbers. Students need to round a number to the nearest ten, hundred, or thousand in random order. An explanation above the number prompts the next step.

The complexity of the tasks is growing! Now, students practice rounding to the nearest multiple of a random number. Happy Numbers provides them with step-by-step instructions. In this task, students combine their knowledge of rounding, reduction, renaming, and estimation! The complex application of various math skills strengthens students’ conceptual understanding, develops fluency, and builds math mindset.

#### Mental Strategies for Multiplication and Division

Students develop their mental math skills by applying knowledge of multiplication properties, factoring out, and powers of ten.

Happy Numbers leads them to repeat familiar patterns and connect them to new skills. Various combinations of math facts and their application teach students to perform operations fluently.

Gradually, students begin to solve equations mentally. At the same time, they always have the opportunity to receive support. Here they can refer to Column Multiplication if needed.

Students apply the same variety of skills to develop mental strategies for division. #### The Standard Algorithm for Multiplication and Division

Happy Numbers expands upon the application of the standard algorithm for multiplication and division of multi-digit numbers. Students develop the ability to regroup and to work across zeros. They start by composing expressions according to a word problem. To advance their conceptual understanding, the standard algorithm is presented alongside other strategies, such as the area model and factoring out powers of 10.

Students expand their skills to multiplication of 3- and 4-digit numbers.

#### Division with Partial Quotients

Students became familiar with partial quotients and the concept of the remainder in Grade 4. They review these skills using simple equations with tangible scaffolding of real objects.

Then, Happy Numbers reduces the scaffolding but leads students to complete the rule. Students receive increasingly difficult tasks. They solve equations with larger numbers by long division using quotient estimation.

Then, Happy Numbers offers them the option to independently build the solution strategy. Finally, students solve division with a 3-digit quotient where a quotient can be over- or underestimated.

## Fractions

#### Equivalent Fractions

Students are introduced to the basics of fraction equivalency. They learn to multiply to find an equivalent fraction and to divide to reduce a fraction. Happy Numbers also presents concepts of common factors and greatest common factor. This will be useful in fraction reducing.  Students review material on operations with fractions and mixed numbers covered in Grade 4 curriculum. This year, they expand their skills of adding and subtracting fractions by learning how to do so with unlike denominators. Happy Numbers supports students in finding the solution through a list of steps students can follow. This teaches students the logical order of actions while at the same time experiencing their application. Happy Numbers increases the complexity of addition and subtraction equations by using mixed numbers. Students reinforce their understanding of number equivalence as they rename numbers to solve problems.

To develop the complex understanding of operations with fractions, Happy Numbers adds visual representations. Here, students learn to estimate the result of addition or subtraction and compare it with benchmarks using a model. This is a helpful skill for self-checking before actual problem-solving. #### Fractions as Division

Who doesn’t have a sweet tooth in fifth grade? Modeling a math operation through a real-life example helps students better understand and grasp its meaning.

It seems math can be the most appetizing subject in the school curriculum! Dealing out flatbreads, students learn to report the remainder and get a mixed number as an answer.

Happy Numbers suggests applying Column Division when the quotient and the remainder aren’t calculated well mentally. #### Multi-Digit Whole Numbers and Fractions

One of the goals of Happy Numbers’ instructional guidance is to build conceptual understanding of any math operation students learn. By identifying patterns in multiplying by fractions less than, equal to, and greater than 1, the software lays the foundation for self-checking and for building number sense. First of all, students learn to determine fractions of a whole number. Happy Numbers creates engaging word problems that will surely motivate students to complete the task.

Then, together with Dino students compose the rule for solving multiplication correctly. Task optimization is one of the many important skills that mathematics teaches. Happy Numbers offers students the option to reduce the fractional equation before finding the answer.

#### Fraction Measurement

In addition, Happy Numbers teaches students to convert units of measure and determine the fractions involved. The program supplies them with a glossary with all units of measurement.

#### Multiplication of a Fraction by a Fraction

Fraction multiplication is easier to master if students begin with the formula right in front of them. Students repeat it several times before solving an equation to memorize it along with applying it.

Multiplication of a fraction by a fraction can also be necessary for solving tasks based on real-life scenarios. Here, Happy Numbers combines fraction multiplication with the area model and word problems.

#### Multiplication with Fractions and Decimals

Students practice converting decimals into fractions to simplify their multiplication by a whole number. To push students toward conceptual understanding, Happy Numbers represents the process visually with the Place Value Chart.

In addition, students learn to perform the reverse operation and convert fractions to decimal form by finding the power of 10 and by using long division as an alternative.  They determine the outcome of multiplication by a fraction or decimal depending on its ratio to one. Along with solving specific comparisons, students build formulas for such math situations. #### Division of Fractions

In the last topic of Grade 5, Happy Numbers introduces division of unit fractions with whole numbers and unit fractions with unit fractions. First, students relate division by a unit fraction to multiplication by the denominator. The visual representation of a tape diagram helps to draw out the meaning behind this relation. By helping Dino develop his cooking talents, students become familiar with division of a whole number by a unit fraction. Happy Numbers shows that school math can extend to real-life situations, which makes learning much more engaging. With the assistance of tape diagrams, area models, and modeling, students learn and work out different ways to approach dividing with fractions.

#### Line Plots of Fraction Measurements

Happy Numbers strengthens students’ analysis skills by introducing line plots. Here they combine knowledge of measurement, rounding, and mixed numbers.

Expert guidance helps students to easily master the new way of problem solving. Friendly Dino follows their path and shares tips when necessary. #### Fraction Expressions and Word Problems

Happy Numbers supplies the curriculum with engaging word problems based on real-life scenarios. By solving such tasks, students sharpen their text analysis and reinforce the skill of drawing up specific math expressions.

Happy Numbers offers multi-step tasks so that students can comprehensively apply their newly-acquired skills.

Students solve word problems when learning fractions as division. The task is supported by the tape diagram scaffolding. Space travel? Always interesting! Also, students practice composing compound expressions based on text. ## Take a Breath and Boogie

Students will have a saturated school year. Happy Numbers has made every effort to facilitate the learning process through visual representations, real-life scenarios, modeling, and grouping tasks to smoothly transition students from concrete to abstract representations. Exercises are supported with optional live voiceover for each step as well as the whole curriculum available in Spanish. Our digital assistance is adapted for diverse classes with students of different math levels. The placement test at the beginning of the year will place each student in the curriculum according to the zone of proximal development. An individual plan for each student allows mastering all the necessary skills for a successful transition to the next grade. Start a trial right now by signing up at Happy Numbers here.

## How can you enhance your instruction with Happy Numbers?

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