5th Grade Math: Number Sense Games

The development of counting skills and number sense in the previous grades is helpful to solve multi-step word problems using addition, subtraction, multiplication, and division. With the knowledge of the base-10 blocks, place-value system, ordering, and comparison of numbers is used to establish the relationship and represent using math symbols. Followed by the representation of numbers as fractions and mixed numbers, a large set of data is represented using line-plot and bar-graphs for easy interpretation.

Grade-5 math skills extend the representation of fractional numbers as decimals. To express numbers in the decimal form, the place-value grid is used to comprehend the technique. Graphical representation methods such as line-plot and base-10 blocks are used to order, compare and depict numbers.

What are “number” games?

The scope of the number-games for the 5th  graders is:

Representation of numbers in the decimal form for fractions and the estimation of the nearest whole to fluently perform math operations.

The upcoming section reviews the associated learning outcomes and prerequisites for grade-5 math.

Math Games for learning about numbers

The in-depth knowledge of number-sense and fractions promulgate mathematical reasoning to comprehend word-problems in geometry, measurement, and statistics. Interactive games aligned with common core math standards from SplashLearn contribute in nurturing fast math skills during classroom teaching.

Following sections delineate the learning outcomes and the corresponding math skills for grade-5 math.

Learning and outcomes

The development of counting skills for numbers in “hundred-thousands” as well as representing fractions & mixed numbers in previous grades foster math inquisitiveness.  The grade-5 math enhances the number-sense with the use of decimal values. As the measurement conversions of physical quantities, drawing angles and data representation deals with significant mathematical values; knowledge of numbers using decimal point is beneficial.

The projected learning outcomes for the grade are listed as follows:

• Comprehending the number-sense for decimal numbers using place-value grid
• Determining the decimal values between two whole numbers using line plot and counting skills in hundreds
• Nurturing the reading and writing comprehension of the decimal values to frame logical answers to word problems
• Analyzing the relationship between two or more decimal numbers to compare and order them with math symbols
• Estimating the nearest whole number for any decimal number to quickly compute the approximate answer
• Converting fractions and mixed numbers to decimal values and whole numbers

Required math skills

The essential math skills to achieve the projected learning outcomes in grade-5 insist on fluency in applying the knowledge of number-sense, counting skills and fractions. Akin to the estimation of nearest multiples of tens and hundreds; decimal numbers are converted to whole numbers for multiplication and division.

Engagement

The comprehensive learning games for SplashLearn are meticulously designed by math experts to contemplate math rationally in the later grades. With a unique set of word-problems, math riddles and puzzles to apply the number-sense skills, kids find the versatile theme-based games highly engaging and motivating to excel in math. The noteworthy learning games as per the curriculum of common core math standards are appreciated by parents engaged in homeschooling.

Grade 5 “Number” games

The number-games for grade-5 are primarily focused on fractions and decimal numbers. The understanding of mixed numbers, components of fractions such as numerator & denominator and correlating the multiples of 10 in solving the problems results in accelerated math learning.

Understanding decimal numbers

To start with the decimal number comprehension, the place-value grid is divided into the two sections. The first section before the decimal place denotes the whole numbers in one, two or more digits. The other section, post the decimal place denotes the value which is 1/10th of the respective place corresponding to a decimal number.

Represent decimal numbers – place value

The decimal numbers exist between two whole numbers. Thus, the first decimal number starts from 0. As 0 can also be written as 0.0. There can exist multiple decimal numbers between 0 and 1.

The upcoming section illustrates the representation of decimal numbers.

Numbers less than 1

The decimal numbers less than 1 exist between 0 and 1. For example, if the value between 0 and 1 is divided into ten equal portions, the numbers can be written as:

• 0.1, 0.2, 0.3, 0.4 and so on till 0.9.

In a decimal number such as 0.4, the place value associated with the digits is represented as follows:

As a fraction, 0.4 can be written as 4/10. The decimal value 0.4 is equivalent to 0.40 or 0.400. The trailing zeroes after a digit do not change the arithmetic value of the number.

Numbers greater than 1

The decimal numbers occurring after the number “one” are the numbers between any two whole numbers which are more than “0”. For example, the value between 2 and 3 upon dividing into ten equal parts, the intermediate numbers such as 2.1, 2.4 etc. are written as:

Any decimal number between 2 and 3, such as 2.6 (2.600 – up to 3 decimal places) can be written as:

Represent decimal numbers – Using line plot

The line plot representation is another method to represent decimal numbers graphically for better comprehension. The value between two whole numbers can be divided into ten, hundred or thousand equal parts to represent decimal values up-to different places.

Numbers less than 1

To represent numbers less than 1 on a line plot, mark the whole numbers on a line first. Followed by marking, divide the space into equal parts (it can be any number more than 2 such as 5, 10, 100 or even 1000).

The figure below represents the decimal number 0.8 on the line plot.

Figure: The decimal number 0.8 exists between 0 and 1.

Numbers greater than 1

The decimal numbers with arithmetic value more than 1 can also be represented on a line plot in a similar way. For example, the intermediate numbers between 1 and 2 are represented as follows:

Ref Image: The decimal number 1.6 between 1 and 2 on a line plot.

Decimals and fractions

The fractions can be written in the decimal form by dividing the value in the numerator with the denominator. The resulting quotient can be a whole number or a decimal number.

The comprehension of decimal numbers and fractions is akin to the base-10 block representation of the whole number along with the remaining value.

For example:

• Represent the fraction 2/10 or the decimal value 0.2

Reference image: The two blocks in the shaded region represent the value 0.2.

Tenths

The first digit to the right after the decimal point is referred as the 1/10th value corresponding to the number.

Hundredths

The two digits to the right of the decimal point are referred as the “hundredth or 1/100th” value for the number.

Mixed numbers

The mixed numbers as decimals are represented similarly like tenth and hundredth value. Depending on the number, suitable representation is chosen.

Number-sense

The number-sense for decimal numbers are like whole or fractional numbers. The upcoming section delineates the comparison and ordering of the decimal values.

Comparison and ordering of decimals

The decimal numbers can be compared and arranged using place-value grid and line-plot for easy interpretation. The suitable math operators “<(less than)”, “> (more than)” and “= (equal to)” are used to frame a mathematical equation.

Less than 1

To compare decimal numbers less than 1, fill the place-value grid as depicted.

• For example

• Compare 0.4 and 0.9

Thus, the equation will be 0.4 < 0.9

• Compare 0.68 and 0.27

Thus, the equation will be 0.68 > 0.27. As the fraction 68/100 is greater than 27/100.        

• Order 0.6, 0.9 and 0.3 in the decreasing order

• The numbers will be ordered as:

• 0.9 > 0.6 > 0.3

Greater than 1

To compare decimal numbers greater than 1, the whole numbers before the decimal point are compared with each other to select the least value. In case, the whole number of both the decimal numbers is same, the values after decimal are compared with each other.

• For example:

• Compare 1.7 and 1.3

Thus, the equation will be 1.7 > 1.3

• Compare 3.87 and 3.92

Thus, the equation will be 3.87 < 3.92, as 0.87 is less than 0.92.

• Order 1.9, 2.6 and 1.5

• Following line-plot represents the decimal values

Thus, the equation will be 1.5 < 1.9 < 2.6

1. Rounding decimals

The rounding of decimal numbers is used in math operations such as multiplication or division to frame answers within a scalable value. Also, rounding of the decimals is useful in the approximation of results. The previous grade math skills employ the concept of rounding the whole numbers to the nearest multiple of ten or hundred.

To round the decimal numbers, the numbers after the decimal point are analyzed. The digits are changed to the figure “zero” and the rounding digit is either preserved or increased by one. The suitable operation is selected on the basis of the arithmetic value of the digits in the right.

1. Terms to Remember

Application

The applicability of decimal numbers is not limited to only mathematics. The decimal numbers are also widely used in subjects like physics, chemical sciences, and geography. To represent time measurement, angles within geometric figures and fluently multiplying or dividing numbers, the knowledge of decimal numbers is highly recommended.

SplashLearn Number Games for Grade-5

The eclectic knowledge of numbers from basic counting to decimals up to 3 digits forms the basis of learning math in each grade. To proliferate the interest in classroom teaching, SplashLearn games offer numerous math riddles, puzzles, and coherent word problems. The comprehensive worksheets for grade-5 envision math as an essential to grasp the operations like division and measurement units conversion using decimal numbers. As a math apprentice to parents for homeschooling children during summer-vacation, fun learning games to practice daily math substantially prevent skill loss. Equipped with a real-time progress dashboard and playful themes, math games boost confidence and nurture problem-solving aptitude to excel in math.