5TH GRADE MATH TUTOR- NYC TOP TUTORS

5th-Grade Math Tutoring 

So what exactly do students learn in 5th-grade math? We broke down 5th-grade math into the following problems and topics, like breaking down a language into parts.

If you need checklists for a breakdown of 5th grade math, we highly recommend Khan Academy and IXL for Common Core Fifth-Grade Math Standards for fifth-grade standards . We also thank Embarc for breaking down 5th grade math into the following standards:

Module 1: Place Value and Decimal Fractions

Topic A: Multiplication and Division Patterns on the Place Value Chart

Videos:
https://youtu.be/49NPo4y9E9A
https://youtu.be/XvUeT3_xNj0
https://youtu.be/NNprxeZ_7JU
https://youtu.be/NA3al1U5mjg

When we multiply a decimal fraction by a power of  10, the result will be bigger than the original number, so we move to the left on the place value chart. How many times we move to the left depends on how big 10 is. When we multiply by 10, we move to the left by one. When we multiply by 100, we move two spots to the left. When we multiply by 1,000, we move three spots to the left, and so on.

Example: Record the digits of the first factor on the top row of the place value chart. Draw arrows to show how the value of each digit changes when you multiply or divide. Record the product on the second row of the place value chart.

a. 3.452 x 10 = 34.52 (34.52 is 10 times greater than 3.452)

When a decimal fraction is divided by a power of 10, the result will be less than the original number. This means that we move to the right on the place value chart. The power of 10 tells us how often we move to the right. If we divide by 10, we move to the right by one place. When dividing by 100, we move two places to the right. When dividing by 1,000, we move three places to the right, and so on.

b. 345 ÷ 100 = 3.45 (3.45 is  times as large as 345.)

Words to Know:

Thousandths – one of 1,000 equal parts; thousandth’s place (in decimal notation) the position of the third digit to the right of the decimal point

Hundredths – one of 100 equal parts; hundredth’s place (in decimal notation) the position of the second digit to the right of the decimal point

Tenths – one of 10 equal parts; tenth’s place (in decimal notation) is the position of the first digit to the right of the decimal point Place Value – the value of the place of a digit (0-9) in a number

Decimal Fraction – a fractional number with a denominator of 10 or a power of 10 (10, 100, 1,000). It can be written with a decimal point. Exponent – tells the number of times the base is multiplied by itself Example: 10- the 4 is the exponent and tells us the 10 (base) is multiplied 4 times (10 x 10 x 10 x 10)

Equation – statement that two mathematical expressions have the same value

Topic B: Decimal Fractions and Place Value Patterns

Videos:
https://youtu.be/IDxYa9hvaY4
https://youtu.be/TbtRistgUBY

Different Ways of Naming a Decimal Fraction

Comparing Decimal Fractions
67.223 < 67.232

Strategy 1: Use a place value chart to compare the decimal fractions. A 5th grade math tutor can guide a student in comparing the decimal fractions.

The place value chart shows that 67.223 is less than 67.232 because the number 2 in the hundredth place of 67.223 is less than the number 3 in the hundredth place of 67.232.

Strategy 2: Use the unit form to compare decimal fractions.
67.223 = 67 ones 223 thousandths
67.232 = 67 ones 232 thousandths
67 ones are the same, but 223 thousandths is less than 232 thousandths.

Things to Remember!

Decimal Fraction – A fractional number with a denominator of 10 or a power of 10 (10, 100, 1,000) that can be written with a decimal point.

Standard form – A number written with one digit for each place value. Example: 52.64 or 52

Expanded form – A way to write numbers that shows the place value of each digit.

Example: 52.64 = 5 x 10 + 2 x 1 + 6 x 0.1 + 4 x 0.01 or  5 x 10 + 2 x 1 + 6 x (1/10) + 4 x (1/100)

Unit form – A way to show how many of each size unit is in the number. 52.64 = 5 tens 2 ones 6 tenths 4 hundredths 52 ones 64 hundredths

Greater than symbol (>)

Less than symbol (<)

Topic C: Place Value and Rounding Decimal Fractions

Videos:
https://www.youtube.com/watch?v=4BndXwTMm-o&t=19s
https://youtu.be/Vm_GdJpbBQo

Rounding 1.57 to the nearest tenth

Step 1: Decompose 1.57 to show as many ones, tenths, and hundredths.

Step 2: 

Draw a vertical number line. Since we are going to round to the nearest tenth,  we need to decide between which two-tenths  1.57 lies and indicate that on the vertical number line.

Step 3: Determine the halfway point or midpoint between 15-tenths and 16-tenths.

Step 4: Locate 1.57 on the number line. We can see that 1.57 is past the midpoint, so 1.57 rounds to 16 tenths or 1.6.

Sample Problem:
For an open international competition, the throwing circle in the men’s shot put must have a diameter of 2.135 meters. Round this number to the nearest hundredth to estimate the diameter. Use a number line to show your work.

Topic D: Adding and Subtracting Decimals

When adding and subtracting decimals students can use place value charts to assist them with regrouping. When adding, students begin by representing each digit in the numbers by drawing a dot in the correct area on the place value chart. Next, they will regroup when there are 10 or more dots in one place.

Example: Represent the digits of the first and second addends on the place value chart. Regroup when there are ten or more in one place. Record the sum.

a. 18 tenths + 13 tenths = 31 tenths (Unit Form)
1.8 + 1.3 = _______

b. 3.64 + 1.47 = ______

When subtracting students will represent the digits in the minuend on their place value chart. Next the student will subtract the subtrahend by crossing out the numbers in the chart. Students will need to regroup if necessary.

Example: 
83 tenths(minuend) –
64 tenths(subtrahend) = _____
8.3 – 6.4 = _____

Problem Solving:

Meyer has 0.64 GB of space remaining on his iPod. He wants to download a pedometer app (0.24 GB), a photo app (0.403 GB), and a math app (0.3 GB). Which combinations of apps can he download? Explain your thinking.

Meyer can’t download all three apps because he needs 0.943 GB of space and only has 0.64 GB of space. He can download the photo app alone, but he can’t combine it with anything. He does have enough space to download the pedometer and the math app together.

Words to Know:

Thousandths – one of 1,000 equal parts; thousandths place (in decimal notation) the position of the third digit to the right of the decimal point

Hundredths – one of 100 equal parts; hundredths place (in decimal notation) the position of the second digit to the right of the decimal point

Tenths – one of 10 equal parts; tenths place (in decimal notation) the position of the first digit to the right of the decimal point

Unit form – shows how many of each size unit are in the number. 52.64 = 5 tens 2 ones 6 tenths 4 hundredths = 52 ones 64 hundredth

Decimal Fraction – a fractional number with a denominator of 10 or a power of 10 (10, 100, 1,000). It can be written with a decimal point.

Addend – any number being added

Sum – answer to an addition problem

Difference – answer to a subtraction problem

Videos:
https://youtu.be/YP6GFofsg08
https://youtu.be/h1kVuS43x7U

Topic E: Multiplying Decimals

Videos:
https://youtu.be/Ua7n4nGZwDk
https://www.youtube.com/watch?v=A3BqbWpdJHA&t=34s

Place value understanding of whole number multiplication using place value charts and area models, help students make a connection between whole number products and products of a one-digit whole number and the decimal fraction.

Problem: 0.423 x 4

Using Place Value Chart: Students know that 423 times 4 means 4 groups of 423; therefore, 0.423 times 4 means 4 groups of 0.423.

In the place value chart, we represent 0.423 four times since we need 4 groups of this decimal fraction. We will regroup when there are ten or more in one place.

Using Area Model: The unit form of each digit of the decimal fraction is written above the model, and the other number or factor is written along the side. Multiply the unit form of each digit along the top by the number on the side. Add each of the partial products to find the product.

Using Estimation

Estimation can be used to confirm that the decimal has the correct placement as well as determine the reasonableness of the product. Students usually want to work on the problem and then round the answer. That is an incorrect procedure to follow when estimating. We round first to give us an idea of the exact answer.

From the choices given below, which could be the exact product for the problem 2.5 x 5?

a.25 b.              b.125              c. 12.5

The answer would be the letter ‘c.’ 12.5 is close to 15, and it consists of a two-digit whole number.

Topic F:  Dividing Decimals

Videos:
https://youtu.be/_GD34gquXuY
https://www.youtube.com/watch?v=k_45Rx5PcMA
https://www.youtube.com/watch?v=HSkL6rj9Z7Q
https://www.youtube.com/watch?v=qEHchlOuBCI

When dividing decimals students will use a place value chart to assist them.

Problem: 6.72 ÷ 3

Step 1: Draw a place value chart and  separate the bottom part into 3 groups  since we are taking the whole (6.72) and dividing it into 3 equal parts.

Step 2: Show 6.72 in the place value chart.

Step 3: Begin with the larger units, which in this problem is the one’s place. We can share 6 ones equally with 3 groups. There will be 2 ones in each group. Now we move to the tenths. We can share 7-tenths with 3 groups by giving each group 2-tenths, and then there will be 1-tenth left. The 1-tenth will be renamed as 10 hundredths. Now there are a total of 12 hundredths which can be shared with 3 groups by giving each group 4 hundredths.

Decimals can also be divided by breaking apart the dividend into unit forms. These parts can then be divided by the divisor and added together to find the quotient.

Words to Know:

Quotient – the answer to a division problem

Dividend (whole) – a quantity to be separated into the number of equal groups or into the amount in each group

Divisor – tells the size of the group or the number of groups the whole is being separated into

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Reference:

(n.d.). Grade 5 Module 1. Embarc.Online. https://embarc.online/course/view.php?id=3