# Math Common Core Standards for 5th Grade: Operations in Base Ten

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Parent Friendly Standards for 5th grade (Actual standard in bold; my “parent friendly revision” in italics).

Operations & Algebraic Thinking

5.OA.1- Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Your child should be able to recognize that parentheses ( ) or brackets [ ] in an equation signal that the operation inside should be performed first.

5.OA.2- Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Your child should be able to write and understand equations without solving for them.  For example, write an equation for the following information: add 8 and 7, then multiply by 2.  The equation for this statement would be written as 2 x (8 + 7).

5.OA.3- Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Your child should be able to use number patterns to solve equations involving input/output machines.  For example, your child might be given the operation +3 and a few factors beneath it such as 0, 1, 2, 3, 4, etc. He/she would then +3 to 0, 1, 2, 3, 4. So, 0 + 3 = 3, 1 + 3 = 4, 2 + 3 = 5, 3 + 3 = 6, 3 + 4 = 7!  Your child will then have a second number pattern such as +6.  He/she would then have to add 6 to the numbers given: 0, 1, 2, 3, 4, etc. So, 0 + 6 = 6, 1 + 6 = 7, 2 + 6 = 8, 3 + 6 = 9, 4 + 6 = 10!  Finally, he/she will need to compare the number line and explain something they have in common.  In the number lines +3 and +6, the +6 number sequence is twice as much as the +3 number sequence.

Number & Operations in Base Ten

5.NBT.1- Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Your child should be able to recognize place value so that a digit in the ones place would be 1/10 of a digit in the tens place.  A digit in the ones place would also be 10 times more than a digit in the tenths place.

5.NBT.2- Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Your child should be able to understand that when you multiply a number by a power of 10, he/she just needs to multiply the ones digit by the tens digit and add a 0 such as 7 x 10 = 70 or 30 x 40 = 1200 (just multiply the first numbers and add two zeros!)  Also, when a decimal number is divided by a power of 10, a zero will be inserted next to the decimal and the other numbers will shift one place to the right.  So, 0.23/10 = 0.023!

5.NBT.3A- Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

Your child should be able to read and write decimals to the thousandths place using base-ten numerals (such as 17.048), number names (such as seventeen and forty-eight thousandths), and expanded form (such as 10 + 7 + 40/100 + 8/1,000.)

5.NBT.3B- Read, write, and compare decimals to thousandths.  Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Your child should be able to compare decimals to the thousandths place.  He/she should be able to recognize that 17.048 is less than 17.480 since there is a 0 in the tenths place in 17.048 and a 4 in the tenths place in 17.480 thus making this sentence true: 17.048 < 17.480!

5.NBT.4- Use place value understanding to round decimals to any place.

Your child should be able to round decimals to the nearest ones, tenths, or hundredths place using his/her knowledge of place value.  For example, given the number 0.628 and asked to round it to the nearest hundredth, your child would need to look at the thousandths place and see there is an “8” in it (0.628).  Since the 8 is greater or equal to 5, he/she will need to round the number “2” in the hundredths place up to 3, leaving him/her with the number 0.63 as the final answer.  If he/she was given the number 1.92 and asked to round it to the nearest tenth, he/she would first need to look at the hundredths place.  Since there is a 2 in the hundredths place, he/she will need to round down since anything that is equal to 4 or below, he/she will need to round down.  So, 1.92 will become 1.90 as a rounded answer!

5.NBT.5- Fluently multiply multi-digit whole numbers using the standard algorithm.

Your child should be able to multiply whole digit numbers by whole digit numbers.  For example, 1,264 x 3 and 31 x 24 would look like this:

11

1,264    Note:  Make sure your carry your ones over to the tens place and hundreds place and add them

X     3     to the total product!

_____

3,792

31    Note:  Make sure you add a “0” as a place holder when you start to multiply by the

X 24   number in the tens place on the second number!

———-

124

+ 620

_______

744

5.NBT.6- Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Your child should be able to four digit numbers by 2 digit numbers using his/her understanding of place value, order of operations and division.  He/she can solve equations, create rectangular arrays and/or pictures to help him/her solve for the correct quotient.

5.NBT.7- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Your child should be able to add, subtract, multiply, and divide decimals to the hundredths place using his/her understanding of place value and order of operations.  He/she should know that the decimals places are lined up vertically in addition and subtraction.  When a decimal is needed in a multiplication product such as when multiplying 5.17 and 8.94, he/she should know that there will be 4 decimal places in his/her answer since there is 4 decimal places in the two numbers thus making the answer 46.2198!  When dividing a decimal, if the decimal number is in front of the division bar such as in 0.4 dividing into 28.0, he/she would first need to move the decimal one place to the right from 0.4, making the number 4 and one place to the right in the number under the division bar, making 28.0 the number 280.  If only the number under the division bar has a decimal in it, you bring that decimal up to the top of the division bar so the decimals are aligned vertically!

Number & Operations- Fractions

5.NF.1- Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Your child should be able to add and subtract fractions with unlike denominators (including mixed numbers) by finding like denominators and performing the operation.  For example, in the equation 2/3 + 5/4, 3 and 4 have the least common factor of 12 in common thus this will need to be the new denominator.  Since 3 x 4 = 12, we will need to multiply the numerator and denominator in 2/3 by 4 resulting in 8/12.  Since 4 x 3 = 12, we will need to multiply the numerator and denominator in 5/4 by 3 resulting in 15/12.  Now, we can add 8/12 + 15/12 = 23/12.  We can also reduce this fractionsince it is an improper fraction (the numerator is larger than the denominator) to 1 11/12!

5.NF.2- Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Your child should be able to solve addition and subtraction word problems using fractions that relate to the same whole and fractions with unlike denominators.  For example, if we pulled the fractions 2/5 + ½ out of our word problem, we can’t just add 2/5 + ½ because the denominators are not the same.  We would have to find a common denominator.  The least common factor between 2 and 5 is 10 so we will need to use 10 as our denominator.  Since 5 x 2 = 10, we will need to multiply the numerator and denominator in 2/5 by 2 resulting in 4/10.  Since 2 x 5 = 10, we will need to multiply the numerator and denominator in ½ by 5 resulting in 5/10.  Now, we can add 4/10 + 5/10 = 9/10!

5.NF.3- Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Your child should be able to solve word problems, understanding that fractions can also be a representation of a division problem whereas the denominator needs to be divided into a numerator (a/b = a ÷ b). For example, “Carlos ordered 3 pizza’s for his super bowl party.  These pizzas are divided into fourths and there are 4 people attending his party; including him.  How many slices of people will each person get to have? “Each person will get to eat 3 slices thus resulting in eating ¾ of a pizza per person.

5.NF.4A- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.  Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

Your child should be able to multiply fractions by whole numbers and other fractions.  For example 2/3 x 4 = 2/3 x 4/1 = 8/3!  Also, we do not need to make like denominators to multiply fractions, so 2/3 x 4/5 = 8/15!

5.NF.4B- Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.  Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Your child should be able to find the area of a rectangle with the length being a fraction.  He/she should be able to tile the rectangle to help him/her find the area.  For example, “Find the area of a rectangle whose width is 6 inches and length is 1/4 inches.”  Your child should solve using the area formula; Area = Length x Width.  Area = ¼ x 6/1, so area = 6/4 = 1 2/4 = 1 ½ square inches!

5.NF.5A- Interpret multiplication as scaling (resizing), by:  Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Your child should understand that a multiplication product will always be larger than any of the factors being multiplied together.

5.NF.5B-  Interpret multiplication as scaling (resizing), by:  Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Your child should understand that when he/she multiplies a mixed fraction by a whole number, the product will end up being larger than either of the two factors being multiplied.  For example, 2 ½ x 4 (remember to change the mixed fraction into an improper fraction before multiplying the factors) 5/4 x 4/1 = 20/4 = 5!

5.NF.6- Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Your child should be able to solve multiplication word problems involving the use of fractions by setting up equations or drawing out pictures to help him/her solve.

5.NF.7A- Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.  Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Your child should be able to divide whole numbers by fractions.  He/she should use the inverse of division (which is multiplication) to solve division problems by using the reciprocal fraction of the whole number.  For example, (1/3) ÷ 4 = (1/3) ÷ 4/1 = 1/3 x ¼ (1/4 is the reciprocal fraction of 4/1) = 1/12!  So, (1/3) ÷ 4 = 1/12!

5.NF.7B- Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.  Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

Your child should be able to divide whole numbers by fractions and explain why (using the inverse of division which is multiplication) 4 ÷ (1/5) = 20 and 20 × (1/5) = 4. To solve 4 ÷ (1/5) = 20, use the reciprocal of 1/5 (the reciprocal is always applied to the second number in the equation) so 4/1 x 5/1 = 20!  The multiplication problem would be solved like this: 20 x 1/5 = 20/1 x 1/5 = 20/5 = 4!  Thus, your child can use the multiplication inverse property to check his/her accuracy with division.  He/she should also draw out fractional models such as circles or rectangles to help him/her visualize the problem.

5.NF.7C- Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.  Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Your child should be able to solve division real world word problems involving fractions.  For example, “How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?” 1/2 ÷ 3 = ½ x 1/3 = 1/6 of a pound!  “How many 1/3-cup servings are in 2 cups of raisins?” 2 ÷ 1/3 = 2/1 x 3/1 = 6 servings!

Measurement & Data

5.MD.1- Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Your child should be able to convert (change) measurements to larger or smaller measurements using like units and use these conversions in multi-step world problems.  For example, understanding that a centimeter = 1/100 m so 5 cm = 0.05 m!

5.MD.2- Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Your child should be able to display a data set of numbers using measurements to the nearest ½, ¼, or 1/8. He/she can then make a line plot (a graph that has his/her measurement data on the horizontal axis and he/she “x’s” off the amount of objects measured and their measurements.) Finally, he/she will possibly need to “re-distribute” the fractional parts to make equal fractional parts such as ½ + ¼ + 1/8 (the least common denominator would be 8 so 2 x 4 = 8 and 4 x 2 = 8) 4/8 + 2/8 + 1/8 = 7/8.  Then, he/she would divide 7/8 into 3 equal groups since there are 3 numbers so 7/8 ÷ 3 = 7/8 ÷ 1/3 = 7/24!

5.MD.3A- Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

Your child should be able to understand the concept of volume as a measurement of solid and liquid objects (such as measuring the amount of water in a beaker would result in finding the volume).  For example, a cube that has an edge of 1 unit is called 1 cubic unit.

5.MD.3B- Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Your child should be able to solve problems/equations involving volume.  When he/she solves for volume (knowing that all the sides of a cube are the same thus equaling 1 cubic unit) he/she would use the formula Volume = side x side x side, volume = 1 x 1 x 1 = volume = 1 cubic unit!

5.MD.4- Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Your child should be able to find the volumes of cubes and rectangular prisms by using the formulas Volume = Side x Side x Side (cube) and Volume = Length x Width x Height (rectangular prism).  He/she should also be able to count unit cubes when given them inside of a shape to find the shapes volume.

5.MD.5A- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.  Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Your child should be able to use multiplication to solve volume problems using the equations Volume = Side x Side x Side (cube) and Volume = Length x Width x Height (rectangular prism).  He/she should also be able to solve word problems involving volume.  For example, if he/she needed to find the volume of a rectangular prism with a length of 7 cm, a width of 4 cm, and a height of 3 cm, he/she should set up the problem like this: Volume = 7 x 4 x 3 = 28 x 3 = 84 cubic cm!

5.MD.5B- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.  Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Your child should be able to find the volume of rectangular prisms using the formulas V = l x w x h or V = b x h with whole number sides.

5.MD.5C- Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Your child should be able to find the volume of 2 different shapes and then add those volumes together to find the total volume of both shapes.  For example, V = l x w x h so V = 7 x 4 x 3 and V = 4 x 6 x 3.  V = 28 x 3 and V = 24 x 3.  V = 84 cubic units and V = 72 cubic units; 84 = 72 = 156 cubic units!

Geometry

5.G.1- Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Your child should be able to locate coordinate points (pairs of number) on a coordinate plane (graph).  He/she should know that the first number in an order pair shows how far the point must travel from the origin (0) across the x-axis and the second point in the order pair shows how for the point will travel up the y-axis and then he/she should plot and label the point!

5.G.2- Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Your child should be able to solve problems that involve graphing points in the first quadrant (quadrant with all positive numbers) of a graph.

5.G.3- Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Your child should be able to name a shape when given a picture of that shape and/or draw a shape when given the name of a shape or clues about a shape.  He/she should recognize that a shape that has 4 right angles and opposite sides equal and parallel are the attributes of a rectangle.

5.G.4- Classify two-dimensional figures in a hierarchy based on properties.

Your child should be able to classify two-dimensional figures when given specific attributes of a shape.  For example, he/she should recognize that a shape that has 4 right angles and opposite sides equal and parallel are the attributes of a rectangle.

#### Heather

Originally from Saratoga Springs, NY. Heather received my Bachelor's in Elementary Education PreK-6 from SUNY Plattsburgh and my Master's in Literacy Education from The College of Saint Rose. After completing graduate school, she accepted a job teaching at Wendell Creative Arts & Science Elementary School in Wake County, North Carolina. There, she taught fifth grade for three years and third grade for a year. Heather was also involved in after school tutoring and after school care where she worked with students K-5. Heather moved back to the area to be closer to my family as it expanded after my niece and nephew were born so that she could be a proud and active Aunt. She spent the 2010-2011 school year substituting in grades K-7 in Saratoga, Schuylerville, Greenwich, Glens Falls and Ballston Spa school districts. Heather is an Education Officer at Premier Transmedia and now a writer for Plaza Familia!

• Jolie du Pre

Heather has done a fine job with her “Parent Friendly Standards for 5th grade” article.  She begins every second paragraph with “your child should be able to,” and this keeps everything consistent and easy for a parent to understand.  Therefore, it contributes to a “parent friendly” article.  Good job, Heather.

• TERI WOOD

The suggestions are parent friendly.  The entire article has shown step by step to
guide the parents. Here the design helps the teachers to pattern their instruction.
Thanks a lot for sharing this.

• ROBERT DAVIES

5th grade operations in mathematics are comparatively
bit complex than before. It requires algebraic thinking to analyze patterns and
relationships. Geometry is another part. Select appropriate units, strategies,
and tools for solving problems that involve estimating and measuring volume. Overall,
the article has nicely explained it.