A big part of common core math is getting students to understand why something works the way it does in mathematics. This is a great goal to have for students. If you understand why something works the way it does, you should have a better chance at remembering it. Does a third grade student trying to remember that 6 times 7 is 42 care about why it is 42? Wouldn’t it be better to just memorize multiplication tables by practicing day in and day out? Do you need to know why long multiplication works? We think these are valid questions.
We currently have one published book for 3rd grade common core practice. You can check it out here on Amazon: Common Core Math Trainer for 3rd Grade.
For the old school parents out there lost in Common Core Math we produced a book with explanations for YOU and practice problems for your STUDENT. Take a look at our book here: Polemics Academy Common Core Math Primer
For parents we are also publishing a book explaining the new methods of Common Core Math. Most of us are guilty of complaining about Common Core Math at one point or another, the truth is that it is here to stay the the majority of States in America and we better get with the times. It does our students no good to resist change. We ourselves should be open to new techniques. Our guide will help you fill in your own gaps and give you what you need to guide and mentor your students.
Common Core State Standards Initiative
This all started with the National Governors Association and the Council of Chief State School Officers trying to establish educational standards across the states. They wanted to make sure students graduating high school were prepared to enter two and four year college programs or to enter the workforce. The initiative started in 2010 targeting English and mathematics.
8 Common Core Math Domains
Students will Study four or five of the below domains each year. Each domain is split into subdomains (also called clusters) which have actual question types. Geometry standards for Kindergarten may be concerned with identifying shapes and counting sides. 8th grade geometry may be concerned with calculating angle degrees in a triangle.
Counting and Cardinality
Found only in Kindergarten, this standard is concerned with knowing number names and count sequences, counting to tell the number of objects and comparing numbers.
Operations and Algebraic Thinking
This category begins in Kindergarten and runs through fifth grade.
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
Represent and solve problems involving addition and subtraction. Understand and apply properties of operations and the relationship between addition and subtraction. Add and subtract within 20. Work with addition and subtraction equations.
Students add and subtract numbers within 20. Solve one and two step word problems using addition and subtraction. From memory students know all sums of one digit numbers. Work with equal groups of objects to get the foundation of multiplication.
Begin simple multiplication by understanding groups of objects. For example 4 groups of three pencils would be 12 pencils in all. Understand the relationship between multiplication and division such as 12 / 4 = 3 and 3 x 4 = 12. In second grade we are looking at two step problems using the big four operations (add, subtract, multiply, divide). Multiply and Divide within 100. Division at this grade involves either whole numbers or use of remainders.
Fourth graders use whole numbers to work problems in the big four operations (add, subtract, multiply, divide). Perform factors and pairing within 100. This means knowing that a number is the product of multiplying two of its factors such as 4×5 = 20. Work with multiples such as counting by 4’s and 5’s.
Introduce parentheses (bracket or braces) and evaluate problems with these types of symbols in them. (Please Excuse my Dear Aunt Sally [PEMDAS] anyone?). Students produce equations using parentheses in the 5th grade. For example a student converts “three times more than four added to six” as 3 x (6+4). Students also analyze patterns and relationships. For example a number series where seven is added to the previous number compared to a number series where 4 is added to the previous number.
Number and Operations in Base 10
This category of Common Core Math will run from kindergarten to fifth grade.
A lot of block counting here. Understand numbers from 11-19. Know that the number 15 is composed of fifteen single items.
Count to 120 starting at any number less than 120. Understand the tens and ones place value. Use understanding of the place values to help add and subtract. Given two 2-digit numbers, students practice adding the tens place to the tens place and ones to the ones place.
Second grade is similar to first in terms of Number Operations in Base 10 except it expands the concepts to the hundreds place. 100 can be thought of as ten sets of 10. In second grade students add and subtract within 1000 and use knowledge of place value to assist the operations. Students mentally add and subtract tens and one hundreds from larger even numbers. For example 90 – 10 = 80.
Use place values to perform rounding to the nearest 10 or 100. Multiply one digit numbers against a two digit number divisible by 10. For example 4 x 20.
Compare two multi digit numbers and record wether one is > < or = to the other. Add and subtract multi digit numbers using the standard algorithm. The standard algorithm is known more by parents as “carrying the one” to the next higher place value when adding or “borrowing from” a higher place value when subtracting. Multiply and divide using placeholder strategies. For example 600 / 6 = 100 and 600 / 60 = 10 and 40 x 10 = 400.
Understand that a digit in the next higher place value represents 10 times the number in the lower place value. For example the number 20, the two represents 1 and 1 but each of those 1’s represents 10 or ten times a digit in the 1’s place. (was that confusing? Let us know firstname.lastname@example.org.
Measurement and Data
This category runs from kindergarten to fifth grade. some parts of measurement and data will overlap into the geometry area. Measurements of areas, perimeters, and volumes for example belong in both .
Describe how to measure objects such as length and width. Compare two groups of objects and report on wether there is more or less of one group. Classify objects by category. For example separate crayons into groups of the same color.
Order three objects by length. Report the length of an object in whole numbers (for example a pencil as 6 centimeters). Tell and write time in hours and half hours. Report on measurement data such as how many objects in each category given a data set.
Select appropriate tool to measure given objects such as rulers, meter sticks and measuring tapes. Use addition and subtraction under 100 relating to the measurement of objects. Use the number line diagram to represent whole numbers. Tell time on a normal and digital clock and distinguish between a.m. and p.m. Draw picture graphs and bar graphs with single digit scales.
Tell and write time to the nearest minute. Measure and estimate liquid volumes using grams, kilograms and liters. Draw bar graphs and solve two step problems beginning with questions such as “how many less” and “how many more”. Find the area of a rectangle by multiplying two sides (this section bleeds slightly into the Geometry category for third graders). Solve real world problems involving perimeter measurements.
Students understand how units of measure relate to each other. For example meters compared to centimeters and kilometers. Represent data in fractions of units such as 1/2, 1/4, and 1/8 of an inch. Recognize that angles are when two rays join at a point. Use a protractor and sketch angles.
Convert from one measurement unit to another such as kilometers to meters or inches to feet. Create line plots that have fractions of units. Apply formulas of length x width x height to get a cubic volume.
Geometry is the only category of Common Core Math that runs from kindergarten through sixth grade.
Identify and describe shapes. Shapes may be of different sizes or orientations. Shapes may have other characteristics such as flat or three dimensional. Construct shapes from other shapes such as joining two triangles to create a rectangle.
Build and draw 2D and 3D shapes. Partition or divide shapes into parts and be able to describe shapes as having fractional parts.
Recognize and draw shapes given specifications such as number of sides or number of angles. Continue partitioning or dividing shapes into parts and describing the fractional parts of the shape such as 1/2 or 1/4th.
Draw points, lines and line segments. Understand right angles, acute angles and obtuse angles.
Identify and classify shapes based on parallel or perpendicular lines as well as presence or absence of angles of certain sizes. Understand a line of symmetry as a line that cuts across a figure to create equal parts of the shape on both sides of the symmetry line.
This is the grade where geometry really takes off. In the 5th grade Common Core Math introduces the 2D coordinate system with the X/Y axis. 5th graders start to classify shapes as they pertain to the 2D coordinate system.
In sixth grade students go towards solving real world problems with geometry. These problems involve surface area, area and volume. Students also find surface area of 3D objects by using nets of connected squares and triangles and summing the area of each square and triangle.