THE FOCUS AREAS OF GRADE 6 ADDRESS:
- Understand ratio concepts and use ratio reasoning to solve problems.
- Apply and extend previous understandings of numbers to the system of rational numbers.
- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- Apply and extend previous understandings of arithmetic to algebraic expressions.
- Reason about and solve one‐ variable equations and inequalities.
- Represent and analyze quantitative relationships between dependent and independent variables.
Math Vocabulary:
IMPORTANT VOCABULARY WORDS FOR 6TH GRADERS TO KNOW |
The importance of common core math: WHY DON'T WE TEACH MATH THE OLD WAY?
Times tables:
If your child does not know his/her basic multiplication facts through the twelves, they need to study nightly. The lack of this skill, more than any other in math, limits their progress.
The Eight Mathematical Practices
1. Make sense of problems and persevere in solving them
What it means: Understand the problem, find a way to attack it, and work until it is done. Basically, you will find practice standard #1 in every math problem, every day.
Good mathematics students know that before they can begin solving a problem they must first thoroughly understand the problem and understand which strategies might work best in finding a solution. They not only consider all the facts given in the problem, but also form an idea of the solution—perhaps an estimation or approximation—and make a plan, rather than simply jumping in without much thought. They first consider similar and related problems to gain insights. Older students might use algebraic equations or technology. Younger students might use concrete objects, drawings, or diagrams to help them “see” the problem. Good mathematics students check their progress along the way, change course if necessary, and continually ask themselves, “Does this make sense?” Even after finding a solution, good mathematics students try hard to understand how other students solved the same problem in different ways.
2. Reason abstractly and quantitatively
What it means: Get ready for the words contextualize and decontextualize. If students have a problem, they should be able to break it apart and show it symbolically, with pictures, or in any way other than the standard algorithm. Conversely, if students are working a problem, they should be able to apply the “math work” to the situation.
Good mathematics students make sense of the numbers and their relationships in problems. They are able to represent a given situation with symbols and operations AND relate the mathematics of the problem to real life situations. They consider the units of measure involved, the size and meaning of the numbers involved, and the context of the problem and its solution. In this way, good mathematics students make sense of a problem and apply that understanding to consider if their answer makes sense.
3. Construct viable arguments and critique the reasoning of others
What it means: Be able to talk about math, using mathematical language, to support or oppose the work of others.
Good mathematics students understand and use assumptions, definitions, and previously learned information in helping them build solutions. They make conjectures and apply logical thinking to explore and test their ideas. They analyze problems by breaking them down into smaller parts, and look for counterexamples. They are able to explain their results to others and answer the questions and objections of others. They analyze all available data and information carefully. Young students can explain and demonstrate their solutions by using concrete objects, drawings, and diagrams. Older students can construct intuitive or deductive proofs of their theories, either in writing, verbally, or by other means.
4. Model with mathematics
What it means: Use math to solve real-world problems, organize data, and understand the world around you.
Good mathematics students apply the mathematics they know to solve problems in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a real situation involving money. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how changing one variable affects the result. Good mathematics students routinely interpret their mathematical results in the context of the situation and think about whether their results make sense.
5. Use appropriate tools strategically
What it means: Students can select the appropriate math tool to use and use it correctly to solve problems. (In the real world, no one tells you that it is time to use the meter stick instead of the protractor.)
Good mathematics students consider all the mathematics tools at their disposal before beginning a problem. Tools might include pencil and paper, manipulatives, models and diagrams, a ruler, a protractor, a calculator, a spreadsheet, a graphing calculator, a computer statistical package, and/or dynamic geometry software, to mention just a few. Students are familiar with, and know how to appropriately use, mathematics tools for their grade and choose wisely the best tools to use for a particular problem. For example, older students should be able to analyze graphs of functions by using a graphing calculator; younger students should be able to use blocks to model a multiplication problem. Students should be able to search out and wisely use mathematical resources such as the library, knowledgeable individuals, and the Internet.
6. Attend to precision
What it means: Students speak and solve mathematics with exactness and meticulousness.
Good mathematics students learn to communicate clearly and completely to others using correct mathematical language and logical arguments. They calculate accurately and efficiently and express numerical answers with the precision required by the problem. In their discussion and presentations, good mathematics students can explain and defend their choice of symbols, operations, and processes to convince other students and adults they are correct.
7. Look for and make use of structure
What it means: Find patterns and repeated reasoning that can help solve more complex problems. (For young students this might be recognizing fact families, inverses, or the distributive property. As students get older, they can break apart problems and numbers into familiar relationships.)
Good mathematics students discover and care- fully observe pattern, logical order, and structure in mathematics. Young students, for example, might discover that all even numbers end in 0, 2, 4, 6, or 8, while older students discover that in the ordered pairs (1, 3), (2, 5), (3, 7), (4, 9), the second number in the pair is always one more than twice the first number. Good mathematics students can also step back to view the whole, but still pay careful attention to the individual facts and numbers in a problem. Good mathematics students should be able to imagine the graph of a function, such as y = 2x + 1, before they graph it, because they understand what each element—y, =, 2, x, +, and 1 does in the algebraic generalization.
8. Look for and express regularity in repeated reasoning
What it means: Keep an eye on the big picture while working out the details of the problem. You don’t want kids that can solve the one problem you’ve given them; you want students who can generalize their thinking.
Good mathematics students know when to apply tried-and-true methods in solving a problem, and when it is most useful to apply a new approach or shortcut. For example, when middle school students convert a fraction into a decimal, they should notice when they are repeating the same calculations over and over again, and then conclude that they have a repeating decimal. Younger students should notice that when multiplying 11 by any number up to 9 they can simply double that digit to get the answer. While working to solve a problem, good mathematics students not only understand basic mathematics methods and correctly apply those methods, but also watch for novel ways to solve similar problems in more efficient ways.
*To read the original academic version of the Common Core for Standards for Mathematical Practice, please visit:
www.corestandards.org/Mathematical/Practices
For more information about the California Common Core State Standards, please visit:
www.cde.ca.gov/re/cc/
For family-friendly articles and activities, visit the California Mathematics Council's "FOR FAMILIES" web pages:
www.cmc-math.org/family/
www.corestandards.org/Mathematical/Practices
For more information about the California Common Core State Standards, please visit:
www.cde.ca.gov/re/cc/
For family-friendly articles and activities, visit the California Mathematics Council's "FOR FAMILIES" web pages:
www.cmc-math.org/family/
RESOURCES FOR STUDENTS:
KHAN Academy
Learn Zillion
Fraction Practice: Khan Academy
2048 Game
Math Resource Videos
TenMarks
Math Review Games
IXL: Practice 6th grade skills
Create a Graph
Practice Math Test
Practice Performance Task
RESOURCES FOR PARENTS:
Engage NY: Grade 6 Mathematics
Paid App. for fractions
California Department of Education
Parent Tool Kit
Engage NY: Grade 6 Mathematics
Paid App. for fractions
California Department of Education
Parent Tool Kit
Instructional Lessons, Tips, and Videos:
Module 1: Ratio and Unit Rates
Module 2: Arithmetic Operations Including Division of Fractions
Module 3: Rational Numbers
Module 4: Expressions and Equations
Module 5: Area, Surface Area, and Volume
Module 6: Statistics
Module 2: Arithmetic Operations Including Division of Fractions
Module 3: Rational Numbers
Module 4: Expressions and Equations
Module 5: Area, Surface Area, and Volume
Module 6: Statistics