Common Core Math For Parents For Dummies with Videos Online
Overview
Help your child succeed with a better understanding of Common Core Math
Common Core Math For Parents For Dummies is packed with tools and information to help you promote your child's success in math. The grade-by-grade walk-through brings you up to speed on what your child is learning, and the sample problems and video lessons help you become more involved as you study together. You'll learn how to effectively collaborate with teachers and keep tabs on your child's progress, so minor missteps can be corrected quickly, before your child falls behind. The Common Core was designed to improve college- and career-readiness, and to prepare U.S. students to be more competitive on an international stage when it's time to enter the workforce. This guide shows you how the standards were created, and how they've evolved over time to help ensure your child's future success.
The Common Core Math Standards prepare students to do real math in
the real world. Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math.
- Understand the key concepts being taught in your child's grade
- Utilize the homework tools that help you help your child
- Communicate more effectively with your child's teacher
- Guide your child through sample problems to foster understanding
The Common Core was designed to ensure that every student, regardless of location or background, receives the education they need. Math skills are critical to real-world success, and the new standards reflect that reality in scope and rigorousness. Common Core Math For Parents For Dummies helps you help your child succeed.
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About The Author
Christopher Danielson, PhD, is a leading curriculum writer, educator, math blogger, and author interpreting research for parents and teachers across the country from his home base at Normandale Community College in Minnesota.
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common core math for parents for dummies with videos online
CHEAT SHEET
As a parent, you’re most likely to encounter the Common Core State Standards for Mathematics (Common Core Standards for short) in the homework that your child brings home. The Common Core Standards are a set of statements about what students should know and be able to do at each grade level from kindergarten through high school.
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Common Core
One unique aspect of the Common Core State Standards is that their focus goes beyond the familiar content of numbers, geometry, algebra, and statistics. They also include a set of Standards for Mathematical Practice, or SMP, that describe how people work when they're doing math.
The SMP apply across all grade levels, with kindergarteners operating at a level of sophistication appropriate to them and high school students working at a much more sophisticated level.
Common Core
Want to avoid raising a math‐o‐phobe? Here are five proven ways to help your child become successful in his or her Common Core math classes.
Talk about math together
Set yourself a goal to ask "how many?," "what shape?," "how do these compare?" and "how do you know?" at least once a day. Don't worry about asking a question that's too difficult; your child can take a guess, and then you can talk.
States, districts, schools, and teachers have invested a lot of time, money, and effort implementing the Common Core Math Standards — to say nothing of parents. Before the Common Core, each state wrote its own standards for math. Now, nearly all states have agreed on the mathematics students will study in school.
Common Core
One important change in the Common Core Math Standards is that students are expected to work through multi-digit computations by thinking about number relationships before they’re expected to follow standard algorithms. For parents who never had to think about their computations in school, this can make homework time a bit daunting.
Common Core
In addition to the content standards that state what students need to learn at each grade level, the Common Core Standards for Mathematical Practice describe how students should approach their mathematical work and what kinds of tasks teachers and curriculum should present to students.
You can use the following list to keep track of the eight Common Core Standards for Mathematical Practice.
Common Core
Math students add and multiply fractions in Common Core fifth grade. These skills require using and extending their knowledge of these operations from their earlier work with whole numbers.
When adding two numbers, fifth graders need to express the same units. Three miles plus four gallons doesn't give you seven of anything because the units are different, which is true with adding fractions, too.
In a Common Core classroom, seventh grade students use algebra to describe their understanding of mathematical relationships in the world. They also learn to state patterns and structure that appear in their arithmetic, and to notice and state new relationships.
In seventh grade, most of these relationships are proportional, which means that there is a constant rate of change in one variable relative to another.
Common Core
In Common Core math, seventh grade students add and subtract both positive and negative numbers using the number line. On the number line, numbers have two important meanings:
A number is a point on the number line.
A number is a distance on the number line.
What the first one means is that each little tick mark you put on a number line represents a number — 0, 1, 2, and so on: Each of these is matched with a point on the number line.
Common Core
As a parent, you’re most likely to encounter the Common Core State Standards for Mathematics (Common Core Standards for short) in the homework that your child brings home. The Common Core Standards are a set of statements about what students should know and be able to do at each grade level from kindergarten through high school.
Common Core
Homework is a hot topic in the transition to Common Core Standards. Homework assignments that ask students to think in new ways can be intimidating to parents. When something comes home that looks unfamiliar to you, don’t panic. Homework is just a way of giving students additional time to think about the things that they’re learning — what teachers call time on task.
Common Core
An important way to think about functions for Common Core math is as relationships between variables. If you think of a function as a relationship, you can keep an eye out for useful features. These features include whether (and where) a function is increasing or decreasing, whether a function is linear or not, and so on.
While we often think of fractions as "parts of numbers" they're also numbers themselves. Because fractions are numbers, you can compare them. Comparing fractions is an important skill in fourth grade Common Core math.
Some numbers are larger than others; children learn this early on. So asking which of two fractions is larger and putting two sets of fractions in order are sensible tasks.
Common Core
In Common Core math, third graders use a number line to see how fractions relate to each other. A number line is useful for showing the relative location of fractions, as well as their distance from each other.
You may remember a number line running across the front wall of an elementary classroom when you were in school, with a point for zero, a point to the right of that marked 1, then 2 and so on, with an arrow on the end to suggest that the line and the numbers continue forever.
Common Core
You will want to make sure that your child is familiar with comparing logarithms for Common Core math. In addition to comparing numbers with ratio and unit rate, you can actually compare numbers a third way — with logarithms.
A logarithm is basically an exponent. In the equation 10x = 100, writing log10(100) is how you solve for x; log is short for logarithm (in this case, x = 2).
Common Core
In math, there are many kinds of sameness. In Common Core geometry, eighth grade students study congruence and similarity as two ways of talking about how two shapes are the same.
Two shapes are congruent if you can move one so that it perfectly matches the other one without stretching or deforming it. Two shapes are similar if you can do the same thing, except that you're allowed to stretch or shrink the shapes proportionally — you can double all the lengths on one of the shapes, for example.
Common Core
In Common Core math, sixth grade students study ratios and fractions that are set in understandable contexts, and they work them in order to ask and answer interesting and challenging questions.
A ratio is a comparison of two numbers that depends on the multiplication relationship between them. Here are some examples of ratios:
A recipe for orange juice calls for 3 cans of cold water for each 1 can of frozen concentrate.
Common Core
Being able to identify and generate equivalent fractions is a tremendously important skill in Common Core arithmetic and algebra alike. Fourth graders use pictures and reasoning to write equivalent fractions.
Equivalent fractions are any two fractions that represent the same quantity, as in
and
You may remember spending lots of time reducing fractions, and even getting test questions wrong because you didn't reduce your fractions, but there is absolutely no reason to insist on reduced fractions.
Common Core
In Common Core math, sixth graders apply their knowledge of factors and multiples to look for the greatest common factor (or GCF) of two numbers and the least common multiple (LCM) of two numbers.
The greatest common factor of two numbers is the largest number that is a factor of both numbers. The first step in thinking about GCF is to think about common factors.
Common Core math students start to work with exponents in eighth grade. In algebra, you can think of exponentiation as repeated multiplication. The following analogy will help you understand the significance of this.
You know that
because there are 12 things in 4 groups of 3. If you didn't know the product
you could find it in several ways.
Common Core
In Common Core math, sixth grade students learn to find areas of a variety of polygons by relating to the areas of known figures — especially rectangles.
You may remember from your days in school the study of area as being about long lists of unrelated formulas — one formula for triangles, another for parallelograms, and a really strange one for trapezoids.
In Common Core math, eighth grade is the first time students meet the term function. Mathematicians use the idea of a function to describe operations such as addition and multiplication, transformations of geometric figures, relationships between variables, and many other things.
A function is a rule for pairing things up with each other.
Common Core
Place value is an important concept to know for Common Core math. The fact that it took thousands of years for humans to develop a place value number system is an important sign that place value is difficult for people to learn. The usual way of writing numbers is a place value number system.
In other words, a limited set of symbols (called digits) builds numbers (0, 1, 2, 3, and so on up to 9) and you can write all numbers using these symbols.
In eighth grade Common Core math, students studied similar figures. In high school, they use the properties of similarity to study new things, in particular, trigonometry.
Two similar right triangles.
The two triangles in the figure are similar, which means that the measures of corresponding angles in the two triangles are the same, and that their side lengths are proportional.
Common Core
In Common Core math, many important questions require comparing numbers to decide which number is greater, or whether the numbers are equal. A kindergarten student who can count to 20 may still need to think hard to decide whether 8 is more than 5.
Questions that require comparing numbers include the following ones:
You have 7 crackers.
Common Core
To learn Common Core geometry, a kindergarten student begins by studying shapes that she finds in her world. Nearly all children will come to school with ideas about what shapes look like and basic names for shapes. Kindergarteners spend time trying to describe shapes precisely.
A student entering kindergarten may think of squares and rectangles as unrelated shapes.
Common Core
In Common Core math, fourth grade students begin to expand their view of geometry beyond shapes. They think about lines, angles, and the relationships that they can have with each other.
This activity generates quite a bit more vocabulary. For example, students study parallel lines, which are two lines in a plane that don't intersect.
Common Core
If your child is in kindergarten, you can help them begin to compare and classify things. This will strengthen their ability in other important areas of Common Core math.
Kindergarteners notice characteristics of things that can be measured. These characteristics are called measurable attributes. Measurable attributes of a person include height, favorite color, shoe size, and bedtime.
Common Core
In Common Core math, first grade students need to begin thinking about the properties of numbers more deeply. One important property of all numbers is that they can be decomposed.
When you decompose a number, it means that you take the number apart. You can do it in many ways; for example, you can think of 8 as 4 + 4, or as 3 + 5, or as 9 – 1, and so on.
Common Core
In fourth grade math, Common Core students begin to study how numbers are built from multiplication relationships. The important relationship here is between factors and multiples.
A number's factors are all the whole numbers by which you can divide it with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
Common Core
In Common Core geometry, fourth graders work with fractions of a full rotation — halves, quarters, and so on. They also work with angle measurement in degrees, where a degree is
of a full rotation. They use protractors to measure angles to the nearest whole degree.
In geometry, two rays with a common vertex form an angle, as you can see in the figure.
Common Core
In second grade math, Common Core students use rulers to measure lengths. By doing this, they are connecting and extending their use of nonstandard units such as paper clips and linking cubes, which they learned about in first grade.
A ruler is a complicated object to use correctly, so you can expect your second grader to be working on this skill for a few years, gaining accuracy over time.
Common Core
In Common Core math, 10 is the most important number that a kindergarten student will learn. It is important because it's the foundation of how you say and write numbers; it's the number at the heart of the place value number system.
In the place value number system, a limited set of symbols (called digits) builds numbers (0, 1, 2, 3, and so on up to 9) and you can write all numbers using these symbols.
Common Core
In Common Core math, your child uses math symbols to solve problems, and so she needs to have some understanding about how to use them. This is where order of operations becomes important.
The order of operations, or the sequence to follow when calculating the result of using different operations, is particularly significant for fifth graders.
Common Core
A few of the more stressful parenting moments include when time is tight and when your child is struggling with a homework assignment in his Common Core math class. To reduce this stress, here is a good strategy, in three parts:
Listen. Ask your child to tell you what he is supposed to do. If something needs to be done a particular way, listen to what it is.
Common Core
Whatever math standards may be — Common Core or anything else — most children will be frustrated with a homework assignment from time to time. The advice to you, the parent, doesn't change just because your home state has adopted the Common Core.
What may change is the ways children are expected to work on their homework.
Common Core
One of the Common Core Standards for Mathematical Practice, or SMP, is "Reason abstractly and quantitatively." This mouthful refers to the idea that mathematical symbols have meaning, and that students should strive to keep that meaning in mind as they work.
For example, a class full of second graders can discuss how many muffins are in the partially filled muffin tin in the figure.
A lot of misinformation is available about the Common Core Standards. These standards guide the math your child learns in school each year. In order to advocate for and to support your child, you need to be well informed. Here are some important facts that counter some of the common myths about the Common Core Standards.
In the Common Core program, eighth grade algebra is mostly linear. Linear relationships, which are equations with straight-line graphs, can include the slope-intercept form, standard form, and point-slope form.
A proportional relationship has a graph that makes a straight line and goes through the point (0,0).
Common Core
In Common Core fifth grade math, students build on what they learned earlier about whole‐number place value, as they begin to study decimal place value — that is, they study digits to the right of the decimal point.
One of the most challenging things about studying decimal place value is that several of the ways of thinking about whole numbers that children commonly adopt don't apply to numbers to the right of the decimal point.
Common Core
In Common Core math, third and fourth grade students begin to study multiplication. The foundation for multiplication is equal‐sized groups, whether they are units, pairs, or arrays.
To prepare for this work, second graders identify and work with equal‐sized groups — even before they name the multiplication and division ideas that follow.
Common Core
In Common Core math, second grade students learn how to draw shapes based on their properties. They also use arrays to partition, or cut, these shapes.
Students learn to imagine shapes that have particular sets of properties. For example, they may be asked to "draw a six‐sided figure with sides that are different lengths.
Common Core
Common Core students partition things in third grade math, and they name the resulting pieces using fractions. Partitioning in this context means cuttings things into equal-sized pieces.
Children have lots of practice thinking about how to share something equally. When you cut a large cookie into five equal pieces so that you and your four friends each get the same amount, you make fifths.
Common Core
In the Common Core State Standards, probability and statistics are intertwined. High school students commit to probability models and then test those models by collecting data. Similarly, they use probability to describe how likely the conclusions they draw from their data are.
Probability is about "How likely?
Common Core
In seventh grade math, Common Core students begin to learn about probability. Probability is the study of how likely something is to happen. Students develop theories about probability and then test these theories with experiments.
The common example is flipping a coin. If the coin isn't weighted, if you let it hit the ground, and if you don't otherwise interfere with the flip, then the probability of getting heads is
The probability of getting tails is also
so these two outcomes are equally likely.
Being able to solve proportions is important in seventh grade math. In a Common Core classroom, the emphasis is on making sense of the solution method, rather than on memorizing a given procedure.
One general rule for whether your child is making sense of his solution is this: Does he know what each number means along the way?
Common Core
Sixth graders solve a variety of Common Core math problems using ratios. The words ratio and rate are both appropriate in sixth grade and can mostly be used interchangeably.
A ratio is a comparison of two numbers of the same type (unit). Usually, ratio is used for part‐part comparisons, but not always. The word rate makes most people think about change, but a rate is a comparison of two numbers of different types (or units).
Common Core
In Common Core math, eighth graders write and solve systems of linear equations. They use symbolic techniques and read approximate solutions from graphs. A system of equations in eighth grade is a set of two equations, each using the same two variables, and the constraint that the same values for these variables must solve both equations.
Common Core
Sixth grade is the first time that Common Core math students start to solve problems using variables and the property of equivalence (specifically, the distributive property).
They typically use variables that closely match the values they represent, so s for side length, v for volume, and so on. They also notice that some expressions — even though they may look quite different — always have the same values as each other, and they explore this property, called equivalence.
Common Core
Probably the most important Standard for Mathematical Practice in the Common Core classroom is to "construct viable arguments and critique the reasoning of others." That's because argumentation is at the heart of math as a discipline.
An argument in math isn't really the same as an argument your children may have in the back seat of the car.
Common Core
In Common Core math, place value is the most important idea that second grade students learn. They develop an understanding of this concept through exposure and through practice.
In far too many textbooks pre–Common Core, the study of place value was limited to naming places, which robbed many children of the opportunity to know place value well and to learn algorithms with meaning.
Eighth grade is when students learn the Pythagorean theorem in the Common Core State Standards. The Pythagorean theorem is this: In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
This definition seems a little bewildering, but the idea isn't nearly so complicated.
Viewed on their own, the seventh grade standards about angles and triangles can seem a little odd. However, when you see these standards in context, you'll understand why seventh graders study what they do in Common Core math.
The road from elementary school geometry to high school geometry has been rocky. Traditionally, children have spent a great deal of time recognizing and identifying shapes in the primary grades but have encountered a huge gap and advance little in their geometry knowledge until tenth grade, when they're expected to prove geometry theorems.
Common Core
Algebra can help to reveal how things are built — what different scenarios have in common with each other and what the important differences are. The Common Core State Standards refer to this idea as algebraic structure.
When you double the side lengths of a rectangle (or any geometric figure), but leave the angle measures the same, the area grows by a factor of 4.
Common Core
In order to solve Common Core math problems later, kindergarten students must first learn to play with the properties of numbers. Among these properties are that numbers can be combined, and that — correspondingly — any number can be taken apart into smaller bits.
Children need practice noticing and thinking about these combinations.
Common Core
To master Common Core Standards in math, children in kindergarten need to learn the sounds and the patterns of the counting words as well as what those words and patterns mean. This helps them learn the difference between counting and cardinality.
When you count a collection of things, the last number you say is the total number of things.
Common Core
In third grade math, Common Core students work on multi‐digit subtraction. The goal is to be able to solve problems such as 753 – 168 quickly, accurately, and with meaning.
Students use a variety of strategies to work these problems. Some students may have a favorite way of thinking about subtraction that they use for all problems; other students may change their strategies depending on the problem.
Common Core
Connecting ideas is an important part of the Common Core Standards for Mathematics. This is because math is rich with connections. Connections basically are relationships between ideas. But math is often taught in a way that obscures these connections.
When teachers insist on memorizing both addition and subtraction facts (which is different from insisting that students be able to produce these facts quickly), they obscure the connections between addition and subtraction, for example.
Common Core
Common Core geometry is rather simple in first grade, but there is an important twist that you may not notice. Students identify, explore, and work with shapes, which is the simple part. The twist? They work with defining attributes.
Defining attributes basically means that they begin to pay attention to what makes a triangle a triangle, not just what a triangle looks like.
Common Core
In Common Core math, students start to focus on the number 10 when they hit first grade. They start to count by tens and decompose ten. They also decompose other numbers in relation to ten (for example, 12 is 10 + 2; 13 is 10 + 3).
This important role of ten is highlighted in the classroom through a number of representations and activities, including the following:
Linking cubes: Students may use linking cubes to show groups of ten.
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