In the 1980 film, Private Benjamin, the main character enlisted in an army which was quite different from the one she had envisioned. Private Benjamin, portrayed by the talented Goldie Hawn, laments, “See, I did join the army, but I joined a “different” army. I joined the one with the condos and the private rooms.”
Just as Private Benjamin found herself in a place for which she hadn’t bargained, perhaps you’re reading this article because your role as a parent has broadened to include being your child’s teacher.
Teaching math at home is not the parenthood role for which you enlisted!
Math is, hands-down, the subject of struggle for a majority of elementary students, and with Common Core standards so different from those we learned as students, there’s a good chance you need a little help understanding, too.
Math for parents
Is the question, “What is Common Core Math?” familiar? Is this math so very different from the way students were taught when you were their age? Is there a best way to teach math? Should the math lessons be supplemented with math activities?
It can be confusing. But good news: you’re already beginning to think like a teacher by pushing your limits and striving to make connections. You’ll need that when you’re helping your kids develop their skills.
How to do Common Core Math
One of the essential goals in Common Core Mathematics is for children to make sense of the mathematical processes. The Common Core standards were developed in an attempt to raise the level of mathematical understanding in the United States. Simply memorizing the algorithms for common calculations, as was often common practice, did not promote mathematical understanding. The mathematical reasoning behind these algorithms needed to be at the core of understanding.
For these reasons, helping your kids understand the meanings behind the mathematical processes will enable them to think through problems and make sense of the process while doing so. Encourage exploration and embrace challenges. Foster the inquisitive nature within your child. Allow questions to be the springboard for discovery and understanding.
In addition, the Common Core strives for a greater focus on fewer topics, allowing for a deeper understanding of each topic while connecting them across grade levels. This coherence will lend itself to a solid mathematical foundation upon which later areas of mathematics will be built.
Elementary math concepts
The concepts taught to kids in elementary school are age and developmentally appropriate. The Core Standards for Math lists the standards in detail. The various focal topics, which illustrate the key shifts in mathematics delineated by the Core Standards for each grade level, are as follows:
- Grades K-2: Concepts, skills, and problem solving related to addition and subtraction
- Grades 3-5: Concepts, skills, and problem solving related to multiplication and division of whole numbers and fractions
- Grade 6: Ratios and proportional relationships, and early algebraic expressions and equations
- Grade 7: Ratios and proportional relationships, and arithmetic of rational numbers
- Grade 8: Linear algebra and linear functions
Here are important Common Core math concepts for each grade level:
K-2: place value
Place value is an important concept taught as early as kindergarten. As students learn about larger numbers, the concept of place value continues through other elementary grades.
In math, every digit in a number has a place value. Here’s an easy example.
In the number 57821:
- 5 is in ten thousands place and its place value is 50,000,
- 7 is in thousands place and its place value is 7,000,
- 8 is in hundreds place and its place value is 800,
- 2 is in tens place and its place value is 20,
- 1 is in ones place and its place value is 10.
There are many ways to help your kids understand place value. Using opportunities which present themselves every day in a casual manner might just be the best way for your child to learn and appreciate math. One of the most useful ways is by using a hundreds chart.
Consider printing this chart, or saving it to your computer or phone for quick reference.
The above is commonly referred to as a “hundreds chart.” Many teachers use it to help students gain a better understanding of numbers according to Common Core standards.
At first, the sequence of numbers can be taught by asking students to read the numbers on the chart from left to right. Scale this by printing a few hundreds charts with some numbers missing, and ask your child to write the numbers in the correct spots. The process of writing, saying, and hearing each step can be key to your child’s understanding, and might prevent them from getting stuck.
Money can be learned at the same time as teaching numbers on a hundreds chart. By placing pennies on each of the squares, you will have a dollar’s worth of pennies when the chart is filled. Your child will have fun trading groups of five pennies for nickels, or ten pennies for one dime, et cetera. Placing nickels on the multiples of five, and dimes on the multiples of ten will give your child a head start in counting money as well as introducing concepts relevant to multiplication.
This concept is common in classrooms, and can be changed as needed to suit your student’s particular level of understanding. Make learning fun and it will engage, as well as teach, your child.
When learning math using a calendar, students can learn by doing all sorts of things: drawing, writing, adding/subtracting, multiplying/dividing, measuring, counting, telling time, and many others. Applying it specifically to Common Core math, you can use simple manipulatives to illustrate concepts. Try this simple one, which builds on the hundreds chart:
- When a new month begins, ask your student to check the calendar and gather one stick per day.
- On the tenth day of the month, gather the ten sticks together and secure them with an elastic band. Announce, “We now have our first ten-bundle!”
- Use the calendar to illustrate that the digit 1 in the 10 tells us the number of ten-bundles we have. The zero tells us there are no loose “ones.” So, for example: on day 14 there will be 1 ten-bundle and 4-ones.
The bridge from ten-bundles and loose “ones” should make teaching addition simpler – carrying a number to another column now has mathematical meaning. This understanding of the mathematical process is our goal.
In grades K-2 classrooms, references to a physical calendar are made every day as part of the learning process. This is easy to do at home.
Reviewing the date starting with the month, day, and year will help your young students child understand the marking of time. Talking about past, present, and future events and indicating them on a calendar is also a worthwhile activity.
Build on this activity, and ask your child to record the date on a whiteboard each day. The act of physically writing the month’s name and the numbers for the date will help cement the concept.
Hanging this whiteboard in a well-trafficked place in your home, where it can be seen by everyone in your family, makes this task authentic and valuable…and that leads to self-confidence in your young students.
In addition to the published Common Core standards, many states also have released tests from prior years, starting with grade 3. While “teaching to a test” should not be your intent, seeing that, for example, reading a ruler is a tested skill might prompt you to help your child explore linear measurements using the markings on a ruler.
There are a few key things that kids learn in grades 3-5 math:
Manipulatives, in the context of education, are physical teaching tools. Students visually and physically interact with objects (like coins, pebbles, beads, puzzles, etc.) as part of learning. There are lots of reasons teachers agree that manipulatives are an effective tool: they’re multisensory, represent concepts in more than a single way, promote critical thinking and communication, and leads to lessened confusion. This, in turn, leads to deeper understanding.
Measurement – linear, time, and capacity
You’ve already got manipulatives at home! Cereal, bottle caps, spaghetti noodles, blocks, toothpicks, measuring cups, beans, or even slips of paper will help bring mathematics to life for your at-home student.
Here’s a fun one to try that helps students learn concepts about measurement, using some fun manipulatives:
Measure a length (any length) using marshmallows laid end-to-end.
Now…what happens when you switch from regular-sized marshmallows to mini marshmallows? (Answer: the unit (marshmallow) is smaller, and the number of the units becomes larger.)
This exercise helps your child draw the connection between measuring with smaller units versus measuring with larger units. This is particularly helpful to kids who are learning to multiply or divide while doing unit conversions.
Connections made by your child during discovery are the best learning connections. Neurologically speaking, if they are having fun while these connections are made, there is a greater probability these connections will be retained.
Fractions and measurement
When students start struggling with math, it often coincides with their introduction to fractions. Before, they’ve been exposed only to whole numbers, with emphasis on the one-to-one relationship between the number and what it represented.
Fractions change all of that. The main challenge is teaching your student how to think about rational numbers in a different way. Once again, taking a creative approach can help kids better understand these concepts.
Most kids love to make cookies. Ask them to help you measure the ingredients with bowls and measuring cups/spoons (which already have fractions included). A dozen eggs in their carton can help illustrate a multiplication array, and this 2×6 array can be used to illustrate the basics of multiplication.
Or, point out the four sticks which make up the pound of butter. One stick is ¼ of a pound. How many other ways could the pound of butter be represented by fractions? What a marvelous opportunity to teach!
Make learning fractions fun and engaging for your kids. Their reward will not only be in the desserts they create, but also in the deeper understanding of math they’re picking up along the way.
Although a deep understanding is our greatest goal, some facts will serve as our greatest tools. Memorizing multiplication facts is one such tool.
Once your child actually understands why a 7 by 9 array equals 63, and a 6 by 9 array equals 54, the next step is to begin helping them put these facts to memory.
The nines’ table is a great example because if has several patterns, like:
- The sum of the digits always equals 9
- Also, the value of the tens’ place in the product is always one less than the non-nine factor
See if your child can spot a few of these kinds of patterns.
You might want to teach the finger method for the nines’ times table. This method is useful when the factor is a whole number less than 10, and the other factor is 9.
Another useful skill is to help your child strategize when a product (the result of multiplying) can not be recalled. When given 8×7, illustrate how a larger factor such as 8 can be broken down into 4 + 4.
These partial products can be added together to find the answer: 4×7=28, and 28+28=56. With this, you’ve arrived at the product of 8×7, which is 56. (A teacher’s tip: caution them to only break one of the factors apart for this example).
Math games for kids
Making math fun help reinforce facts and concepts. A game your student may enjoy is quite simple:
- Take a deck of cards leaving out the J,Q, and K face cards.
- Split the deck in half.
Now you and your child are ready to play a math-focused game of “Who Can Gather the Most Cards?”
- You’ll each lay down a card face up.
- Allow your child a little lead time to shout out the product for the two numbers on the cards.
- Whoever correctly says the product first gets both cards.
Shorten your lead time for subsequent games as your child’s skills improve. Soon your child will be earning all the cards!
Make memorizing their multiplication facts as easy, and as much fun, as possible, allowing time for practice on one table before moving to another. There are numerous websites which offer other suggested games, like this one.
Grades 6, 7, & 8 middle school math
The common theme in teaching math with these grades often revolves not around the reasoning within math, but rather the reason for learning math. Since understanding proportional relationships is very valuable to understand, find real-life ways to demonstrate concepts, like taking the time to share snapshots of the household budget with your middle schooler might be a valuable lesson.
Proportional relationships, algebraic equations and linear functions
Let’s look at how a utility bill can teach math.
The relationship between the kilowatt hours used in a month is directly proportional to the utility bill at the end of the month.
The amount of this bill is, in turn, inversely proportional to the amount of excess money available for the family to spend.
Your child might enjoy the challenge of bringing the electric bill down by unplugging curling irons and turning off lights if he or she knew the excess money would be put towards a family vacation. Making a table of the data and graphing it would the icing on the pi.
(Yes, that was a math joke.)
Shopping with a middle schooler? Computing sale prices when items are on a percentage-off sale will sharpen your young adult’s mathematical skills (and teach them real-life ones, as well). An understanding of money always opens the door to being able to compute with decimals, a skill, which by now, should have been covered in their classrooms using all four operations.
Keep your mathematical eyes open and grab teaching opportunities when you see them. In the teaching trade, these are known as “teachable moments.”
Enrichment and support
If you’re looking for challenges, or just clarification of various topics that will help your students master math, consider using the services of a tutor. Like all teachers, tutors connect with students in different ways, and personalize each lesson. A tutor will approach difficult concepts a different angle, customizing their teaching to the unique needs of your child. They engage, encourage, and motivate a love for learning.
Children have a natural sense of wonder. What an honor it is to build on this natural curiosity. The joy of teaching may well have you thinking that the ‘Parenthood-now teaching army” for which you enlisted was certainly the correct one! Much like in Private Benjamin, the lessons you and your child learn will be priceless!