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Take this checklist with you to your parent-teacher conference as a helper, mark off the items as you go.

Carol R. Rinke and John F. McAdam, Marist College

5 x 3 is not the same as 3 x 5? What are those strange arrays? The Internet is ablaze with criticism about the Common Core’s “cruel and unusual” new methods for teaching math. Our children’s math homework has pictures of cookies in place of numbers and we worry about what this means for their future! Whether or not we support the use of Common Core approaches in today’s classrooms, it is important that we as parents come to understand where these methods are coming from and what they mean.

Common Core math starts with an
important underlying assumption: Numbers can be used more flexibly when they are
taken apart and put back together. Just like children learn to decode words by
putting together the sounds of individual letters, children can also learn to **decompose **and **compose** numbers by taking them apart and putting them back
together. This often involves finding “hidden” numbers inside of larger
numbers. For instance, the number 63 actually contains a “hidden” 60 inside of
it, so we know that 63 is the same as 60 + 3. Likewise, the position of digits in
the number conveys meaning, such that 22 also can be represented as 20 + 2. While
numbers can be decomposed in a variety of ways, it is familiar and sensible to
decompose numbers into sets of 1’s, 10’s, and 100’s, thus building on place
value concepts.

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A second fundamental principle of
Common Core math involves using physical manipulatives as well as pictures to help
children **visualize** numbers and the
relationships among numbers. Children begin to form mental models of
quantitative relationships by first using concrete objects such as two cookies.
They then bridge their understanding to paper by representing those objects
through pictorial methods such as . Finally, they are
ready to connect more meaningfully with abstract numerals such as the number 2.

These fundamental concepts of composing and decomposing numbers, along with the process of visualizing numbers, are taught to young children and carry through Common Core math during their school years. Below is one example of how these approaches build coherently across many years of math.

When introducing numbers, the Common Core encourages children to compose and decompose them in a variety of ways. For instance, they learn that 7 can be composed of 6 + 1, 5 + 2, 3 + 4, and so forth. Along with this understanding, they also are introduced to strategies for visualizing numbers. Using a tool called the tens frame, children can begin to visualize 7 in different ways.

Tens Frame

Looking closely at the tens frame, children can visualize how 5 + 2 = 7. Using the same image, they might even be able to visualize how 10 – 3 = 7. Using the tens frame helps children anchor their understanding of number in relation to benchmarks numbers of 5 and 10.

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Children later apply their ability to compose and decompose numbers to addition, subtraction, multiplication, and division. Here again, this skill is paired with strategies that help children to visualize numbers. One such approach is used for multiplication, in which children decompose factors into extended form, then use an array to visualize the operation.

For instance, given the multiplication problem:

- Children would first decompose the factors into (10 + 4)(10 + 3).

- They would then arrange the extended factors on a visual array (see Figure 1).

- The extended factors are then multiplied together to generate the partial products of 12 + 30 + 40 + 100, which are added to together to find the final product of 182.

While younger children are busy
composing and decomposing numbers and visualizing those numbers in spatial forms,
they are actually building the foundations for algebra. The ways that children
understand whole numbers in the multiplication problem above parallel how they
will later come to understand variables such as *a* and *b *in the following example.

Take the basic algebra problem (*a*+*b*)(*a*+*b*).
Using the traditional method, students could find this equal to a^{2} +
2*ab* + b^{2}. However, students
can also solve the problem using the model** **shown above, replacing whole numbers with the variables *a* and *b* (see Figure 2). Rather than simply memorizing how to solve this
algebra problem, students come to understand the ways in which mathematical
patterns and processes appear time and again in more complex forms.

Traditional approaches to the teaching and learning of math have relied heavily on memorization, step-by-step procedures, and “plug and chug” approaches to solving math problems. Completing tasks such as double digit by double digit multiplication involved little more than using a rote multiplication procedure to arrive at an answer. The goal of Common Core is instead to focus students’ thinking on the important mathematical concepts involved in such a problem. Through the examples we have provided, students build deeper understanding of how to compose and decompose numbers, develop place value concepts, illustrate operations, and construct visual models of the mathematics at hand. The very good news is that when younger students better comprehend these underlying concepts, they are prepared to apply them throughout their school years. And the more we, as parents, understand the concepts the more support we can offer our children.

States across the country are implementing new standards for student achievement. The academic growth chart presents benchmarks to help parents understand the course material covered in each grade.

There are many more additional resources that parents can consult when seeking support and guidance. Included here are some links that may be helpful.

These tips for parents offer advice and suggestions for activities designed to help you help your child learn. They provide ideas for ways in which you can be a more active partner in your child’s education.

Categories: Academics // Common Core // Education Policy // Elementary School // High School // Homework // Math // Middle School // Parental Involvement // Parenting Advice

All children have the potential to achieve success in math if they believe that their perseverance can make them better. Here is some advice on how you can help your children feel confident about their mathematical abilities and develop their appreciation for learning.

Nothing may be more feared in the minds of young children and their parents than learning the basic math facts. Just hearing the times tables takes many of us back to our own childhoods. The good news is that our own children should not have to suffer the same fear.

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