Common Core Math

Screen Shot 2015-04-12 at 9.56.56 PMWe like the Common Core. If you read this blog, you have probably already figured that out. When we say we like the Common Core, we mean that we like the set of learning standards that the document sets forth as important to learn in each grade level. We like that the Standards encourage thinking, problem-solving, and practical applications. We do not particularly agree with the testing programs or tying teacher salaries to test results. But, for a set of standards of learning, they are pretty darn good.

We also don’t agree that teachers should take the Standards and work through them one by one and then give a test and call it a day. But, I haven’t met any teachers who want to do that or believe that is the right way to teach. Most teachers like the Standards (when that question is asked independently of testing programs). They like the Standards if they can teach in ways that they know to be effective while still figuring out the best ways to help children in whatever particular way they need help.

So, why do I like the Standards? Let me talk about math for a second. One of the old ways of teaching math would be to give kids a set of numbers, show him how to create an equation, and teach them how to solve it. This is how I learned a very long time ago. When I learned fractions I became very good at setting up the equation and solving the problem but I couldn’t apply those skills to real life. I ended up doing a lot of math when I turned sixteen and started waitressing, but I taught it to myself. I didn’t pull out a pen and paper and set up equations. Now, I’m not saying teachers were teaching this way before Common Core. When I went to graduate school in Education in 2000, I was thrilled to re-learn math and to hear about what teachers were doing in the classroom. I was thrilled to get out there and teach kids about number sense and show them how math could be fun. The Common Core just standardizes this. Successful schools probably already did what the Common Core suggests, in fact they probably go a step or two further. But, unsuccessful schools probably appreciated the help in figuring out what kids need to learn about math and how to teach it. Not all, but some.

And, of course, the Common Core Standards set forth an outline of when kids should learn major concepts. This makes it so much easier for transient families in a time when many kids will go to at least two and maybe more schools before they graduate from high school. This means those kids won’t miss anything in transition, they can rest assured that the concepts they were learning in their previous school will also be in progress in their future school.

Lastly, I love that the Standards give me an outline for what my child needs to know at each grade level. I created “After School Plans” that list the Standards for math and language arts so I know what my kid should know. I also added suggested books that directly deal with each Standard. Books are a fun and easy way to help kids learn. My kids love to read and then they tell me (teach me) what they learned. Finally, I have a list of easy activities I can do around the house that support their learning. Since math is no longer about sitting down at a table with two sharp pencils and a couple of pieces of paper, I can talk about math in my daily life. Fractions aren’t about formulas anymore, they are about grocery shopping (hamburger is $6.00 a pound and I want half a pound) or cooking (we need to add 3/4 cup of sugar to the cake) or having a party (there are ten kids and four pizzas with six pieces of pizza each). Math is fun! Math is a part of our daily life!

For more on our education plans, click here: https://afterschoolplans.com/educational-consultants/education-plans/

Here’s an example:

Number & Operations – Fractions

Extend understanding of fraction equivalence and ordering.

CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Build fractions from unit fractions.

CCSS.Math.Content.4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

CCSS.Math.Content.4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

CCSS.Math.Content.4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

CCSS.Math.Content.4.NF.B.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

CCSS.Math.Content.4.NF.B.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

CCSS.Math.Content.4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

CCSS.Math.Content.4.NF.B.4a Understand a fraction a/b as a multiple of 1/bFor example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

CCSS.Math.Content.4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

CCSS.Math.Content.4.NF.B.4c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.

CCSS.Math.Content.4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

CCSS.Math.Content.4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Books

Working with Fractions, David A. Adler

If You Were a Fraction, Tricia Speed Shaskan

Full House: An Invitation to Fractions, Dayle Ann Dodds

Spaghetti and Meatballs for All, Marilyn Burns

The Multiplying Menace Divides, Pam Calvert

Baking Kids Love, Sur La Table and Cindy Mushet

Williams Sonoma Kids in the Kitchen: Sweet Treats, Carolyn Beth Weil

Activities

  1. Fractions Dinner Party. Invite friends over for a fractions dinner. Serve chips, pizza, and cake. Put the right amount on the table and divide each serving equally. Express each serving as a fraction. For instance, Mark has 3/5 of the chips, 1/6 of the pizza, and ½ of the cake!
  2. Test a Parent. Write a page of fractions as word problems and see if your parent can express them in numbers. Ask them to give you the same challenge.
  3. Playing Card Fractions. Playing with a friend, take a deck of cards with just the numbers and draw two cards. Express the numbers as a fraction. If possible, reduce the fraction to the lowest form. If you do it correctly, keep the cards. If not, return them to the bottom of the pile. The person with the most cards at the end wins!
  4. Fractions Memory. Write fractions out as numbers and as word problems. For example, write ½ and then a card that says “I ate one of two pieces of cake.” Make ten sets and then turn them all over. Play the memory game.
  5. Car Fractions. When in the car, practice fractions. We have five miles to go before we get home. When will we be halfway there? We have been in the car for fifteen minutes but it will take us an hour to get there. How can we turn that into a fraction? Find other ways to make fractions from time and mileage.
  6. One of the best ways to practice fractions is to bake. Bake a cake and discuss the measurements, particularly the fractions. Using water or flour, show how four ¼ cups equals one whole cup. Do this for teaspoons, cups, and any other measurement that comes up.
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