Category Archives: Math

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.

Math and Reading for Middle School

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Looking for ways to connect math and literature? Just want to learn more about the history of math, the secrets to being good at it, or who has been influential in the field? We compiled this list that is appropriate for children in middle school or higher. Even adults who want a fun brush up might find some of these books interesting.

  • Short Cut Math, Gerard Kelly
  • The Memory Book: The Classic Guide to Improving your Memory at Work, at School, and at Play, Harry Lorayne
  • Secrets of Mental Math, Arthur Benjamin
  • Math on Call, by Great Source
  • Mathematicians are People, Too: Stories from the Lives of Great Mathematicians, Dale Seymour
  • Who was Albert Einstein?, Jess Brallier
  • A Higher Geometry, Sharelle Moranville
  • Kiss My Math: Showing Pre-Algebra Who is Boss, Danica Keller
  • Math Doesn’t Suck, How to Survive Middle School Math without Losing your Mind or Breaking a Nail, Danica Keller
  • The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathmatics, Clifford Pickover
  • The Joy of Pi, David Blatner
  • Sphereland, A Fantasy about Curved Spaces and the Expanding Universe.
  • Mathematical Mysteries: The Beauty and Magic of Numbers, Calvin Clauson
  • The Cartoon Introduction to Statistics, Grady Klein
  • A Gebra Named Al: A novel, Wendy Isdell
  • Life by the Numbers, Keith Devlin
  • The Number Devil, A Mathematical Adventure, Hans Enzensberger
  • The Joy of X: A Guided Tour of Math from One to Infinity
  • The Math Behind the Music, Leon Harkleroad

Common Core Math

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It has become a bit of a sport to mock common core math problems. The amount of explaining and figuring has parents suggesting that the easiest way to do math is still to line the numbers up and then perform the operations. The thing is, I learned math this way. And, I can do math. But, I didn’t really understand it until I took a class on teaching math during my graduate program in education. The teacher taught us math using manipulatives. He want back to the basics, addition, subtraction, multiplication, and showed us how it worked using squares, blocks, and lines. I couldn’t believe it. I had so much fun and it felt like a new world had opened for me. Suddenly, I knew why I got the numbers that I did. I learned several ways to come to the same answer. I could see it, literally see the answer, right in front of me.

That is what the Common Core does. It asks teachers to make sure children can show how to solve a problem and why it works. Because, in life, we don’t solve problems that look like this: 124-65= _____. We see problems that look like this: Shoot, it’s 2:40 and I have to be at the school to pick up my kids at 3. It takes me twenty minutes to drive there but I need to stop and pick up some dish soap and that will take me fifteen minutes. Can I make it?

So, doing problems in neat lines with sharp pencils just simply isn’t real life.

Here is the article: http://www.vox.com/2014/4/20/5625086/the-common-core-makes-simple-math-more-complicated-heres-why

 

 

 

 

Bath Tub Math

Bath time is for play in my family. My kids play cars and trucks, barbies and mermaids, and color and draw. We have a ridiculous amount of bath toys and a ridiculous amount of fun. I recently started trying to direct some of the games in a slightly more educational direction. Luckily, no one seems to notice they are learning while playing. Here are just a couple of easy ideas:Image

  1. Start using measurement terminology when your young child is in the bath. Let them play with measuring cups and measuring spoons and experiment with how many teaspoons fit into a quarter of a cup. Let them figure out the different variations of smaller cups that can be combined to make a full cup. Talk through all of the options.
  2. Purchase bathtub crayons and a plastic ruler. Measure the bathtub, the washcloth, the spout. Let your child write the measurements down. Then, ask your child to mark off an inch, six inches, a foot. Flip the ruler over and try it with centimeters.
  3. Use crayons to write down math problems. Practice whatever it is they are doing in school. Alternatively, you could write problems on the tub or shower wall before they get in and have them complete them all before washing their hair!
  4. Tell time. Using bathtub crayons draw clocks with simple instructions. At 7:15, wash your hair. At 7:20 condition your hair. At 7:30 sing Jingle Bells. Add in fun activities and required actions.
  5. Throw some plastic balls into the bath and practice word problems. “If you have five plastic balls and I have three, how many do we have together?”

 

Learning Subtraction?

Is your child learning subtraction at school? Help them along by showing how the skill can be used at home.

  1. The kitchen really is the best place for math. Tell your child to grab three apples. Then, talk through the math problem. “I had five apples, but we are going to eat three. How many do we have left? Do I need to go and buy some more?”
  2. Before you go shopping, write your grocery list. “We have five rolls of toilet paper left. If we use one today, that means we’ll only have four left. I better buy some more.”
  3. Math is great when you are cleaning up the house. “There are three matchbox cars on the floor. If I put three away on the shelf, how many are left on the floor?”
  4. Take a walk! “There are eight steps and we have already gone down five of them. How many steps are left?”
  5. Go to the playground. “There are four seats on the merry-go-round and three kids are sitting. How many seats are left over?”

We do this sort of math all the time, but it helps to talk it through out loud so that children can see that subtraction is a part of daily life. It will also make the paper work make more sense if they can connect to real life experiences.

Subtraction Books

  • The Action of Subtraction, Brian P. Cleary
  • Hershey’s Kisses Subtraction Book, Jerry Pallota and Rob Bolster
  • If You Were a Minus Sign, Tricia Speed Shaskan, Christianne C. Jones, Francesca Carabelli, Melissa Kes

Measuring and Making Ice Cream

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Standard

  • CCSS.Math.Content.3.MD.A.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.2

Books

  • Ice Cream: The Full Scoop, Gail Gibbons
  • The Ice Cream King, Steve Metzger
  • The Sundae Scoop (Math Start 2), Stuart J. Murphy
  • Curious George and the Ice Cream Surprise, H. A. Rey
  • From Cow to Ice Cream, Bertram T. Night

Activity

Make Ice Cream! Ice cream measurements are easy and a good place for kids to start learning to love cooking and baking and working in the kitchen. An ice cream maker is a fun addition to the kitchen and an appliance that even first graders can learn to use. Read about ice cream with your children and then follow the directions to make wonderful treats. Get adventurous and add your own ingredients. Can you come up with an entirely new ice cream flavor? What will you name it?

Our Favorite Ice Cream Recipe from Cuisinart

Peanut Butter Cup Ice Cream

1 Cup peanut butter, 2/3 cup sugar, 1 cup milk, 2 cups heavy cream, 1 teaspoon vanilla, 1 cup chopped peanut butter cups.

  1. Mix peanut butter and sugar until smooth. Add milk and mix for 1 to 2 minutes. Stir in heavy cream and vanilla. Cover and refrigerate 1 – 2 hours or overnight.
  2. Turn on Cuisinart ice cream make. Pour mixture into bowl and let mix until thickened, about 15 to 20 minutes. Five minutes before mixing is completed, add candy and let it mix completely.

Fractions and Baking

Is your child learning fractions at school? There are many fun ways to practice fractions at home. The most obvious way, of course, is to bake a cake or cookies. First, take a look at the work your child is doing at school to get a sense of what the class is working on. Then, pull out your recipe books and get to work!

  1. Practice measuring with cups with your child. Pour four of the 1/4 cups into the whole cup. How many 1/2 cups make a full cup? How many 1/8 cups go into the 1/4 cup and the whole cup? Physically practice as many combinations as you can think of.
  2. Cut a piece of paper into 8 even pieces. Show that 1 piece of paper is 1/8 of the whole paper just as the 1/8 cup is one of eight portions of water that will fit into the whole cup. Show that two of the eight pieces of paper is the same as 1/4 of the entire paper. Connect that to the cups of water.
  3. Ask your child to practice measuring with 1/4, 1/2 and 1 teaspoon. Compare the calculations with the paper fractions.
  4. Make a cake together and follow the recipe. Ask your child to use the measuring cups and talk through each fractions.
  5. Double the recipe! See if your child can write down a new recipe by doubling all the fractions, or you can actually make a few extra cakes for your friends or neighbors!
  6. Halve the recipe! Work together to figure out the fractions you would use if you wanted to make half of a cake.
  7. Pretend you are having a huge party and triple or quadruple the recipe. Write down the new recipes and compare them to the original.
  8. After the cake is finished, cut it in half, then in quarters, and then in eighths. Talk about the different words you can use to express fractions (1/4, one quarter, one of four, one part of a whole, etc.)
  9. Buy your child a recipe book and write down every recipe you create. If possible, take a picture to illustrate each new recipe.
  10. Eat Cake!

Math can be fun! It is important to remember that most of us do math every single day. Math becomes easier for children when they see (and taste) the practical applications. Baking, cooking, and measuring in the kitchen are fun ways for children to practice basic math skills.