As a teacher, I always had parents asking me about new math. Let me set the record straight, THERE IS NO NEW MATH. The math hasn't changed, but some of the strategies that we teach with have. I am going to go over a few strategies that your child is learning in school and show you how to help them practice these at home.
We are going to start by looking at the standards. Teachers always begin by looking at what their students have to know. I taught in Texas, so we are going to begin by looking at the Texas standards called TEKS. (These are available online to everyone.) I will also include the common core standards because they are used by most other states.
3rd Grade Texas Standard: "The student is expected to: represent and solve one step and two step multiplication and division problems within 100 using arrays, strip diagrams, and equations.
TEKS can be found at this website.
http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111a.html#111.5
3rd Grade Common Core Standards: CCSS.MATH.CONTENT.3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
Common Core Standards can be found at the following website.
http://www.corestandards.org/Math/Content/3/OA/
As you can see they are very similar. There are a few things in each of these standards that I would like to show you.
#1 Arrays
Arrays are basically just a picture model of a multiplication problem. They are something that is supposed to be used as a building block when students are first learning to multiply. I am going to show you some basic arrays and then explain what you and your child need to understand about them.
Problem 1. The array in the picture above is representing the problem 5x3. The goal of the array is for your child to be able to draw a picture that is going to help them solve the problem. The choice in what picture does not matter. I always had my students do something quick and simple. There is no reason for the array to be too elaborate.
Problem 2. This array is representing the problem 3x8, and shows that it does not matter which number is on which side. The answer will be correct either way. Your child should be able to count the pictures and find that the answer to the problem is 24.
Problem 3. I chose to do this picture to show a non example. This problem does not show an array. The purpose of an array is to create an organized picture that will help your child solve the problem. If they are just drawing a picture with the correct number of dots, x's, stars, etc. they probably know the problem well enough to not use an array. If your child struggles with creating an array that they are actually able to read, I suggest using graph paper to help them. You can find graph paper on google that you can print. You can also find graph paper on teacherspayteachers.com.
#2 Equal Groups
Equal groups are fairly simple because they are exactly what they sound like. These are similar to arrays, in that they are a picture, but they are more spread out. To show multiplication as equal groups, you need to begin by determining how many groups that you have. The number of groups will be the first number in your multiplication problem. Next, you must determine the number of objects that will be in each group. The second number in the multiplication problem will give you the number in each group. Once again, in the end you will be counting the total.
Problem 1. This problem will show you a basic example of what an equal groups picture is going to look like. Once again, it isn't anything fancy. Your child should be able to quickly draw the picture and find the answer.
Problem 2. I always like to include a non-example to show what not to do. This second problem is a non-example as the dots in each group are not equal.
#3 Strip Diagrams
Let me add the disclaimer that as a teacher I always hated teaching strip diagrams. They have the least number of resources to teach them, but always appeared on the test. There are several different types of strip diagrams; addition, subtraction, multiplication, and division. Strip diagrams are another way to show a multiplication problem using a visual. In my opinion, they are more difficult for children to understand. In Texas, your child will usually be asked to identify what problem is being represented by a strip diagram. After hearing all of this, I'm sure you are just dying to see an example of a strip diagram.
Problem 1. This is the basic multiplication strip diagram. It is split into equal groups, similar to the equal groups method of multiplication. The question mark just represents the answer.
Problem 2. I chose to put this example just to show that it does not matter if the answer bar is on the top or the bottom. In multiplication all of your digits (numbers) will be on one row, and the variable (the question mark) will be on a different row. I chose the word variable because the question mark could be replaced with any letter, depending on the problem.
Problem 3. This is the non-example. The first one is wrong because the groups are not even. This happens often when kids are making their own strip diagram. The second one is wrong because the variable is mixed in with the numbers. It is also wrong because 7+7+? cannot equal 7 in this strip diagram.
#4 Equations
You are probably thinking finally we get to the real math. The equation is literally just the problem. For example, 5x3=... As a fourth grade teacher, I am going to tell you that there is no substitute for just learning your math facts. Your child needs to memorize their math facts through tens. Meaning, 1x1, 1x2, 1x3, etc. This will help them so much in the future. As you saw earlier in this post, the methods shown above are things that your children are required to learn. These methods are great building blocks and will help your child learn their math facts.
I hope that this post will help you to help your kids.
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