Homeschool Math Blog

While I feel that most of the Common Core math standards are fairly good, here's one place where I disagree with them (3.MD.7.c). It has to do with the topic when a larger rectangle is broken into TWO parts, and then children write a math sentence from it such as (3 × 4) + (3 × 2). This is in 3rd grade in the CCS. I feel it is a bit too difficult for that level, and would better fit 4th or even 5th grade. Someone just wrote me recently concerning this topic, wondering WHY do we do all this in the first place. Here's my answer. The reason for breaking the rectangle into two is to get students familiar with this: 7 × (2 + 8) = 7 × 2 + 7 × 8 which is (essentially) the distributive property. The idea is to familiarize the students with how multiplication works with addition , and we use an AREA MODEL to show or prove that. I decided to edit a video for this topic to help the person who asked... The video just explains HOW we do the rectangle thing, not why. ...

As many of you are preparing for school work again, please take note (and bookmark!) these comprehensive worksheet lists that include most math topics for any given grade: Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Best of all, the worksheets are free! They are dynamically generated so you get a different one every time you click on the link. You can also save them to your device and edit them in your favorite word processor. Also, I recently formatted the above pages so they look good on mobile devices.

Here's a little sample of what is keeping me so busy right now - third grade math, aligning things to the Common Core standards. This is a complete lesson (4 pages) about area for grade 3 math. It's not the initial lesson - it assumes the student already knows how to find the area of a rectangle. (Sorry - there is no answer key at this time; it hasn't been made yet!) The lesson (worksheets) is specifically about these two standards: 3.MD 7.c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.  d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Let's be reminded first of all that there are two basic "interpretations" of division: 1) Sharing division. In it, you think that 16 / 2 means "If there are 16 beads divided between 2 people, how many does each one get? 2) Quotative division. In it, you think how many groups of the same size you can form. Or, "how many times does the divisor fit into the dividend?" For example, 16 / 2 is interpreted as: "If you have 16 beads, how many groups of 2 beads can you make?" Sharing division is easy to understand as a concept, but it's hard to do without the knowledge of multiplication tables. Just imagine, if a child who doesn't know their times tables is trying to find the answer to the question, "If there are 56 strawberries and 8 people, how many will each one get?" It'll take some guesswork, trying and checking. But quotative division is easy for children to do with the help of manipulatives (or by drawing pictures). Just make...

I have a new book to add to the Blue Series collection of worktexts: Math Mammoth Add & Subtract 4 Math Mammoth Add & Subtract 4 covers the following addition and subtraction related topics which are approximately for the third and fourth grade level: * mental addition and subtraction strategies; * adding and subtracting in columns; * Roman numerals; * the connection between addition and subtraction, missing addend problems, and solving word problems with bar diagrams; * order of operations; * bar graphs, line graphs, and money problems. Price: $5.00 Buy now Samples pages include: Contents and Introduction Addition Review Adding Terminology and Practice More Subtraction Review Subtract in Columns Word Problems and Bar Diagrams Rounding Line Graphs

Great news! The LightBlue Series books are now available as downloads. These are designed to be a complete curriculum for a given grade. They follow the lesson format of my Blue Series books: explanations, then problems (worktext). In fact, the two series do share a lot of material. The LightBlue is for you if you need a math curriculum for a given grade that covers all the topics needed. These are practically no-prep for the teacher, and in fact, kids can probably teach themselves the majority of the time (assuming they can read). Please read more by following these links: Math Mammoth Grade 1 Complete Worktext Math Mammoth Grade 2 Complete Worktext Math Mammoth Grade 3 Complete Worktext I will have grade 4 ready sometime this spring, February or March I think.

... are ready as of today! There are lots of sheets for multiplication concept and multiplication tables, division concept, geometry, measuring, for example. Check out the sample sheets: Math Mammoth Grade 3 Worksheets

I'm going to talk again about the new report released by NCTM, Curriculum Focal Points. For each grade, it describes THREE focal points, and also explains to which other mathematical topics these focal points connect to. By familiarizing yourself with these few points, you can see the basics of school mathematics unfold before your eyes. Knowing the basic goals is essential for being a good teacher. By the way, these aren't the only things kids might study on a given grade. They are the focus areas. Many of the other topics would connect with these. Go look at the pics at textsavvy.blogspot.com about the way textbooks and programs typically present the topics, versus a "VISION OF CURRICULUM" laid out by the Focal Points document. On grade 1, the focus is on addition/subtraction : basic basic addition facts and related subtraction facts. Learning to add and subtract two-digit numbers. Understanding whole numbers in terms of tens and ones Composing and decomposing ...

As I mentioned, I have recently started on a new project in creating a worksheet package for third grade. So... I have had to take a real close look on what exact topics are usually taught in third-grade math. I have been looking at two third-grade (public school) math books. One is from 1978, the other from 1992. I have been quite amazed at the differences between the two! I knew about the 'trend' in mathematics curriculum where topics seem to get introduced on earlier and earlier grades. But it was eye-opening to see it "in action" in comparing the books. I think it's good for homeschoolers to be aware of this trend, too. The 1978 book is full-color, illustrated, very clear layout, and fairly little text. The word problems are extremely word-scarce. They've even put little symbols in the text instead of words (for sandcastle or beaver or squirrel or an LP record player, for example). The 1992 book is still full color of course, less clear layout, and this ti...