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. ...

Hot off the presses! I wanted to share this 7th grade lesson on the distance of two integers that I recently wrote for the upcoming Math Mammoth grade 7. I'd be interested in feedback, as well! It is written specifically to match the Common Core Standard 7.NS.1 (c) Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. In easier terms... the lesson deals mostly with integers, and teaches that the distance of two integers m and n can be found by taking the absolute value of their difference: | m − n |. Download the lesson here (a PDF file). There is no answer key at the moment -- sorry about that!

I know some of my readers are teachers, and are looking for materials aligned to the Common Core. For them, I have made a simple page on my site that lists the materials I offer that are aligned or follow the Common Core. These include the complete curriculum, free worksheets, and short topical units at my TPT store and Teachers Notebook store.

I have created yet one more free worksheet generator. This one makes problems that give the student an expression in words , such as the quotient of 7t and 5 , the difference of x and 8, divided by 2 , or the quantity 8 plus 2t, cubed , and ask the student to write a mathematical expression to match that. These worksheets suit best grades 6, 7, and 8, including pre-algebra and algebra 1 courses. They specifically address the Common Core Standard 6.EE.2: Write, read, and evaluate expressions in which letters stand for numbers. However, this skill is also practiced in grades 7 and 8, or in pre-algebra and algebra 1 courses. When using the actual generator , you can control the number of problems, workspace, border around the problems, and additional instructions. Here are some quick links for ready worksheets. Refresh the worksheet page to get another of the same kind, until you are happy with the problems and layout. One operation; 12 problems per sheet Two operations...

Here is the newest worksheet generator that I have added to HomeschoolMath.net: Area and perimeter of rectangles/squares  It is very versatile and makes many different kinds of problems related to the area and perimeter of rectangles and squares. You can make: problems for the area and perimeter of rectangles and squares, with grid images or normal images word problems, including ones asking for a side length when area or perimeter is given problems with irregular rectangular shapes problems to practice distributive property with two-part rectangular areas (required by Common Core Standards in 3rd grade). You can make worksheets with just one type of problems from that list, or mix them up however you want. For example:   (in your browser options, make sure background colors get printed) I especially made this worksheet generator because I feel many children may have some difficulty with the new Common Core Standards requirement for 3rd grade, that is 3.M...

Math Mammoth Grade 5 revised version is now out! If you are an old customer and would like the updated files, please use the contact form here and include your purchase information (email/name used, if at Kagi or Co-op). Currclick customers can log in to their account at Currclick and download it from there. Download below: 5-A contents and samples 5-B contents and samples Here's a summary of the changes between the old and the new. You can also find this information here . The biggest changes in grade 5 are that the two optional chapters (percent and integers) have been removed, and the topics in geometry chapter are different. However, overall, the structure and contents of this grade is very similar to the old. Chapter 1 starts out like the old version, with some review topics and multi-digit multiplication. There is now more focus and practice problems on long division with two-digit divisors. One big change is that the lessons on problem solving and equation...

Questions about Math Mammoth and the Common Core Standards alignment? I made a new, hopefully comprehensive FAQ on this topic. Please refer to that document, and hopefully it will answer everyone's questions.

So, Math Mammoth Grade 4 is now aligned to the Common Core Standards. I will mention here some of the main changes as compared to the previous edition. The main changes in the revised edition of Grade 4 are that some topics were taken off and moved to 5th grade, and several topics were added in. Again, this is all due to the CCS. Other than that, the basic framework and conceptual development did not change substantially. Of course, I edited the lessons to make them better, added more space or grids for calculations, etc. so there were many cosmetic changes. Topics moving to 5th grade: Numbers beyond 1,000,000 multiplying a 3-digit number by a 2-digit number 2-digit divisor in long division multiplying decimals by whole numbers circles volume In measuring, the problems about conversions between units are easier, and the more challenging conversions will be in 5th grade. Topics added that weren't in 4th grade before: divisibility prime numbers finding factor...

Math Mammoth Grade 3 is now aligned to the Common Core. In this post I try to outline what is same and what is different about this edition compared to the previous one. What is same? -  The focus on single-digit multiplication and division is the same. I did add more varied word problems to these two sections, and other little 'enhancements' as I edited the lessons, but no major changes here. - Also, much of the addition,  subtraction, and place value topics are the same. There are some slight differences, yes, but not major ones. - Time and money sections are the same. What is different? - The geometry chapter has been pretty much redone. Now, it concentrates on the concepts of area and perimeter (according to Common Core standards). Before, I did have one lesson on area, but also other concepts, such as right angles and parallel lines. Those will be moved to 4th grade. - In measuring, I have removed most of the content that dealt with conversions between the ...

Math Mammoth Grade 2 Complete Curriculum is now aligned to the Common Core Standards. Here is a document listing the lessons and the corresponding standards .  I will record here the main changes in its content as compared to the earlier edition / version (through April 2012). You can tell the new edition and the earlier ones apart by their cover image: the edition aligned to the Common Core Standards has these new cover images. The topics of rounding and finding 1/4 of a number were taken off as they are not in Common Core Standards for grade 2. The topics of regrouping in addition and regrouping in subtraction are now split so that 2-A contains regrouping in addition, and 2-B contains regrouping in subtraction. There is now more explicit (more scaffolded) instruction about adding four single-digit numbers, and then adding four two-digit numbers in columns (in 2-A). Regrouping in subtraction with three-digit numbers is also scaffolded more (the progression of...

Math Mammoth Grade 1 Complete Curriculum is now aligned to the Common Core Standards. Here is a document listing the lessons and the corresponding standards . I will record here the main changes in its content as compared to the earlier edition / version (through April 2012). You can tell the new edition and the earlier ones apart by their cover image: the edition aligned to the Common Core Standards has these new cover images. What used to be chapter 4 (Place Value) switched places with Chapter 3 (Addition and Subtraction Facts within 0-18).  The topics of rounding, even & odd numbers, and parenthesis were taken off as they are  not in the Common Core standards for grade 1. There are many new lessons about adding and subtracting within 20, and adding and subtracting two-digit numbers without regrouping, explaining basic  mental math principles. The lesson "Exploring Measuring" is split into two lessons (Measuring Length and Exploring Measuring). B...

QUOTE from Common Core standards for 7th grade: The Number System 7.NS c. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Okay, I am not with this totally. For example, let's say you are supposed to find the distance between −4/7 and −5/9. Two negative fractions. They want the student to construct the difference −4/7 − (−5/9) and then find its absolute value. Remember we are in 7th grade. I find a more natural approach (and isn't it easier to SHOW this to students?) is to find the distance between 4/7 and 5/9, which is of course equal to the distance between −4/7 and −5/9. I feel students might have difficulties if they are supposed to take the difference of two negative numbers, and find the absolute value of that. They might make mistakes even in writing out the expression −4/7 − (−5/9) correctly. ALSO, the standard actually words it ...

In general, I really, really like the Common Core Standards for math. There is some emphasis and explicit mentions of  mental math skills, there is emphasis on conceptual understanding -- even a mention of the "bar models" (though they were called line diagrams) -- yet fluency of math facts and of the four operations are included as well. So I'm not really complaining here! But I've found a few little things there, pet peeves of mine, if you allow, that I don't quite follow, so I thought of posting such here and seeing if any of you have some ideas for me. Here's one for 5th grade. 5.OA Analyze patterns and relationships. 3.     Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given th...