I just ordered these Battista books to help implement the common core math standards for each grade level at school. To my delight, the books list a link to extra free resource tasks! There is a book for place value, multiplication and division, fractions, geometric measurement, and addition and subtraction, hence there are FREE resources for all of these.
Next click on the link that says “companion resources”. This will take you to all of the free tasks for that particular math book.
Here is a sample of one of the tasks:
After years of seeing students mix up math operations in word problems, I have finally figured out how to help students understand what operation to use in word problems. This little word is causing students much of the confusion–EACH. Haven’t we all taken for granted that students understand what this word means. The word ‘each’ is in nearly every multiplication and division problem, but many students don’t know what it means–every one in the group. If we teach students to read a word problem and replace the word each with its meaning, every one in the group, students somehow have a light bulb experience.
In conjunction with teaching students to understand the word each, also asking them questions about the problem helps facilitate understanding. For example when you ask, “Is this a joining or a separating situation,” students start to make sense of word problems. Students generally understand that words like altogether and in all mean that they are joining groups. The word total may need to be taught as a word that means in all, but total isn’t a difficult term for students to become comfortable with.
To help students further differentiate between multiplication and addition, ask questions like: are we adding the same amount over and over or are we adding two different sized groups? If the answer is adding the same amount over and over, then multiplication is repeated addition of equal sized groups. If students are confusing division and subtraction, ask, “are we subtracting different amounts or are we subtracting the same sized amounts over and over. If the answer is subtracting the same amounts over and over, then teach students that division is repeated subtraction of equal groups.
Several years ago I worked at a charter school the first year it opened. The school implemented Singapore math, so that was my first year to test the waters of Singapore math. Our trainer instructed the 3rd grade teachers to go ahead and teach branching even though it was a skill the students should have learned in second grade. To teach children the procedure of branching, it took about four weeks total, and then not all of the students perfected the ‘procedure’ of addition and subtraction branching. The students had more success learning addition than subtraction branching. With the mandates of testing, we weren’t able to solely use Singapore math, but I had to supplement with other materials. Then as you are all familiar with, testing approached and likewise the pressure along with it. Then we didn’t have ‘time’ to teach number sense SO deeply since other skills are tested. Unsurprisingly, the teaching of Singapore Math somewhat fell apart midyear. Please don’t take this wrong I LOVE Singapore math because it works, but the conditions of testing hindered us from teaching it wholly.
Fast forward to four years later. After teaching small groups today, I have reflected on the year that I taught branching and its effectiveness. Yesterday I pulled small groups of average math students to teach them regrouping for the second day in a row, I had them build double digit numbers with base ten blocks blocks. I repeated this process today with the same group of students. After that I started notating their thinking with branching representation on a small white board. Students intently watched and helped me notate the thinking they had done with the blocks in (abstract) numbers . They began to understand grouping with tens and how to decompose numbers to build more tens or hundreds. Then I told them that they couldn’t use paper or blocks, but could only look at the addends I was about to write on the board. I asked them to whisper the answer in my ear so that others could still think. I was amazed! Half of them could answer the question correctly doing mental math. The other half were only 1 away from the correct answer. I was so proud.
I shared the above to really say the kids taught me something in just two days because of their adept ability to add mentally. Teaching branching worked so much better four years later–all I had to do was provide an experience with branching directly after building with base ten blocks. Why didn’t I start out with the concrete blocks first before I threw abstract numbers at them…duh me! Branching made so much more sense to them after building a concrete foundation. Reflection is priceless!
The first grade teachers at school absolutely love introducing subtraction and addition number sentences to their kids using the book Ten Flashing Fireflies by Philemon Sturges. I discovered this book in a lesson recorded in a Math Solutions book entitled Minilessons for Math Practice K-2. There is also a similar lesson (I think…not positive) in another Math Solutions book entitled Teaching Arithmetic. In the lesson students model the action of gathering fireflies into a jar using snap cubes. In the book there is a jar printable to use or the lesson suggests using a sheet of blue construction paper to represent the night sky. Not only is this lesson good for introducing the action of subtraction and addition, but it is also good for discussing one more and one less. Because this is such a beloved book that builds a great foundation for addition and subtraction, I worked on building this free SMART Board lesson to accompany the book this weekend, and so here is an example of this lesson. Just click to download the SMART Board lesson for free.
Two years ago I was introduced to math number discs and began using them in my classroom. I have come to rely on teaching regrouping using the math number discs after modeling regrouping with base ten blocks on a mat. These number discs (which are really expensive to purchase) are marked with 1′s, 10′s, and 100′s. An inexpensive alternative to using the ready made number discs is buying colored bingo chips and writing numbers on these yourself. Every place value position is a different color. The ones are white, the tens are red, the hundreds are orange, and the thousands are yellow. Students group the discs to represent a number on their place value mats and then take away the needed discs. Moving the discs around on the mat themselves does not seem to help students make the connection as much as having them draw and mark out the discs as they subtract. When they notice there are no more discs to mark out in the tens place for example, students realize they have to borrow from the hundreds place, mark out a hundred disc, and draw ten tens discs. If you scaffold this understanding to the actual borrowing and show students that when you borrow from the hundreds place to bring over ten tens, students have a light bulb moment and see the connection to all the marking out and rewriting of numbers that occurs in the abstract algorithm we call subtraction with regrouping.
Also, I am including a link below to my July 14th post in which I am showcasing a Smart Board lesson and practice pages that I created using interactive number discs.
One of my favorite math games for elementary math students to play is “Close to 100″. This lesson and game can be found in TERC math Investigations books for third grade. The game instructions, number card blackline masters, and score sheets are in the unit Mathematical Thinking. In this game one student of a pair draws six numeral cards (0-9) without looking from a deck and selects four cards to use. With these four cards students are to build two two-digit addends to find a sum as close to 100 a possible. The player’s score is how far away from 100 the sum is. For example if the sum is 102, the score is 2. If the sum is 95, the score is 5. Each player totals up his scores at the end of the game, and the player with the least score wins. What I like so much about this game is that students are practicing facts, learning place value, buildingnumber sense, adding, and subtracting while they are engaged in cooperative learning. The only quibble I have with this lesson is that the only assessment to be gathered is informal teacher observation. To make up for the lack of assessment provided in the lesson, I recommend that after playing the game to give students a scenario in which they draw six cards. Have students write about which of the cards they would chose to use to get as close to 100 as possible. To differentiate this lesson, struggling students can pull only 5 cards and choose 3 number cards to make 20 (First grade Mathematical Thinking book), or advanced learners can pull 8 cards and choose 6 to build 1000 (Fifth grade Mathematical Thinking book).
See an example of this game here: http://www.pearsonschool.com/live/images/custom/investigations/Investigations_widget1.html.
I just read a fabulous article from the periodical Teaching Children Mathematics (March 2011 issue) about the effectiveness of teaching subtraction with regrouping. A group of students was given a pretest beforehand and scored about 16% proficient at subtraction with regrouping from the instruction they had received the year before. The teacher showed students examples of the error patterns they were making. Next, to teach students about the errors they were making, the teacher gave students magnifying glasses and investigator hats so that they could become investigators to find a particular error pattern. Students relished the idea of finding the mistakes. As a result, the post test revealed a dramatic–more than 60% increase in proficiency of subtraction with regrouping. This article is not available for free online, however you can purchase it at http://www.nctm.org/eresources/toc.asp?journal_id=4&Issue_id=973 or your library may have a copy.