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.
This past week I was asking a first grader how she had solved a math problem. When she showed me how she had used her fingers, I realized something amazing. She actually saw doubles on her fingers. I had never paid attention to exactly how students had used their fingers to solve problems. She used each hand as the separate addends in a problem, but more specifically she used each hand as the addends of an addition problem with doubles. So for example, she was easily able to see that 4 and 4 make 8 and that two more fingers (doubles plus 2) make 10– put one more finger up on each hand to make five fingers on each hand or ten fingers altogether. She used this strategy fluently, but it had never dawned on me to see patterns with doubles on two hands. I had always thought of the number four as just four fingers on one hand alone–not as two fingers on two different hands.
Last week we held a final championship for students in second through fifth grades for the classes’ highest percentage of correct answers during “Math Wars”. “Math Wars” is our affectionate name for math fact races. Surprisingly the underdogs (second graders) won the final championship while a fifth grade class had been winning all year. So, of course as second graders are, they were so EXCITED that they had won– as was their teacher. Since I didn’t have any funding for anything extra special, I, we’ll say ‘renovated’ an old trophy, which I found gathering dust. I cleaned it up a bit and made a new plaque for it as you can see below. I also handed out a golden abacus to each grade level winner. The golden abacuses were awarded and switched among classes all year after each “Math War”. Pictured below are all of the awards. I hope they give you some ideas.
For the math timed tests I used for math wars, click here.
For an example of how a teacher kept up with her own math races to prepare for math wars, click here.
For more about the math fact races, click here.
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!
I have been working with many small groups of average leveled students to help build their number sense since there will be so many gaps in common core understanding with students moving up to 4th and 5th grades. Up until earlier this year I confidently thought that students in second grade needed to learn the traditional regrouping algorithms for addition and subtraction. After some common core training, I humbly realized that students aren’t necessarily expected to know how to complete this traditional procedure, but rather be able to make sense of a problem by decomposing and composing numbers using strategies that are comfortable for them. I said all of that to say that because of this thinking, I gave students in my small groups base ten blocks and NO paper. I gave a double digit addition problem that would give students the opportunity to regroup 73 + 48 (mind you they should have been able to handle larger numbers). I thought I would start with a really easy problem. Well, I was wrong! The students struggled to get an accurate answer with blocks to solve this problem. Of the four students I had in this particular small group, only one student was able to find the correct answer. Well, I changed my mind on the no paper and gave them a sticky note. I instructed them to write their answer on the sticky note just so I could do a quick assessment of who could accomplish finding the answer with the blocks without blurting it out. To my chagrin two of the students were trying to solve the problem on their sticky note with the procedural algorithm. I promptly reminded them while replacing their sticky notes that we were solving the problem with the blocks and not paper. When all students had finished thinking, I listed all of the students’ answers on the board and asked them who was correct. After having students count and recount their blocks, they finally came to a consensus of the correct answer …121. They struggled with counting past 100 especially by 10′s… 110, 130, 140… and they would correct one another to say 110, 120, 130, 140. Surprisingly enough to me, the students felt more comfortable lining up numbers in an algorithmic procedure with no understanding to obtain an answer than they did counting out blocks past 100 to obtain the correct answer.
Below is a picture of the students counting out their blocks. I had them place their addends onto small sheets of square paper to help keep them organized since they were getting their extra blocks confused with the ones they were counting. I wanted to use small paper plates to help them organize their blocks, but I didn’t have any. I happened to have some origami paper lying around, so I just used that instead.
In order to make addition and subtraction more engaging, there are several things you can do to help keep students attention. Have students play games such as Close to 100, Close to 0, Close to 20, and other such games. In addition to the games that are already available from many of the Math Solutions books by Marilyn Burns and other authors, I developed some card sorts to help keep students’ attention on solving problems. I have developed a variety of card sorts to teach addition and subtraction within 100. Students match a picture card of unifix or snap cubes to an equation. To make a card sort more challenging, I like to include a card which doesn’t match any other card. This helps target some misconceptions that develop around addition and subtraction. If students solve card sorts in pairs, then this creates much students’ higher thinking as they evaluate each other’s decisions about where to place cards. If you would like to try out one of the these card sorts, just click on the picture below to download a free sample of an addition card sort without regrouping. This link will take you to TPT where you can download the preview file.
Yesterday I spent some time in a second grade classroom helping students who were adding double digit numbers. When working with one student, I realized he didn’t know he had ten fingers on his hand, and he didn’t know that four fingers on one hand and five fingers on another made one less than ten–nine. While at a CGI (Cognitively Guided Instruction) training today (I am in Year 2 of the training), some things dawned on me about this children. Children do not innately know that they have 10 fingers, nor do they necessarily discover this on their own. With that said, the CGI trainer today told us that she knew of a teacher that has students do finger flashes. She calls out numbers and the students hold up that many fingers. I had never thought to do something so simplistic. I know that in kindergarten we do such activities with dot cards, but I had never thought of finger flashes–WOW!
In this same second grade classroom, I moved on to another little girl who had difficulty counting on from the larger number. Even after I showed this student how to count on, I noticed that when looking at the problem she didn’t know where to get the other number to count on with her fingers. I showed her how to look at the problem to find the number. Again at the CGI training I realized for students to develop the number sense they need to count on, the teacher can push students toward counting on by posing a very large number in a word problem followed by a much smaller number. For example, with the problem 62 + 3, 62 would be easier to start from and just count up 3 more. Once a child is counting up just 3 more, the second number could be increased. As my mentor always used to tell me–You know better, then you do better. That is me.
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.