## Mastering the Basic Math Facts- Part 2

**Our Math PLC**

** We will con****tinue to work as a vertically aligned ****professional learning community** (PLC) to:

1.Create a more student-centered math classroom, where students are able to select their own tools to investigate math concepts.

2. Add to our professional toolkit, strategies that we may use to differentiate instruction.

**Requirements**

We will answer two questions and then comment on at least 2 of the posts made by members of our PLC.

In responding to posts, we will clearly state which aspect of our peer’s comments resonated with us and then add additional insights/examples either from the text or classroom experiences.

*We will earn 16 professional development credits for the book study.*

**Week 4 – July 2-8**

**Chapter 3 – Zero**

**W4Q1:** After reading chapter 3, whether you teach kindergarten or fifth grade, how would you justify the importance of zero in our number system to our students?

**Chapter 4 – Adding Ten**

**W4Q2:** Why is adding ten an important foundational skill?

**W4Q3:** What visual tools might help students better understand +10 facts?

**W4Q4:** Why are so many activities in the book focused on partner discussion? What are the benefits?

**Week 5 – July 9 – 15**

**Chapters 5 & 8 – Doubles and Using Doubles**

**W5Q1:** In what ways will visual experiences help simplify doubles facts? What tools provide effective visuals of doubles?

**W5Q2:** How might using the terms double and half support or confuse students?

**W5Q3:** How might you assess fluency for students who struggle with written Fact Checks?

**W5Q4:** How might you differentiate tasks for different levels of learners to help them use their doubles facts or doubles +1 or doubles +2?

**Week 6 – July 16 – 22**

**Chapters 6 & 7 – Making Ten and Using Tens**

**W6Q1:** What games and practice activities might help support automaticity of making and using ten?

**W6Q2:** How will students’ understanding of tens or the power of ten support them with more difficult facts/tasks?

**W6Q3:** What activities would be good choices for math fact centers/stations/tubs? Why?

**W6Q4:** What is the role of language in developing math fact strategies?

Zero

The last week in June I read a book called Less than Zero by Stuart J. Murphy. It details the experience of the main character who learned that it was possible to have less than zero if you borrow “money” from friends. The entire experience was captured using visual representation (graph) and it was very kid-friendly, although based on our current TEKs it is more suited for a 6th grade class because it addressed negative numbers. If students do not have a good understanding of what zero represents, then it will be hard to grasp the concept of less than zero. I can imagine using a number line to extend this thinking, as students get older.

At the elementary level, we have a huge responsibility…to help students understand the abstract concept of zero. What activities/strategies/experiences may we do to help accomplish this goal?

Yes! When we are teaching these concepts, I really feel like our main goal is to solidify and build a firm foundation of number sense and automaticity in math. Zero is a very abstract concept for some students. I learned early in my teaching career (in music, no less) that some students had no clue what “zero” was. They knew words like “none”, “nothing”, “no more”, but had no concept of the word zero and how it related to numbers.

I think that the strategies and experiences we give them in relation to zero need to be applicable to more than one concept. We should use visuals, games and partner work to help them really grasp how it works. Let them manipulate zero in scenarios so that when zero becomes more in later grades, they are more able to utilize it the proper way.

W4Q3 – I think some of the most powerful visual tools in adding 10 can be fingers (or toes!). Kids love to be the “teachers” and demonstrate the skill. Most kids at the kindergarten level can automatically identify or show 10 with their fingers. It’s an easy way to “flash” 10 and then add it to a given addend. I also like the visual of the “triangle cards” – I think this gives a very concrete way to show the relationship between addition and subtraction by showing all possible combinations on one card. I would have the children make their own, so it is more meaningful, and keep them as a visual.

W4Q4 – It’s important for children to discuss concepts between themselves. First, because it always shows a deeper understanding of a concept if they can discuss or “teach” it to others. It gives them confidence and makes them FEEL smart – which is huge at this age. Also, some children respond differently to peers than to their own teacher. They might feel more comfortable and might be willing to express some doubts or misconceptions to a peer that they would not want to share out loud to the whole group. Sometimes children can explain a concept in a way that we have not even thought of – because it’s the way their brain works! And when they share it with a peer, they might understand it in a different way as well. We want children to understand that we can all learn, but we can also all teach!

Hello Michelle,

As I read your post for W4Q4, I agree that the more ownership we give to students the more they will be able to master the concepts they are being taught. When students are able to teach others, then it is proof that they have a deeper understanding of the material. Considering the fact that we have no idea what jobs our students will be doing when they get older, the best thing we can teach them at this time is to take ownership for their own learning. Show them the path, and then allow them to continue on their journey.

Michelle,

I completely agree, students need to work with other students. If they really understand the concept, they will be able to teach it to a peer. If they do not understand it, the other student may have a way to say it differently than the teacher in order to make them understand.

I have found that students learn a whole lot better from other students than they will ever learn from a teacher. I love partner learning!

When I also like when they use their fingers and toes when working with 10’s. I’m always afraid that they will become dependent on their fingers to add and subtract all the facts. If they are given multiple ways to figure out the answers before they automatically recall it, they are less likely to be finger counters in the long run.

W4-Q2

I call 10 the magic number in my classroom. Kids must understand that our number system is based on the number 10. One of the things that really stuck out to me as I was reading is that kids need to understand that adding ten to a single digit creates a new place…a two digit number. That seems so very simple but to kids, even some 2nd graders, it is a very complex concept. If students cannot grasp this basic understanding, then, in my opinion, they will have difficulty understanding all numbers that come after 9. Understanding that every group of 10 adds a new place also moves into how three digit numbers are created (10 groups of 10), thousands (10 groups of 100), millions and so on. Therefore, learning to add 10 is a critical fundamental skill that all students must grasp in order to begin to understand place value and the relationship of all numbers that will come after. Learning to add 10 is a key component to building this basic understanding.

W4-Q3

One of the best tools I feel that I utilize is the tens frame. It provides a quick way for students to visualize 10 and continue adding from there. Even when we draw objects to represent numbers, students must draw them as if they were set upon a tens frame. I think using the tens frames is also a good way to show the commutative once kids have established adding a number to 10. Unifix cubes or pop blocks are also a great tool since they come in groups of 10 and make it easy for students to group the objects accordingly.

I agree that learning to add 10 is a basic building block. It’s a concept that, once understood, will be vital throughout their math career. It’s interesting to me that Mary Ellen says even 2nd graders struggle with that concept. It makes me want to make sure we are working hard with that idea when counting days of school, taking attendance, all the day-to-day operations so that they have a real understanding of how it works.

I also see the 10-frame as a great way to make 10 and add on from 10. It’s a set model that does not change. In a lesson, I may use 4 girls, 9 erasers, or 6 circles on the white board. A 10-frame is always 10. Last year with pre-k, we taught a number with the numeral (1), with the dots on a di, with fingers, with objects, and on a 10-frame. Even though we weren’t using them in adding, they knew what a 10-frame was and that if we put something in each spot, there would be 10 all together.

I agree with Michelle on the importance of student discussion. I think one of the most important aspects of student discourse is that students speak the same language. I have seen kids struggle with concepts that I have explained and modeled many times only to hear “Oh, I get it!” when it is explained by one of their peers. I like what Michelle said “Sometimes children can explain a concept in a way that we have not even thought of – because it’s the way their brain works! ” as well. Kids think the same way and they are often wired similarly. Letting them talk to each other cements their own learning and also allows for a deeper and sometimes new understanding by sharing their thinking with a partner.

W5-Q3

I love so many things about the way students are assessed in this book. I am planning to make an individual graph for each student to keep in the front of their math notebooks. As they progress, using the Facts Check, they are going to graph their progress. This allows them to focus on the positive (what I know) and also allows them some privacy so that they are not comparing themselves to others. I also plan to use the grid and have them mark the facts they know so I can tell at a glance which facts are missing. This is helpful to keep track of every student.

However, with the strugglers it is critical to keep up with their areas of difficulty. Using the graph/grid, I plan to use several activities from the book. One of my favorites, is to do one on one assessment with the fact cards. The child is shown the card and gives an answer. As the child misses a fact it is set aside. After five facts are missed, the student is given the chance to take those cards and study them to mastery. Giving the kids some two colored counters (like spray-painted lima beans) to take home, they can practice building and memorizing these five facts. (They should also work on these facts during fact fluency time.)It does not seem overwhelming to them because it is only five facts. Then, a recheck is done maybe a week after to assess their mastery of just those five facts. The shorter assessment should relieve their anxiety and leave them feeling successful. Then, I plan to continue on and repeat the process until mastery of the set is achieved.

W5-Q4

Differentiating is a key component to keeping kids interested and engaged. If I already know my facts, why do I have to keep repeating them? I think this is where it is so critical to have small skill groups so kids can work at their level of mastery. For my highest kids, I think the challenge for them would be to create word problems on their own using the facts. Then, these can be used for another group of students to solve at a later time, they could switch and solve each others problems, or they could be used by the teacher for class review. The author of the problem can be the instructor while the problem is being solved. I also think kids that have achieved mastery love to time themselves on their facts. They could do this and keep a chart of their times to track their progress.

For both high kids and those kids with a good grasp on the facts (but those who may need to work on fluency) they can also begin working to understand how those facts can be helpful solving two digit problems. I know my kids were able to solve two digit problems using mental math by finding the tens and then adding up or counting back. This challenged all my kids middle and high because it was done in their heads. They loved it! Last year, my kids had decks of cards 1-10 and played a game using three kids in each group. Two kids picked one card each and put it on their head without looking at their own card. The third person said, “The sum is 10, or the difference is 2.” Then, because they could see each others card, they had to guess the math fact. They rotated play so that everyone got a chance to play each part of the game. They couldn’t get enough of this game.

Of course, for my strugglers, the need to continue supporting them with the use of manipulatives is key. They need to build it until they’ve got it. Using a variety of manipulatives and activities will keep them interested and moving forward. Also, feeding the facts to them in smaller chunks will also help reduce the anxiety and give them many opportunities to feel successful. I think guessing type games would also be good for this group. “I have a group of ten. You can only see 4. How many am I hiding under my hand.”

In response to W4Q3… I once observed a student taking off his shoes during math class. I know he did not have “stinky feet” and I watched keenly to ascertain the reason for the removal of his shoes. To my surprise, he was simply adding! Well, I have always shared that our bodies are natural manipulative so he was taking the initiative and using what he had. I also realized that regardless of the type of counters provided, students will select the ones they are most comfortable using. As facilitators the onus rests upon us to provide multiple experiences to help them build their confidence.

Visuals are important to help anchor students’ understanding. I like the idea of having three different graphic representations at all times – number bonds, number lines and the ten frames are great start (after they have been explicitly taught and reinforced in small group of course 🙂

Sherry,

I agree, students will use whatever they are comfortable with as a manipulative when adding or subtracting. I joke with my students to do whatever it takes to get the right answer and to use their fingers, toes, nose…whatever!

Sherry, I agree with your statement that kids should be allowed to choose their own manipulatives. I did that with my kids last year and it was like they couldn’t believe they had a choice. It made them more excited about problem solving because they had some control over how they were going to solve the problem.

I also saw that same reaction when giving them the choice of HOW to solve the problem. Giving them that freedom of choice really kept them motivated and engaged because they could use the strategy that made sense to their own way of thinking. It prompted a lot more discourse between kids as well because they would often ask the other student why they were solving it in a particular way versus the way they chose to solve it. I am very excited with the direction our math program is headed. I truly believe it’s what is best for our kiddos.

W4Q1: After reading chapter 3, whether you teach kindergarten or fifth grade, how would you justify the importance of zero in our number system to our students?

The number zero quantifies values such as “nothing”, “none”, “no more”, etc. In reading a word problem, students must be able to quantify each portion of the problem from the sentences given. In learning the number 0, we are allowing them to give those words a value. It also represents the distance between a number and itself on the number line. Zero is important in our number system for primary kids, but it becomes critical as they advance in mathematics in junior high and high school.

W4Q3: What visual tools might help students better understand +10 facts?

I think one of the most widely used visual tools is the number chart where students can see patterns. 8 plus 10, is the number directly below it on the chart, 18. While I like the concept presented in the book about having students showing their 10 fingers and then adding another students’ fingers, etc, I am cautious about using it. I know from personal experience with myself, sister and my daughter, that students quickly become reliant on their fingers as a source for answers. While it is a great way to start, it’s very difficult to wean them off of it. You can take away manipulatives, but not fingers. Instead, I would use something else that represents 10, such as a tree with 10 leaves or a ladybug with 10 spots. In using these visuals, students can see the groups of 10, but they are varying so that they do not become reliant on one manner in which to visualize it.

Kristi – I think what you said about relying on your fingers is a very valid point. Too many kids become dependent on counting on their fingers, and then it’s hard to get them to use other things. This becomes more difficult as they get older and need to have more automatic recall, and instead they use a lot of their time counting on their fingers.

Krisit,

I like the way you talked about how 0 is the distance between a number and itself. That is a real eye-opener, I think, for kids and is a great activity to practice on the number lines to give them a deeper understanding of that number. Zero is so much more than just adding nothing…kids also need to understand it is the place holder for each period. If you have 0 tens, you do have none, but it must be used to keep that place available for when you do have tens. Learning the value of zero is a huge part of our learning place value, adding and subtracting, and is building the foundation for those higher level mathematics that you mentioned.

W4Q1: having a strong foundation and understanding zero is really important and what’s scary is that even in third grade some students don’t know what zero is. These students quickly find themselves at my small group table with manipulatives as I pound this concept into their brains. If you don’t know that adding zero doesn’t change how much you have then you will have a very difficult time understanding that when you multiply a number by zero you have zero (which is another very difficult and abstract concept!) Math concepts build upon each other and it’s so important for a student to have a strong foundation.

W4Q3: I like to use base-ten blocks and number lines to show +10 because they show patterns.

W5Q1 – I think visuals are always important to the learning of any new concept. I think it would be good to start with a visual of what the word “half” means. Show half an apple or half of a pizza. Something they are familiar with and will know immediately that the concept is “half”. Then discuss what it means when we say half. I think the visual of seeing “half” of a real object will help them cement the idea. Really any visuals that you can split in half will help them with this idea – also demonstrating what is NOT half. You can talk about this again as you introduce “doubles” and talking about if it’s not equal then it’s not half.

W5Q3 – in Kindergarten we often assess verbally. I think this could be done with fact fluency as well. While written automaticity is certainly the goal if children are struggling with recording the answers or doing it in a specific amount of time, I think you could test them verbally and let them use manipulatives if necessary. Automaticity in writing will come in time but it’s most important to make sure they have a concrete understanding of the concept first.

Visuals are key to teaching “half” to a class of kindergartners. Some may know what it means already but others don’t. I use cutouts of pizza, cookies, cake, etc. I have 2 of each with one split in half and one split unevenly. I also have pictures of sets split evenly and sets that are not. I tell a story where I am greedy and my “friend” is not. The class looks at both sets and chooses which are halves. We may a t-chart with the pictures. Students can then make up their own stories to share with a partner. You could even put this into writer’s workshop and make a class book.

W4Q2) Automatic recall of facts that have 10 as an addend, greatly helps students in finding the sum of more complex facts. Continuos practice of adding 10s helps them understand that only the number in the tens place is changing. This gives them a deeper understanding of the place value system and therefore expands their number sense. Focusing on adding tens also helps them use tens and make tens while doing several different problems with ease.

W4Q3) In order to help the students better understand the concept of adding tens, using visuals like a double ten- frame or a 1-20 number line an be used, along with counters. By using a double ten-frame the learner can see that if one of the ten- frame is full then he has 10 and the answer would be 10 + the other number of squares that are full in the tens frame. He does not need to physically count all the counters.

Using a number line could be a another way to add 10s. In this the student gets a _+10 fact card and places one counter on the first addend and then counts ten more to see where they landed. Doing this repeatedly they will know where to place the 2nd counter without the need to add 10 physically. The fact cards can also be reversed to show them that the answer will not change (further emphasizing the commutative property).

The students can also use their fingers as manipulatives and work in pairs to add.

Ms Truncali,

Ever since you told me about the ” Magic of 10″ I have used it all the time in my class. Only an experienced teacher like yourself can make it sound so simple that “adding ten to a single digit creates a new place…a two digit number.. “. Certain things that we consider simple can actually be so complicated for our students. The art of a good teacher is to simplify these basic things for the students. I have so much to learn. Also teaching them that every group of ten adds a new place value, will greatly help them expand their number sense.

Ms. Johnson,

Taking off shoes to count is Indeed the most unique way of counting I have seen or heard. I agree with you that there are always the natural manipulatives as we tell them to add using their fingers or doing addition with a partner by using their fingers as tens frame. Each student has their own comfort zone manipulative that they feel most comfortable with, as teachers we can offer them all the manipulatives that we have but its up to the students what appeals most to them.

Ms. Truncali,

I loved the idea of a privately stored individual graph for showing their progress with fact fluency. It is indeed a very positive approach for the student to see him move up the graph. Also the idea of doing fact cards in small groups for the struggling students is great. This will also help them work hard to get the cards mastered.

W5Q1) Visuals are indeed very helpful in introducing any new concept to all learners. Since I am going to be teaching an ESL class next year I will start each new concept with a visual. In this case we could start with showing a picture of 1 orange and then adding another orange to it to show that there are two, then to start with 2 oranges and then adding 2 more oranges to get 4. I can keep doing this to show how the numbers are doubling and not simply increasing by 1 or 2. Definitely the visuals speak before the words. In a similar way we could show them halves by cutting an orange in half or taking 2 away from 4 or 3 from 6 and so on.

Ms. Bellomy,

That is such a great idea to introduce with a visual of half. I started with doubles and then spoke about doing halves. But this can give them a great perspective and also help introduce fractions in a away. As you are also telling them NOT half , that is a great visual introduction.

W4Q2

Adding 10 is an important foundation skill because our math system is based on 10. In kindergarten, we use 10 frames to count the number of days we’ve been in school. We use a 100 chart where there are 10 horizontal lines and 10 vertical lines. We use 10’s to teach place value. When our student’s add 10 to a one-digit number, they get excited to see that they’ve made a 2-digit number.

Having a strong foundation on using 10 as a benchmark is so important. When students get to 3rd grade and beyond we break down larger numbers into 100’s, 10’s and 1’s to multiply and divide. So helping our students understand and use 10s as early as kindergarten and continue to build upon that knowledge in 1st, and 2nd grade is so important.

W4Q3

I use 10 frames to help teach +10. When I taught 3rd grade math, we used a 100’s chart to show the pattern of adding 10 to 2-digit numbers. We also used a place value pocket chart to show what it looked like when we add 10. We did exercises and made a chart as we did 10 more. Example: Girls are going to jump 3 times. Boys are going to jump 10 more times than the girls did. I’d ask if they knew how many times the boys we’re going to jump. We’d write 3 on one side of the chart and 13 on the other side. Though we didn’t do the activities in 1, 2, 3 order, I made the chart in 1, 2, 3 order. I’d then keep this chart on the wall for reference.

W5Q1

Anytime students can physically see or act out a strategy, they are more likely to understand what they are learning. I had difficulty learning doubles has a child. We were taught addition in order from 1’s (1+1, 1+2) then 2’s, 3’s, and so on. Doubles weren’t taught as a separate concept. As a teacher, I see that it’s important to do this separately as well as with the same number facts. We make a class chart showing pictures and numbers for doubles addition. As they are learning doubles, I introduce a doubles poem in reading workshop.

W5Q3

I like to use games to assess fluency when they struggle with written equation checks. You can use dominos, playing cards, or dice to check for fluency. Flash cards are similar to written checks but some students do better with verbal assessments than written ones. I also believe that students with high test anxiety levels do better with games and individual flash card checks. It’s awful for some to with their offices up in a quiet class while they wait for the timer to go off. I also use file folder games to check fluency. It doesn’t take more than a few minutes with a student or a small group to figure out if they know their facts.

Games are amazing tools to use for students with test anxiety! I myself have anxiety issues and if you say the word “test”, “quiz”, “exam”, etc, my mind immediately starts racing and I can’t think straight. Unfortunately, tests have become the standard of assessing and evaluating student progress. I’d love to see this change in the future, or at least be more fluid. Perhaps a way to be able to gather and evaluate data without so many tests. However, I think the way we view student progress will also have to be more broad as well.

W5Q4) Differentiation is key to working in a mixed ability classroom. Just as Language arts teacher have established different spelling groups based on ability in the same way I plan to form different groups depending on their ability and level of the kids addition facts. It could be very boring for a student to practice adding 1 and 2 when they have mastered adding tens. Hence I shall form groups and assign them on to adding numbers they currently comfortable with and push them a little further. On the same note I can have another group doing small group with me. The students can get regrouped depending on how they move with their fact fluency.

I have heard arguments made for an against ability grouping in classrooms. Those that are against it argue that the lower students need the higher students grouped with them in order to catch on to difficult concepts. People that are pro-ability grouping feel like the higher kids will be held back and the lower kids confused. I’m more of a pro ability grouper on this one. I agree, adding 1 and 2 is very boring for those that have mastered it already. The higher kids need to be pushed a bit, while the lower kids need repetition. In order to truly differentiate instruction, all kids need to have an equal opportunity to learn the concepts on their own level and in their own way.

you could even have the students who have shown mastery to peer teach the struggling students as one of your groups!

W6Q1

I like activities where my students can get up and move while learning at the same time. With student lineups, you can not only use how many boys/girls, you can use long hair/short hair, shorts/pants or dresses, glasses/not glasses, etc. The kids can all participate and by using white boards, they can all practice writing down the equations. I also find that using manipulatives gives that hands on approach that keeps them interested and focused. Chenille stems and beads not only help with making tens it also helps with fine motor skills. They can practice making tens and when they are finished, they can keep one and turn it into a bracelet. They can go home and as homework, tell their family about making tens. When making and using ten, using a 10-frame is extremely helpful in supporting automaticity. By changing the counters, you can keep it theme/holiday related and revisit the skill all year.

W6Q3

There are many choices of games and activities that are suitable for centers/stations/tubs (CST). I think the most important thing about games is that they need to be familiar with the game before it goes into a CST. The directions need to be simple and visual (usually with pictures). The students enjoy card games, dominoes, and (soft) dice because these are things that they are more familiar with. I also like using games like Candyland, Chutes and Ladders, HiHo Cherry-O!, Jenga. These can be manipulated to teach the specific set of math facts or they can be used as a reward. Example: The students are doing math facts flashcards with a partner. For each correct answer they get a Candyland card. In the end, they see how far they can go on the path. The furthest one wins.

The activities need to be hands on and not worksheet based. They need to actively participate for the CST to be effective and engaging.

The activities also need to be self-checkable (?). There needs to be a way for them to see if they are getting the answers right or if they are doing the activity correctly. If not, they could end up wasting time getting the answers wrong or doing an activity with no purpose.

Jamie – that is something I need to work on more this year, is ways for children to “self-check”. I always feel like if there is a way for children to self-check than the answers are already there and they will just use them instead of doing the work first. I guess maybe I just need to trust them a little more 😉

W6Q2) A very important idea that the students should know is that our number system is a system of 10s. By knowing the addition facts that have a sum of 10 helps them solve so many other addition facts and do mental math efficiently. Since the students have explored the ten- frames and hundred charts they have worked with numbers organized in tens. This helps them to understand place value.

Shradha,

I love your comment, “Differentiation is key to working in a mixed ability classroom.” and agree 100%. It can be difficult to differentiate for kids without adjusting the mindset that one has for the general ed classroom. Once that mindset has been changed, it becomes easier and easier to see all the different ways one can meet a variety of needs for our kids to achieve their maximum growth.

W6Q2 Students need to understand that our number system is based on 10. Once they deeply understand this concept, they will be able to begin to understand the flexibility of numbers. If they know that 10 is just one more than nine, they can easily solve 9+6 by making a 10 and then adding 5. This type of thinking helps students make other connections with more difficult facts and tasks because they know how to simplify numbers to make problem solving easier.

Last year, we did a lot of work on making 10s. My kids were able to think more deeply about numbers when adding, subtracting, and using a number line because they understood they relationship of numbers in sets of 10. That led to further understanding sets of 100 and eventually a set of 1000. They learned that 5 was half of 10, so 50 was half of 100 and so on. This allowed them to begin visualizing those number relationships in their head instead of always having to put pencil to paper or to build the numbers.

W6Q4 The role of language cannot be over emphasized when learning math facts or anything else, in my opinion. If students cannot discuss what they are learning and put it into their own words, then they rarely, if ever, have an understanding of the concept they are learning. I have found that students who cannot talk or write about a skill are usually the ones that are struggling. I also think that students listening to other students explain and talk about math fact strategies gives them an opportunity to hear it in a way that they are more likely to understand…kidspeak, if you will. They are less likely to feel intimidated asking another child versus they teacher. And, if I can use language to teach another student which strategy I am using, I am cementing my own learning.

I agree with the idea about students listening to other students. I think it’s a great way to assess student learning in a different way. I also like the phrase “kidspeak” 🙂

I agree that having “kidspeak” time is beneficial for students in all lessons. We can teach and reteach using different variations and some kids will still not understand. When students communicate what they know in their words, it might help a struggler. It also reinforces the skill for someone who fully comprehends what was taught.

I love hearing my students teach each other about the concepts they are learning. You can totally tell who gets it and who doesn’t really quickly. The kids who struggle will typically walk away with better understanding because they have heard it explained in a different way. I think it also gives the the students who may not realize they know more than they think they know about a concept more confidence in their own understanding!

Jamie, I think your ideas for math games for the kids are great. Using a game as a reward for practicing and getting correct answers will keep kids motivated and make that practice fun. I also agree with you about the self-checking. I think we, as teachers, sometimes think that they are cheating or not getting the full benefit of the practice if they can look up the answer I disagree. If they are looking up an answer, they are reinforcing the correct answer again and again in their own mind until there is no longer a need to look. I think it is a win-win for the students all the way around.

W6Q1 – I think any memory or concentration game is good for teaching automaticity in identifying “friends of 10”. Children will quickly start recognizing what numbers go together. They love playing memory or concentration type games and I think they will help them quickly identify the numbers that go together. I also really like the idea of using “Ten Apples up on Top!” for teaching the concept of 10 through addition and then again for teaching subtraction. They will already be familiar with the story and so it is logical to use it when relating to subtraction and it’s a great way to show how addition and subtraction are related.

W6Q3 – one of the activities I like to use for math small groups or centers is my magnetic ten-frames. There are magnetic pieces that are every variation of a ten frame. One has one dot, one has two dots, etc….all the way up to 10. Each piece has different colored dots (the one dot is yellow, the two dots are orange, etc…) I have children start by just choosing two pieces and counting the total. Then I ask them to choose two pieces that will make a complete ten frame, and we talk about what two pieces they use (the 4 piece and the 6 piece). As a last activity I give them a piece and ask them which piece they would need to complete a ten frame. After they have made an educated guess I let them try out their answer. It’s a great way for them to visually see the way two numbers make 10.

Michelle,

I like your usage of the magnetic 10 frames. What a sneaky way to get them to add without knowing it! I guess this could even be transferred into other visual forms as well. When they count the pieces, they could write the numbers down. That would get them used to seeing it written and not just represented. They could also write about it, like make up a word problem. It could really be used to differentiate the activity for the whole class.

The magnetic ten frames sounds like a great tool to have in math. Did you make it? I like that the dots are color coded too. You’ve got me wanting to make games with the idea of colored 10 frames. 😄 I’m going to make colored 10 frame cards and the students could match (or play memory) with 2 cards that add up to 10. A 10 frame with 2 orange dots could match up to a 10 frame card with 8 purple dots. I’d make a self check card that would only need an orange line and a purple line together. (If you’d like a copy, let me know…. 😄) Thanks Michelle!

W5Q1: In what ways will visual experiences help simplify doubles facts? What tools provide effective visuals of doubles?

Visualization of doubles could be as simple as having students put their hands on their heads, stand up or even raise their hand. In the book, it was mentioned that visually demonstrating the process of joining 2 equal groups is important. So, having students count out 4 red chips, then 4 blue chips, setting them on opposite sides of the table after counting. Then, have the students physically move the red and blue chips together. How many chips are there now? For some students, they must see this moving together process in order to understand the concept of addition. Having students drawing animals/insects and counting legs is also a useful strategy. The students are physically involved and counting each group individually before adding them together.

W5Q2: How might using the terms double and half support or confuse students?

I have first hand experience that the word “half” is often confused with the word “have”. When teaching note values, we discussed halving a whole note to make a half note. I would frequently get awkward stares from kids all the way up to 5th grade. What I had to start doing was breaking it down into steps. First, we would count the beats in the whole note, then the half notes. I would have to physically show them that the half notes were the whole note cut in half. If I just said we were going to “half” the whole note, some students thought I was saying we are going to “have” the whole note.

I think this also causes confusion because of halving being a subtraction process. We teach it after addition and I think that some students feel like we have to add before subtracting.

I love the idea of halving a whole note. Using instruments could be a tool to help the kinesthetic and musical learners understand this concept. Don’t worry Kindergarten friends, it’ll be an outside activity. 😄

I’m loving the idea of combining flashcards with Candy Land!!! I need to write these down because there are so many useful ideas.

I like that the students get a reward for working on their facts. It’s not like you are bribing them, but it is a natural, achievement based reward. It’s very realistic and similar to life.

W6Q1: What games and practice activities might help support automaticity of making and using ten?

The book suggested multiple games and activities to help support this concept. One I liked was Triangle Fact Cards where they have to think about it as part-part-whole. They work with a partner and not a group, which I think it important because they are in a one-on-one, low risk setting. I liked the Mystery Word Problems activity, but would probably only use it in a center instead of with the class. Some students are very anxious about anything they do being presented to the entire class, even if what they did is correct and amazing.

I want the games and practice activities we use to be purposeful and with the intent of helping the students grasp the concepts with a deep understanding, leading to automaticity and strategic thinking.

W6Q2: How will students’ understanding of tens or the power of ten support them with more difficult facts/tasks?

If students can learn that 10 is a benchmark number in our numerical system, they will be able to simplify calculations, resulting in a higher level of automaticity. It will also help them think strategically when solving problems. If they forget their facts, they can still figure it out. Students can compensate for facts they don’t know by using those that they do know. For example, 6+5=? The student could say that they know 6+4=10, so 6+5 (which is one more) must be 11.

By using 10 as a benchmark, students have a “safety net” in case they forget their facts. Instead of feeling frustrated and angry for not remembering, 10 gives them a tool to figure it out.

Kristi,

I agree that teaching our students that 10 is a benchmark is so important. When students realize this you can tell they feel more confident and it’s almost like they feel a sense of relief that they don’t have to memorize all the facts. I think talking out how we solve mental math with our kids helps them understand that there are so many ways to make 10.

W5Q1: In what ways will visual experiences help simplify doubles facts? What tools provide effective visuals of doubles? Visuals are always important when students are learning a new concept. Our students are surrounded by visuals all day long when they use their smart devices so we need to utilize visuals in order to grab their attention and help them make a connection and lasting memory. I loved the idea of using dominoes to help the students identify the double numbers and then having the students write matching facts. An extension to the activity could be to have the students create their own giant custom dominoes. You could give them a template of a domino on a sheet of paper and instead of using dots they could draw hearts, clovers, or whatever they wanted. Then they could write a word problem for the domino they created. I think it would be more fun for the students to use their creativity and it would help them remember their doubles because they created the domino.

W5Q2: How might using the terms double and half support or confuse students? When I use the term double with my students I always use the term half to describe the opposite action. I think when we use these terms in regular conversation consistently with our students they start to build a better understanding. For example, when I’m lining up my students I often call tables or even individual students numbers. I may say something like “#10 line up, double 10 line up (that’s #20’s que to line up)” then I may say “half of 6 line up (so #3 would take their place in line). It takes longer for kids to line up but it enhances my instructional time instead of wasted time during a transition.

W6Q1: What games and practice activities might help support automaticity of making and using ten? Students could use dice to create ten. They could roll two dice and when they roll a total of 10 they record their roll by drawing in the dots on a dice template and then writing the math fact to match. For example they roll a 4 and a 6. They would put 4 dots on one dice and 6 on the other and then write 4+6=10

W6Q4: What is the role of language in developing math fact strategies? I like the idea of using a story like Ten Apples Up on Top! Reading the story first to get the students engaged and then using the story to guide discussion as they complete an activity. Using stories is always helpful when you need to refer back because students have been able to follow the story line and have made a connection between the story and the math. This is especially helpful for struggling students. For students who have shown mastery a great extension would be for them to write their own short story to share with a struggling student.

I think one of the best ways to visualize 10 is using a tens frame. Anytime that I have my students draw base 10 blocks I have them draw them like a ten frame. Having them count by ten and realizing even if you aren’t starting with an even 10 how easy it is to add on 10 is huge to understanding number concepts.

W4-Q4 – I think there are so many activities that focus on partner discussion because it is key to them mastering a concept. When students discuss concepts between themselves if shows a deeper understanding if they can teach it to each other. Many times hearing a peer explain a concept will help students to grasp it better than a teacher. If a student is able to clearly explain it to someone else then most likely they have mastered it themselves.

W5-Q1- I think visuals are an important way of introducing a new concept. Doubles are easier if you start with explaining the word half and giving them hands on experiences to show half. Also, using visuals or real life objects of doubles such as an egg carton as 6+6=12, spiders legs as 4+4=8, insects legs as 3+3=6, or wheels on a car as 2+2=4 as just a few examples. It gives them the visual to relate to the doubles facts.

W5-Q4 – I think it is beneficial to have ability groups for mastering math facts like spelling groups are formed. Students could be given a pre-assessment to see where they are and have groups formed from there. They would be able to practice and advance on their own. I would be working in small group with those that were needing to start from the beginning to get them caught up to the others.

W6-Q1 – There are a lot of great games for making ten in these chapters. A few of the ones that I like are using the 10 beads to make 10 as well as the fill 10 and fact dominos. There are so many great ways to help students recognize sums of 10 that it becomes automatic.

W6-Q2 – When students learn that 10 is the benchmark/foundation of addition then they begin to realize that adding 10 to an single digit is simple. If students are able to make ten then the addition becomes easier by knowing that they can make 10 then add the remaining on. Helping to understand that they can decompose a number to make it easier to add will help the automaticity of their facts.