Yes, you can even use ten frames to teach multiplication concepts! Here are my mini ten-frames with dot cards from 1 – 10: Click HERE to get a free copy. These are helpful to use, especially if you don’t have enough tens/ones blocks . . . or you prefer manipulatives that are slightly easier to manage. These provide a strong connection to place value, and the commutiative and distributive properties.
I recommend two sets of the cards (1-9) per student. Each set has multiple copies of the same number. They can be laminated, cut, and placed in a baggie for ease in handing out and storage.
Multiplication Examples:
After students get practice using these manipulatives (concrete), then proceed to pictorial models to draw them as simply as possible. This will give them a good foundation to apply to the abstract (numbers only) problems. I always pitch for the CPA progression whenever possible!!!
I will pause a while for the summer and just post once a month until school starts up again. Take care, everyone! But please don’t be shy. Post your comments, ask your questions, etc.
]]>Thanks for checking in on another multiplication strategy! The focus for this post will be on the equal groups strategy — looking at how students can efficiently use this strategy to help learn basic multiplication facts. My angle will be at the conceptual level by using concrete and pictorial methods. Be sure to see the links at the end for books and my free equal groups story cards.
Basics:
What things normally come in equal groups? Conduct a brainstorming session. I love the book “What Comes in 2’s, 3’s, and 4’s” as a springboard. After reading the book, let students brainstorm other things that come in equal groups. See the pictures below for some more ideas. After some internet research, I also made this attached list to use (in case you or your students draw a blank): click here: Equal groups pictures and list template
Use these lists to help students generate stories about equal groups. When students can create (and maybe illustrate) their own stories, they are much better at solving problems they must read on their own. This also helps students think carefully about what in the story constitutes a “group” and what the “groups of” represents:
Ways to show equal groups with objects and drawings:
Objects to use to show equal groups:
Teaching concepts regarding equal groups:
Activities to practice equal groups strategy:
Enjoy!! Many of you are now off for a well-deserved summer break. Use your summer time to catch up on my postings from this past year, or email me for more information. Also, feel free to comment on any article about your experience or additional tips.
]]>In the last post, I shared my thoughts about multiplication strategies using the repeated addition strategy. This time I will focus on using arrays. Do you have some arrays in your classroom? Look for them with bookshelves, cubbies, windows, rows of desks, floor or ceiling tiles, bricks, pocket charts, etc. Students need to know arrays are everywhere! It is also very helpful for students to build arrays with objects as well as draw them. This assists students with moving from concrete to pictorial representations — then the abstract (numbers only) can be conceptualized and visualized more easily. Some good materials for arrays:
Array Basics:
Ways to incorporate arrays into story problems:
Activities to encourage concrete and pictorial construction of arrays:
In a future post I will show some ways to use manipulatives and pictures arrays for double digit multiplication problems. Stay tuned!!
]]>The next few posts will continue to focus on the basic multiplication concepts one at a time. This will allow the opportunity to dig deeper into the concepts we want students to understand. This one will focus on the concept that multiplication is repeated addition. These posts will be helpful to teachers introducing multiplication to students in 2nd and 3rd grade as well as those in 4th, 5th, 6th and beyond who have missed some of these basic concepts. Future posts will focus on the area (array), set (equal groups), counting, decomposing, and doubling/halving models as well as the associative and distributive properties. Freebies below!!
Do your students know what the “times” sign means? They may hear it frequently, but not realize what it means. I like to interpret it as “groups of.” So a problem like 3 x 4 can be said as “3 groups of 4.”
To show repeated addition, that same problem would be 4 + 4 + 4 = 12.
Repeated addition can be shown with numbers, and also with arrays and equal groups. These pictorial models are great for developing multiplication concepts (and will be topics of future posts). However, when students are presented with these models they often count the individual pieces one at a time rather than adding the same amount repeatedly. Observe your students to see how they are counting. . . and encourage counting in equal groups to promote a growth of the multiplication mindset.
Do your students apply the commutative property of multiplication? This means if the problem is 3 x 4, it can also be solved by thinking of 4 x 3 (which is 4 groups of 3 OR 3 + 3 + 3 + 3). I want students to know even though the answers are the same, the way the factors are grouped is different. When used in a story, 3 x 4 is a different scenario than 4 x 3.
Do your students practice repeated addition, by combining 2 or more numbers? See the following for an illustration of 15 x 6:
Do your students apply the concept of repeated addition to multiple digit multiplication problems as well? I have witnessed students numerous times who only try a problem one way and struggle. For example, on a timed test I witnessed a 5th grader attempt the problem 12 x 3. I observed him counting by 3’s. He was trying to keep track of this by skip counting by 3’s twelve times (using his fingers). I could tell he had to start over frequently, thus spending a lot of time on this one problem. It became obvious he had no other strategy to try. He finally left it blank and went on. Just think if he had thought of 12 + 12 + 12. This should have been relatively easy for a 5th grader. He also could have decomposed it to this: (3 x 2) + (3 x 10).
Do your students always go to the standard algorithm when they could perhaps mentally solve the problem by repeated addition? If the problem was 50 x 3, are they thinking 50 + 50 + 50? Or are they using paper-pencil and following the steps?
What about a problem such as 45 x 4? Using repeated addition, is your student thinking of 40 + 40 + 40 + 40 combined with 5 + 5 + 5 + 5? This is then solved as 160 + 20 = 180.
Here are a few resources (FREE) that might help with this strategy:
Students who are able to use repeated addition skillfully are showing a healthy understanding of place value and multiplication. This strategy also enhances mental math capabilities. Conducting daily number talks are highly advised as a way to discuss multiple ways to solve a given problem such as those mentioned above. Check out “Number Talks” in my category list for more information on this. Also check out some recommended videos about conducting number talks (above black bar “Instructional Resources”).
]]>Are you looking for some ways to help your students learn the multiplication facts? Or ways to help them solve multiplication problems while they are in the process of learning the facts? One way is to skip count or repeatedly add the number over and over again. While this is one acceptable strategy, I see many students skip count using their fingers, often starting over numerous times. And if the child miscounts just one number in the sequence, then all of the remaining multiples/products are incorrect. Sometimes the student will write down the sequence in a horizontal row (better than using fingers in my opinion), but again – if they miss one number . . . all the rest of the numbers in their list are wrong.
What I want to show you today (in Part I of my series about multiplication strategies) are ways to relate the multiples/products in recognizable patterns which may facilitate recall and help with committing the facts to memory. Yes, students should also know the following about multiplication – and I will focus on all of these in future articles:
Stay tuned for more blog entries about multiplication!
]]>Since many of you may just now be coming back together with your students in person due to hybrid or virtual teaching models, I thought I’d revise this post I wrote 3 years ago concerning establishment of a classroom community. While you may feel extra pressure to get back into some serious catch-up learning lessons, time spent on creating a genuine classroom community is definitely worth it and should pay off.
Creating a sense of community within your classroom puts emphasis on establishing a climate of mutual respect, collaboration, kindness, a positive atmosphere, and a feeling that each one is a valued member of the class. This is also critical to help you prepare for small group collaborative practices for your reading and math instructional program. See the freebie of fun teamwork activities in the last paragraph!
There are many ways to accomplish this, of course. But I will share my favorites. Before Great Expectations came to SW Oklahoma, I became familiar with an organization called Responsive Classroom (click to link to their website). They are similar to GE, but primarily train teachers in the NE part of the U.S. Like GE, they also focus on a strong link between academic success and social-emotional learning. You can subscribe to their newsletter and order wonderful books via their website. I started with one of their books called “The Morning Meeting Book” (click on title). It promotes ways to create a classroom community by having a daily “Morning Meeting.”
In my classroom, we formed a circle every morning and greeted each other by name in fun ways. See some ideas below in the bulleted section. You might be surprised to know that students often don’t know their classmates names, even after several weeks of school! Knowing and using a child’s name is a sign of respect. Through this circle, we also shared successes and concerns for one another, began discussion topics about how we should behave and respect one another, welcomed new students, made group decisions, and set the tone for the day. Every student was acknowledged and felt valued every day. Students don’t want to disappoint a teacher or classmate they respect, and it almost eliminated the need for time consuming behavior plans. For a great plan to get students in a circle in a timely manner see Activity #22 in the Teamwork Activities linked below (last paragraph)
Name Greetings:
Teamwork Activities:
Through my years of GE training, I added teamwork activities to our classroom routines – especially at the beginning of the year. And then we continued them once a week because caring has to be practiced. We loved “People to People” and “Black Socks” and the “Woo Game.” I am attaching a pdf of 22 Movement, teamwork, energizer activities – I hope you will try some. Many of them require no advance preparation. I feel taking the time to create a caring atmosphere was worth every minute. When students have the opportunity to engage in fun activities together and learn their names and interests, they are more likely to show genuine respect toward one another.
Enjoy your time together! Share your favorite teamwork activity!
]]>Resource – http://illuminations.nctm.org
This is a math resource I absolutely love! It is a product of the National Council for the Teachers of Mathematics (NCTM).
This site includes lesson plans and interactive activities. Search in several ways: by topic, by standard, or by grade level. Need some strategy games? Check out “Calculation Nation” (some of which can be played against other players), and “Brain Teasers.” I have just added this link to my Resources page (on my blog home page). Pass this along to parents for them to use with their children at home!
Many of the lessons connect to exploration projects and literature. The interactive features are outstanding!! These are perfect for the smartboard, on laptops, or tablets. Doing Zoom lessons? Then these are also wonderful for sharing the screen to introduce or review concepts. Once you are on the home screen, click the Interactives box (right side) and then the desired grade level. There are dozens of great applets, but here are a few you might really like. I have linked them for easy reference, so just click on the title and you’ll be there:
Dynamic Paper: Customize graph paper, number lines, spinners, nets, number grids, shapes (to include pattern blocks, color tiles, and attribute blocks), and tessellations. You can also choose inches or cm. These can be customized, saved and printed as jpeg or pdf. I created the spinner shown here from this application.
Five Frame and Ten Frame tools: Geat activities to build number sense using five or ten frames. These may take 1-2 minutes to load.
Cubes: Build a rectangular prism one cube, or row, or layer at a time and then compute the volume or surface area.
Coin Box: Drag and exchange coins. There is also a feature I like (the grid at the bottom right corner), which puts coins in blocks (by 1s for pennies, 5s for nickels, 10s for dimes, and 25s for quarters). This really helps see the value of the coins. Want more info about coin blocks? Once on the Coin Box page, click on the “Related Resources” tab.
Try these for fractions: Fraction Models (which includes decimal and percent equivalencies) and the Fraction Game.
Geometric Solids: Create a shape (either transparent or solid) and swivel it around to see all of the faces, vertices, and edges. It has a cube and pyramid as far as basic 3D shapes are concerned. I wish it had more that 3rd-5th students would encounter.
Here’s a nice multiplication game: Product Game Two players (or a player vs. the computer) choose factors from the bottom bar to create products shown on the game board grid to get 4 in a row (and try to block your opponent from getting 4 in a row). Be sure to see the directions included.
Some of the interactives require an NCTM subscription. The ones I have listed above should be okay to access without membership. I have subscribed for years and just paid $94 for this coming year. Well worth it if you plan on using their site extensively. This subscription also entitles you to a print and and online journal, blog capabilities, and more.
Enjoy these and so many more!!! Let us know if there are others you recommend. I’ll highlight more on my next post.
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This post contains some of my favorite sight word activities and resources to help your students practice those sight words and high frequency words. If you haven’t read part 1 (Sight word instructional tips), be sure to do that as it contains information about research based teaching strategies. These all focus on ways for the child to actually read / say the word and use in a sentence, not merely matching, copying, or building the word. Here goes!!
Notice that in all of these methods, the students need to read and say the word (and perhaps use it in a sentence). Be sure your sight word activities reinforce these. Activities in which students just merely match, stamp, copy, write in different colors, recreate with letter tiles, etc. do very little to help them really know the word. Have FUN!!!
What other sight word activities have you tried that you’d like to share? Take care, friends!
]]>Sight words are those which students can identify automatically without the need to decode. They often do not follow phonics “rules.” Examples: who, all, you, of. They may include some high frequency words (HFW). High frequency words are those which occur most often in reading and writing. By learning 100 of the HFW, a beginning reader can access about 50% of text. According to Fry, these 13 words account for 25% of words in print: a, and, for, he, is, in, it, of, that, the, to, was, you.
When are students ready to learn sight words? According to the experts from Words Their Way (Bear, Invernizzi, Templeton), student need to have a more fully developed concept of word. Concept of Word is the ability to track a memorized text without getting off track, even on a 2-syllable word. In other words, does the child have a one-to-one correspondence with words? When tracking, does their finger stay under a 2-syllable word until it is finished, or are they moving from word-to-word based on the syllable sounds they hear? In the sentence shown, does a student move their finger to the next word after saying ap- or do they stay on the whole word apple before moving on? Students in the early Letter-Name Stage (ages 4-6) start to understand this concept. It becomes more fully developed mid to later stages of Letter Names (ages 5-8).
Students with a basic concept of word are able to acquire a few words from familiar stories and text they have “read” several times or memorized. Students with a full concept of word can finger point read accurately and can correct themselves if they get off track. They can find words in text. Therefore, many sight words are acquired after several rereadings of familiar text.
Instructional Strategies KG-2nd Grade
1. To help children gain concept of word:
2. Explicit Instruction: Dedicated time each day for sight word work
3. Flash Card Practice (Research based method) with no more than 10 words:
4. Word Wall Suggestions:
What are your thoughts on sight word? We would love to hear success stories from you!
P.S. This was a revised article on sight words from one I published earlier. Stay tuned for more sight word strategies and activities.
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Last week I reposted my blog regarding use of number lines to assist students with number sense and rounding. Check it out for free activities and rounding charts. Today I am sharing some more rounding activities I developed and used with students to practice (with either whole numbers or decimals). These activities can be varied to suit your students’ needs.
These grid templates are to use the activities with 2-4 students (or teacher vs. student if working one-on-one online). I developed 3 different grid sizes (4 x 4, 5 x 5, and 6 x 6). You will also need something to generate numbers for each set of players:
The objective of the game is for a player to capture 4, 5, or 6 squares in a row (horizontally, vertically, diagonally). You decide based on the size of the grid and the skill level of the players how many captured squares are needed.
The teacher can write in possible answers on the grid and laminate for continued use (samples below). Then students can use a game piece (flat stones, two-color counters, etc.) or different color dry erase marker to mark their square.
Here are some different variations of the game (whole number rounding to nearest 10, 100, 1000 and decimal rounding to the nearest tenth or hundredth).
Rounding to the nearest ten: You can use the blank grid to write in your own numbers randomly. Consider which number generated options you are using. If you use 1-6 dice, the biggest number on the board has to be 70 and remember there’s only 2 ways to achieve 70 (by rolling a 6 and 5 or a 6 and 6). If you use 1-9 dice or number cards, then you can place numbers from 10-100 on the board. This gives a few more options and a chance to round higher numbers.
Rounding to the nearest hundred:
Rounding to the nearest thousand:
Rounding to the nearest tenth:
Rounding to the nearest hundredth:
Other tips for playing:
Let me know if you try these! Pass along any extra tips you have.
Also, a reminder to contact me if you would like personalized professional development over any reading or math strategy. I can do a Zoom session with you or a group of teachers. Flexible payment options. Also, check out my link on the side bar for Varsity Tutors regarding the opportunity for you to tutor students online or in person (and earn a bonus for using my name).
Take care, stay safe!!!
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