Understanding Multiplication

Multiplication – The art of increasing gold or silver by magic, — attributed formerly to the alchemists

Younger students need to have the magic of multiplication broken into little pieces of reality! I think the best starting point is showing that multiplication is repeated addition. If I add two 6 times, I have multiplied two by six. It actually takes saying that word “times” quite a few times before everyone catches on to the idea that we also say “times” when we multiply.

Of course, by showing I actually mean showing. Students need manipulatives in their hands. If they are edible all the better! 15 candies in one roll of Smarties. If everyone on your team has one roll, how many candies does your team have? We make arrays out of cubes, then we draw the arrays with circles or Xs. Sometimes we get fancier and do hearts or stars, but it is important to be able to draw quick arrays to see that they can be useful in problem solving when you get stuck on a problem.

Important vocabulary surrounds multiplication. I love to have them figure out the analogies such as, plus: addition :: times: multiplication and addend: factor :: sum: product. Later on, we realize addition: multiplication:: subtraction : division. Besides factor and product, there’s other important multiplication vocabulary or key words. Each and every usually mean to multiply. I tell my class to watch out for same number and equal groups, because those words change each and every to division, every time. Kids need to know the words twice, double, triple, and quadruple means to multiple. Then we have total and altogether, which they already recognize as addition words. These words provide a chance to reinforce the idea that multiplication is actually just FAST addition.

When learning our facts, we use many strategies: fact families, number lines, repeated addition, arrays, groups, sets, music, movement, discussion, breaking apart numbers.

I made this poster for my kids to discuss all the ways they know to multiply. I have attached the pdf for you.

Understanding Multiplication

Understanding Multiplication

I have made an Understanding Multiplication Scavenger Hunt. Here is a page from it:

Understanding Multiplication Scavenger Hunt.

It also explores multiplication as repeated addition, arrays, skip counting, and fact families.

I hope that you find some magic in multiplication in your classroom!




Compare and Contrast Matrix

Morpheus: There is a difference between knowing the path and walking the path. The Matrix 1999

Wow, I just found a new graphic organizer. Or maybe I knew about it before, but I didn’t understand it well enough to realize its potential. This matrix should be great for vocabulary development. It will help students make connections, organize their thinking, and use their new vocabulary appropriately.

Here is an example from a new product I am currently creating. Students will grow in understanding about the similarities and differences among these various grasslands as they research information to complete the matrix. The new words prairie, savanna,  steppes, and pampas will become more familiar and better understood. (My newest product “Grassland Animals Scavenger Hunt” could be used with this matrix.)

Compare and Contrast matrix

Another matrix that could be used with many grade levels compares the seasons. From kindergarten upwards students could add information at their own level of understanding.

Comparison Matrix Seasons

Comparison Matrix Seasons

I am excited to explore further uses of this matrix, especially anything that could be vocabulary specific. Does anyone have any ideas?


Always, Sometimes, Never

Thinking: the talking of the soul with itself.


We need our students to think. For many they are trained to put answers on a line. If there is no line, there must be no question. The directions and information above the lines can easily be ignored. The whole exercise, for those who can get it all right without reading and for those who can get is mostly wrong without reading, is a waste of time. This is one example of why I feel so strongly about conversation as a learning tool. This same exercise, shared with a partner with the expectation that answers need to be defended, requires thinking. The students can learn more about what they know and/or what they don’t know.

Graphic organizers are a great way to have students think. I have created a formative assessment called “Know or No”. I give students a list of words on a current topic for them to rate their knowledge. They can then line up in a continuum showing their understanding. This line is then folded and students are paired to talk about the word(s). This formative assessment can used before, during, and after instruction. Students, of course, should grow in their knowledge, but they should also be aware of that growth.

Know or No

Another great graphic organizer to use is a tree chart. Students fill in each section with whatever information they can think of. For example; thinking – always…  helps, thinking – sometimes…  is hard, thinking – never…  costs money. I have seen many of these on TPT and have made many of my own. Here is a new one on Thinking for today’s blog. The others are examples of ones I have used with my class.

Thinking Graphic Organizer Find more at my blog.Thinking

February Tree Map 1



I hope you give your students many opportunities to think and talk every day!


Building Comprehension

We have been working hard to help our students make use of the comprehension tools available within sentences and paragraphs.

Some sentences give examples:

The farm implements, plow, shovel, and spade, had been used so often for planting, that they need replaced.

Others give an explanation:

Our teacher seemed infallible because she always knew the answers.

Many sentences offer synonyms or antonyms:

Penny was mortified, or shamed, by her poor bike riding skills.

A comparison is another structure to be watched for:

Some people are perplexed by puzzles, while others figure them out quickly.

Additionally, sentences can provide information that contrasts:

Something seemed wrong with David today; he made only cursory effort on his schoolwork, unlike his usual careful work.

Clues for Context Clues are sparkling gems to help a struggling reader!

I use this product with my struggling readers. The cards are reminders to look for help in comprehending meaning. As they are reading if they use one of the clue cards, they get to put in their “gem collection”. This complete lesson is available at my store on Teachers Pay Teachers and it is free!

I found a new idea for a lesson idea today. It uses a sentence with just a letter clue for a word:

Mary loves to eat b________ ?????????

Students brainstorm possible words to complete the sentence: bread, broccoli, brownies, bananas, burgers, etc. Then the sentence is repeat with the remainder shown:

Mary loves to eat b________, although her mom doesn’t want her to have too many sweets.

Another example:

Lisa has a new j__________ ???????

jump-rope, jersey, jacket, etc.

Lisa has a new j__________ for writing her thoughts about each day.

I am excited to use this new idea with my students. It will make clear to them the need to read on not only to help with unknown words, but also to add to the context of the word.

Do you have any ideas for increasing comprehension?



Picture It!

“Of all of our inventions for mass communication, pictures still speak the most universally understood language.”
― Walt Disney Company

I am planning a new set of products that I call “Picture It!” Pictures are so important for vocabulary development. I am planning to make posters for multiple meaning words and also for homophones. Check out my sample and let me know if  you think this idea would be helpful.

Picture It! Sample

Infer Meaning

Words mean more than what is set down on paper. It takes the human voice to infuse them with deeper meaning.
Maya Angelou

Once again Ms. Angelou states beautifully a truth. This time it is about comprehension. Here is the difficulty for children; once they can read the words, they must learn to read beyond, beneath, and between the words. We want children to be able to discern the author’s true purpose and meaning. We must help them learn to infer meaning. This inference can begin with understanding individual words and move on to finding the universal theme set forth in the text.

The Comprehension Toolkit lessons by Stephanie Harvey and Anne Goudvis provide several fine lessons for this in their 4th  book of the set, Infer Meaning. Its biggest lesson is Background Knowledge + Text Clues = Inference. (BK + TC = I). They give the students strategies for learning to do this important work. I love how the first lesson focuses on vocabulary. We refer to this lesson often in my classroom.

Infer the Meaning of Unfamiliar Words


Book 4 includes 6 lessons. All of them bring important skills to the students’ attention.

1. Infer the Meaning of Unfamiliar Words

2.Infer with Text Clues

3. Tackle the meaning of language

4. Crack Open Features: Infer the Meaning of Subheads and Titles

5. Read with a Question in Mind

6. Wrap Your Mind around the Big Idea


My poster set includes a poster for each lesson (10 – 15) and a wrap-up poster. All 7 posters are free here at my Teacher Pays Teacher store.

Read with a Question in Mind


Another strategy we use often is to read with a question in mind. Students need to look through the text features to pique their interest. They may bring some background knowledge to the text. They should stop first to think what they already know and ask a question of the text.

Wrap Your Mind around the Big Idea


One of the most moving lessons is on theme. It uses the text Cheyenne Again by Eve Bunting. The lesson helps the students feel more deeply the meaning of the text and helps them gain a more profound understanding.

These are valuable lessons. I hope you can use them.


Ask Questions

Judge a man by his questions rather than his answers.

The third book of The Comprehension Toolkit by Stephanie Harvey and Anne Goudvis focuses on asking questions. This is such an important way to learn and to build vocabulary. I have a little guy in my class who is so interested in every topic we touch on in class (science, social studies, etc.), that he gets non-fiction books on the topics from the library each week. Then he shares with me all of his new learning. Our conversations help him clarify what he is reading and to build his understanding. These Toolkit lessons helped him and his less interested classmates notice and respond when questions float through their minds while reading. It suggests ways to help students stop and think about how what they are learning fits with what they already know. Sometimes students need to realize that what they “know” isn’t actually so and they need to give up that thinking and update it with the new information they are discovering. Of course, this can also be true for adults!

This set of 4 posters for lessons 7 – 9 is available free at my Teacher Pays Teacher store. The set includes a strategies wrap up page.




It is through asking questions that we learn more about what interests us. Teachers ask questions of themselves and their colleagues about how to best reach and teach each child. We ask question of the child, too, to help access and assess what learning is taking place.

Questioning is an important skill, it needs to be taught.