‘Naked’ Numbers But Not Before Discovering Patterns
The common core standards for first grade state that students must become fluent with adding and subtracting tens. To promote fluency, students need to discover patterns and how they change numbers. Only when students have examined patterns and become comfortable with them should they be given timed “naked number” problems to assess and improve their efficiency in recalling the patterns. Finding the answer to a “naked numbers” problem needs to be merely a by product of knowing the pattern.
When trying to figure out how to teach fluency with adding and subtracting multiples of ten to first graders, I struggled to find resources to do this. Because of the lack of resources, I developed these sheets for next week to lead students and their teachers into guiding discussions about patterns on the hundreds chart. They are simplistic activity sheets but necessary. I will be trying them out this week. I am providing a link to them below. If you would like to try out one of the lesson sheets, the preview file will give you a sample for free at TPT.
Discovering Patterns
Naked Numbers
What’s the Difference in Reasoning Abstractly and Quantitatively?
I recently attended a fabulous professional development which discussed the Eight Mathematical Practices for Common Core Standards. One of these practices is having students reason abstractly and quantitatively. I have always required students to label the answers to their equations when supporting an open ended question, but I didn’t realize the depth of what I was requiring. Consider this. Which is more– 5 or 8? We would all agree that 5<8. This is an example of reasoning abstractly. Now, consider this. Which is more–5 quarters or 8 pennies? We would all agree that 5 quarters > than 8 pennies. This is an example of reasoning quantitatively. When students answer a word problem by labeling each component of their equation, they are reasoning quantitatively. When students merely solve a “naked numbers” problem without labeling the quantities with which they are reasoning , then they are reasoning abstractly. When students are reasoning with specific quantities, then the foundation being built is stronger for them to then build abstractly. Just think. The math textbooks are backwards. Quantitative reasoning problems follow abstract reasoning, however students understanding is built first with quantitative problems and should be followed with abstract understanding.
Have A Few Extra Minutes? Play SQUAT!
To practice math facts, spelling words, or any other quick answer type learning, you can play Squat. To play Squat, two students from two different teams approach the board. The teacher calls out a fact or a spelling word. The two students at the board race to answer the question correctly and then they squat when they think they have the correct answer. If they are correct they earn a point for their team.
When I have played this, I usually split my class into two teams. Different students on the teams take turns to be at the board to earn their team points. Team points can be taken away from students who aren’t waiting quietly or who blurt out an answer when it isn’t their turn. Students love this game and will beg to play it after you have played once. If you have some extra time (heh, heh, who has that?!) during a spot in your day, this is a fun way to reinforce skills or fill time.
How Can Your Students Easily Generate Writing Topics?
I just spent a day in a writing workshop. Our presenter discussed Ralf Fletcher’s new book Marshfield Dreams: When I Was a Kid about his childhood memories. He described how Fletcher wrote different short stories about his childhood in this book, which would be great for mentoring students in their own writing. Since the pieces are short in Fletcher’s book, they would mirror the length of a short story that a child may write. What I especially liked about this workshop is when the presenter had us to draw a map of our childhood homes and neighborhoods with all the places that were important to us. First, the presenter showed us a map copy of Ralf Fletcher’s childhood neighborhood home which is in Marshfield Dreams so that we could see an example (great idea to model for kids as well). Then the presenter had us to put an F for fear next to a place that we thought was scary. We put an S next to a place that was secret. We put an L next to a place where we learned something or did something for the first time and so on. Then the presenter had us write a short piece using one of the places on our childhood map. I thought this was a great way to lead us into writing especially because kids like to draw pictures.
How Can You Use Your Hands as Multiplication Manipulatives?
Another math coach related to me today the story of how a student she taught had named fingers sections as something that comes in groups of threes. She took this concept and helped students use this to develop multiplication strategies to learn their threes multiplication tables. Fours multiplication tables can be learned as well if students include counting the top part of their palm. See the pictures below for more clarification.
Update September 2017: Due to one of the comments below, I made a video describing how this works with the 3s multiplication facts. Click here for the video.
How Can You Teach Common Core Standards with Number Bonds
Well, I have let my blogging activity slide as I have been trying to give more attention to developing my materials for Teachers Pay Teachers. My sales have done better this year than ever–I suppose due to the work I put in on some lesson activities from this summer. I have TONS of math activities I could sell that I have made over the years for all grade levels however to sell them I want them to be perfect so it takes me a while to make them look as good as I want them to look.
I hope you will be pleased with the most recent activity I posted today. First graders at my school are working on becoming fluent with their number bonds (sums) up to 10. They have been building number bonds with two colors of snap cubes and then coloring a model of what they built. They have been using the printables I just uploaded to TPT. I also developed a Smart Board lesson to match the number bonds printables since one of the first grade teachers reported at our last planning meeting that the students were confused about how to write an equation. The Smart Board lesson allows the teacher to model the bonds of ten with snap cube virtual manipulatives and move the symbols, and numbers around to build an equation. See below. Click on the picture to read more.
Help Strugglers with Rounding by Using This…
To alleviate misconceptions that crop up when teaching rounding, use a number line that counts by the number you are rounding to. For example, if you are rounding to the nearest 10, then have a number line that counts by 10’s. If the number is 34, students will be able to find that the 34 will fall between 30 and 40.
0 10 20 30 40 50 60 70 80 90 100
Often students will assume a number like this rounds down to 20 because they see that the 2 in 20 is before 3 in 30 so it only stands to reason to students that 20 is the number 34 would round down to. When students are able to see a number line, they are able to actually visualize which ten the number is closest to. For a free number line that counts by ten click here.
How Can You Make Finding Author’s Purpose Easy for Students
I recently attended a Maria Banks training, and she suggested ways to help students identify the author’s purpose for writing a passage. Below is the list of clues that we developed to help students identify a passage. I am sure there are more that we didn’t think of that can be added. To help students identify these, create a chart in class with the students, and make an anchor chart of author’s purpose clues.
Download Author’s Purpose chart here.
How Can You Make Almost Any Math Lesson Deeper?
I am currently at a regional NCTM math conference on algebra readiness. I am going to share one of the things I learned at the conference. Use conjectures while teaching math to make the task deeper. For example, when teaching the commutative property, have students find at least three pairs of equations with factors that have switched places and allow students to draw a conclusion.
3×4 = 12
4×3=12
7×6 =42
6×7=42
4×9=36
9×4 =36
Ask students what they notice about the factors that have switched places. Hopefully, students will say that the products are the same when the factors have switched places. Ask students if this is always true. Allow students to experiment with their conjecture by using other examples. Ask other students if they can prove this wrong. When all minds are settled on the conjecture and agree, then reveal the name of their conjecture as the commutative property. Teaching with this method of discussing conjectures allows students to take ownership of their learning and be involved in the process of discovering mathematical concepts. Less reteaching will occur and your teaching will be closely aligned with Common Core Standards.
