Dec. 10 Session
Focus: Building conceptual understanding using tools, models and strategies.
Grade 3
Slide Deck - Multiplication of Larger Factors
Math Learning Center Apps - Partial Product Finder (link to Beta version - shows partial products in different colors)
Multiplication in Purposeful Pathways - Lite Version (Not for Distribution)
Summary of Session: This session focused on multiplying factors between 6 to 12. We looked at a progression from concrete items (base-10 blocks, Cuisenaire Rods) placed in a rectangular array to an open array. We discussed how we could “chunk” or partition the factors. For example, instead of using 5 dots or counters to represent 5 we could use a line or the yellow C-Rod to represent that amount. We also discussed the need for students to flexible in interpreting and decomposing factors and analyzing expressions.
Next Steps: Teachers should think about the progression (C-R-A) that is needed to support students deeply understanding how they can decompose and break apart (partition) factors to create equivalent expressions.
Grade 1
Slide Deck - Addition/Subtraction , 10 More, 10 Less
Summary of Session: This session focused adding and subtracting and also determining 10 lesson or 10 less of a double-digit number. We used the number bead string, money ($10, $1), place value mat, two colored counters as place value discs. We also, looked at how to support students in making the connection between the number bead string and the number line. Specifically, we focused on building additive thinking as opposed to using a counting all or counting on strategies. We discussed how to help students become flexible with the number bead string. For example, if solving 39 - 19, one might model removing 20, then adding one back on to the difference because too many were taken off.
Additionally, we focused on using a ten-frame to get students to visualize using the place value chart.
Next Steps: Teachers should build, as needed, and use number bead strings in their classrooms consistently. Teachers need to use large place value mats for students to structure their manipulatives on. Teachers need to work on developing additive thinking by using decomposition of numbers and compensation strategies.
Grade 5
Multiplication of Fractions String (no addressed in session)
Video: 1/4 x 2.3 Using an Area Model
Video: 2 x 3/5 Using Snap Cubes
Illustrative Mathematics Task - To Multiply or Not to Multiply
Grade 5 Division of Fractions String (for session)
Summary of Session: This session focused dividing fractions and decimal amounts. We also addressed how to introduce volume as related to rectangular prisms. For the work with the division of fractions (i.e., unit fractions and whole numbers) we complete a problem string that focused on building conceptual understanding. We used Cuisenaire Rods to model the situations. We focused heavily on interpreting the quotient and connecting that to models that were created.
This session also focused on the division of decimals (i.e., when the divisors had numbers tenths or hundredths places) as the teaches noted that the topic was on the horizon. We used a ten-frame model and also equivalent fractions strategy.
We closed out the session by focusing on introducing volume. I took the teachers through the experience of building a rectangular prism. This process is written up in the Grade 5 Envisions unit planning document.
Next Steps: Teachers should practice using the C-Rods for division and also the ten-frame strategy. Additionally, teachers need to review the unit write-up on volume.
Grade 4
Slide Deck - Multiplying and Dividing Using a Number Bead String
Grade 4 Number Bead String w/ Dr. Nicki
Summary of Session: This session focused mainly on the division of whole numbers. Teachers noted that even though they had completed this unit or were almost finished student were struggling with using the open array/area model to solve these problems. I shared a Place Value/Equal Groupings strategy with them. This is strategy used in EngageNY. We modeled this strategy with a student. I also modeled the use of the ratio table.
We also discussed how to support students in solving multi-step word problems. I modeled using Number, Numbers, Numbers and making a mathematical sketch/visualization by unpacking a problem with a student.
Next Steps: Teachers should revisit the strategies used to divide by thinking about what make conceptual sense to students and how can they model these ideas. Teachers should work to used the strategies modeled. Additionally, I recommended giving students 1 sentence from a multi-step word problem per day for HW. Students should visualize out the problem and determine if they can figure out anything mathematically from the visual. Each night adding on to the problem.
Kinder
Slide Deck - Understanding Teen Numbers
Ten-Frame Cards (K - 1)
Math Learning Center Apps - Number Frames
Subitizing with Teen Numbers in a Ten Frame
From Scholastic:
Your child will begin to develop a deeper sense of these numbers in kindergarten and first grade, but you can encourage your child's ability to identify, read, and write teen numbers at home with these five activities:
1. Rote Counting: Practice counting out loud from 10 – 20 with your child. Take turns saying each number and correct her if she makes any mistakes. Help her say each number correctly. The more she practices, the better she will become at saying the numbers!
2. Teen Number Cards: Write index cards with the teen numbers. Put one number on each index card. You can use these cards in so many different ways:
Mix the cards up and have your child put them in order from least to greatest.
Use them as flashcards to identify each teen number.
Play the game Teen War – just like regular Math War, but with teen numbers only
3. Three-Four-Handed Teens: Play this game to show your child that teen numbers are made up of 1 ten and some ones. Hold up all 10 of your fingers. Then, have your child hold up some fingers as well. Together, all these fingers represent a teen number. For instance, if your child is holding up three fingers, and you're holding up all your fingers, then the number is 13.
4. Sand Tray Teens: Use a paper plate or a tray and some sand to have your child write different teen numbers as you say them aloud. You can also do this with shaving cream or whip cream! (If you're somewhere warm, try these 10 ways to practice math at the beach.)
5. Bundle Teens. Have your child use a rubber band to bundle together 10 straws. That represents 1 ten. He can use Cheerios to represent the ones. So one bundle of 10 and seven Cheerios represents 17. For an extra challenge, your child can write the equation to match the teen number: 10 + 7 = 17.
Video: Number Bonds 11 - 19 - SHOW. Entertaining and conceptually correct.
Summary of Session: This session focused recognizing, saying and understanding teen numbers. We discussed several activities that teachers could engage students in help support their development. Primarily we noted (and modele) the used on subitizing sets and a “how many more game”. The main focus was getting students to recognize the 10 that was nested in the teen numbers. We also discussed using number bead rings made with different combinations of teen numbers to get students seeing and talking about teen numbers. We discussed sacrificing some Unifix Cubes by glueing them together to make a ten. Base-10 blocks should not be used. We made a distinction between appropriate and inappropriate videos and songs to teach this topic by emphasizing the videos and songs that focused on the concept rather than rote memorization.
Next Steps: Teachers should create and use the number bead strings. Use the subitizing cards consistently. Play the ‘how many more’ game with students.