https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy Read Children’s Mathematics pages 110 - 116 to learn more about invented algorithms. Add an important idea from the reading that you want to take with you into next school year and why. en-us 2020-06-15 00:24:18 UTC 2026-01-24 17:03:35 UTC hello@padlet.com https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637764802 Students need to be able to see that 42 is 4 tens 2 ones, but also that it's 3 tens and 12 ones. They need to know that there is more than one way to see units in numbers. Showing their work gives us insight to their thinking.]]> 2020-06-23 17:35:43 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637764802 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637765100 Children use their foundational knowledge of breaking up 10's to progress through strategies and continue into making their invented algorithms.  It is important that they have the basics of working with directing modeling, breaking down 10's etc. to be able to grow.]]> 2020-06-23 17:36:02 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637765100 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637766532 Doubling Strategies are common when students are inventing multiplication and division algorithms]]> 2020-06-23 17:37:33 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637766532 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637766668 "Children need to be flexible in understanding that tens can be broken apart"]]> 2020-06-23 17:37:41 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637766668 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637767926 Children use modeling with tens, counting strategies, and invented algorithms to solve for multiplication and division problems. I think this is important because it shows the development of student thinking when applied to multi-digit multiplication and division. We need to understand student thinking progression, so that we can continue to challenge their thinking.]]> 2020-06-23 17:38:49 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637767926 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637768722 I realized while reading that how truly important it is to give students the time and space to struggle and solve these problems. Additionally, it drove home that it is so important to listen to them explain their thinking. Those students came to the solutions in different ways, but their solutions were accurate. ]]> 2020-06-23 17:39:36 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637768722 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637769519 students can use direct modeling to organize ideas into groups with more than ten objects in each group. They can break tens apart or trade tens for ones to form groups. This will challenge their knowledge of base-ten concepts.]]> 2020-06-23 17:40:20 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637769519 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637769734 children see numbers and groupings differently just as we did with the choral counting patterns. students will often rely on the number patterns and groupings they feel most confident with]]> 2020-06-23 17:40:33 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637769734 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637770410 Decompose numbers to make it easier for them]]> 2020-06-23 17:41:16 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637770410 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637770734 Being able to decompose numbers aids in solving multiplication/division problems]]> 2020-06-23 17:41:34 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637770734 mxa1591 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637771113 Students need to have a strong base ten understanding to solve multiplication and division problems.  They need to be able to break numbers apart and understand that numbers can be represented in different ways.  For example, 53 can be represented as 50+3 but also as 40+13.  ]]> 2020-06-23 17:41:55 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637771113 chelseanschneider https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637771541 Students start exploring division with Direct Modeling strategies.  They use individual counter with smaller numbers, but when the numbers get larger they tend to use base ten blocks.  In order to use the base ten blocks to help them they need to know that 1 ten is the same as 10 ones and not see the ten as a 1.  Students need to have place value understanding and grouping ideas.  1 ten is 1 of this group (of tens) but also 10 of this group (of ones).]]> 2020-06-23 17:42:20 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637771541 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637773207 Students need to have a strong knowledge of base ten to be challenged.]]> 2020-06-23 17:43:46 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637773207 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774254 The development of multiplication and division strategies are just like addition and subtraction strategies with some "added twists". Therefore my students must have a strong add/sub foundation to move into mult/div with multi digits numbers in fourth grade. I think those holes or gaps that some students have lead to frustration in the upper grades. ]]> 2020-06-23 17:44:46 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774254 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774388 Measurement division and partitive division will push students to do different strategies.]]> 2020-06-23 17:44:54 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774388 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774757 Children need to be flexible in understanding that tens can be broken apart.]]> 2020-06-23 17:45:14 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637774757 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637775185 Students were solving the problems by what made sense to them. There was a lot of decomposing.]]> 2020-06-23 17:45:37 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637775185 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637775374 I do see that there are similar strategies for multiplication/division as for addition/subtraction.  I've also found that my students do need to become more comfortable with breaking tens apart or seeing numbers differently]]> 2020-06-23 17:45:48 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637775374 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637776001 it is extremely important for students to be exposed to the representation of numbers/strategies at an early age... this will lead to really understanding and being able to solve problems. this leads into remembering that all students come knowing something and it is important to challenge their thinking. ]]> 2020-06-23 17:46:21 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637776001 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637777157 Direct modeling with 10's can be broken into the following subcategories:  multiplication, measurement division and partitive division.  Similarly, adding strategies for multiplication and division problems can be broken down into the same subcategories:  multiplication, measurement division and partitive division.]]> 2020-06-23 17:47:20 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637777157 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637777383 Invented algorithym provides students different ways to solve for answers using their math background knowledge and skills ]]> 2020-06-23 17:47:36 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637777383 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637778787 Children should know that they can break up tens or add to them in order to solve problems. Ex, adding groups of 12's]]> 2020-06-23 17:48:48 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637778787 https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637778881 Solid understanding of numbers (Base Ten) is key to success.  ]]> 2020-06-23 17:48:54 UTC https://padlet.com/jenniferlawyer31/vbqb7drrcg8iymfy/wish/637778881