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young children can solve a variety of multiplication and division problems, not only addition and subtraction.

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young children can solve a variety of multiplication and division problems, not only addition and subtraction.

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Allow students the opportunity to solve word problems using different strategies/approaches and allow them to share their thinking with others. Doing this allows them to further their thinking and visualize new concepts. 

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Allow students the opportunity to solve word problems using different strategies/approaches and allow them to share their thinking with others. Doing this allows them to further their thinking and visualize new concepts. 

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"In order to use base-ten materials to solve most multi-digit division problems, children need to be flexible in understanding that tens can be broken apart." We need to be very purposeful when choosing numbers when we present problems so that students can develop their understanding of place value.

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"...children need to be flexible in understanding that tens can be broken apart. For example, if children do not understand that 42 can be represented with 3 tens and 12 ones as well as with 4 tens and 2 ones, they will have difficulty using base-ten materials to solve a Partitive Division problem..."  My goal is to move my students to more efficient strategies for division, focusing on decomposing numbers in multiple ways  early in the school year may help them.   

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"...children need to be flexible in understanding that tens can be broken apart. For example, if children do not understand that 42 can be represented with 3 tens and 12 ones as well as with 4 tens and 2 ones, they will have difficulty using base-ten materials to solve a Partitive Division problem..."  My goal is to move my students to more efficient strategies for division, focusing on decomposing numbers in multiple ways  early in the school year may help them.   

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Students need ample opportunities to grapple with math and solve varied types of problems so they can organically arrive to and understand different strategies.

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Students need ample opportunities to grapple with math and solve varied types of problems so they can organically arrive to and understand different strategies.

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I have also felt that young students seem to understand division (partitions) and multiplication when they are younger. They understand sharing equally or distributing equally among classmates.

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I have also felt that young students seem to understand division (partitions) and multiplication when they are younger. They understand sharing equally or distributing equally among classmates.

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Understanding place value is important for students to understand even if using manipulatives. It is a necessary skill for all four operations so they are able to understand the difference between the ones, tens, and hundreds etc.

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Understanding place value is important for students to understand even if using manipulatives. It is a necessary skill for all four operations so they are able to understand the difference between the ones, tens, and hundreds etc.

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The base 10 for students becomes automatic and helps the students visualize the concept of multiplication and division.  Allowing the student to develop their own strategies helps them to internalize and visualize new concepts.

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The base 10 for students becomes automatic and helps the students visualize the concept of multiplication and division.  Allowing the student to develop their own strategies helps them to internalize and visualize new concepts.

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Children should be given many opportunities to solve word problems and write equations to represent their solutions  - this gives children the opportunity to learn to read a word problem and to write an equation to represent the problem before they solve.

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Children should be given many opportunities to solve word problems and write equations to represent their solutions  - this gives children the opportunity to learn to read a word problem and to write an equation to represent the problem before they solve.

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Students use addition, subtraction, and multiplication in a variety of combinations to solve division problems. We need to be ready to see all these and honor all these and not get stuck on teaching a strategy a textbook tells us to.

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Children can model different strategies to help them figure out multiplication and division.  Using manipulatives or drawing pictures helps students make connections.

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I used a lot of CGI problems during remote learning and the kids were very successful with them

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Direct modeling and using stories students can relate to allow them to show us that they can multiply and divide because they can group things together and partition things to share.

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Direct modeling and using stories students can relate to allow them to show us that they can multiply and divide because they can group things together and partition things to share.

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Exposure to these problems are crucial

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We should expose children with problems that involve groupings and partitioning.

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We should expose children with problems that involve groupings and partitioning.

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One thing that stood out to me was the beginning of the multiplication/division section where it said that for students to be able to direct model  with tens and ones for division they have to understand that 42 can be broken down into 4 tens and 2 ones and 3 tens and 12 ones, which is important when getting students to start using those direct modeling strategies with tens in division.

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A strong understanding in place value, how to break down tens into one and others is key to students creativity in math.

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A strong understanding in place value, how to break down tens into one and others is key to students creativity in math.

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Invented algorithms is a way in which students demonstrate their knowledge of number sense. It is how students find strategies to solve problems.
Standard algorithms limit students because of the rules and procedures that are involved.

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Many problems can be solved straightforwardly using one operation, but the article seems to highlight that students will often used different strategies and break down multiplication or division problems to get their answers. Which means, students will have different approaches when it comes to solving problems.

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Many problems can be solved straightforwardly using one operation, but the article seems to highlight that students will often used different strategies and break down multiplication or division problems to get their answers. Which means, students will have different approaches when it comes to solving problems.

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Direct modeling w/ base ten is foundational for multiplication and even division. Through this skill, students are able to decompose numbers and multiply/divide with larger digits. One example used was that if a student understands that 42 is the same is 4 tens and 2 ones BUT ALSO 3 tens and 12 ones. When a student understands this, they are able to manipulate/decompose numbers confidently

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I often use the direct modeling with students. They on the other hand usually respond by either using the measurement or partitive strategies. I was not aware of these terminologies, but I do see them in may classroom.

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I often use the direct modeling with students. They on the other hand usually respond by either using the measurement or partitive strategies. I was not aware of these terminologies, but I do see them in may classroom.

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I took with me the idea that children can use multiple ways to solve a problem based on their understanding of the base ten model. This can initially be easier to some students than others, but once they talk amongst themselves, they can learn from one another.

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Students who use Base-Ten blocks to solve word problems often count by ones. 

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Students who use Base-Ten blocks to solve word problems often count by ones. 

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I attended a math PD focused on fractions. My math coordinator suggested I explored it with my kinder kiddos. Through this reading I’ve learned that I was working on partitive division number stories with kindergarteners and they rocked!

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Children begin multiplication and division by using direct modeling because it makes the most sense. As their thinking develops they can utilize alternative strategies to solve. Also, they can see the difference between measurement and partitive division.

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Children begin multiplication and division by using direct modeling because it makes the most sense. As their thinking develops they can utilize alternative strategies to solve. Also, they can see the difference between measurement and partitive division.

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Gordon

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A solid knowledge of using Base Ten Materials is helpful for children to figure out multiplication and division problems. I will be utilizing these manipulative items more in class for students to practice with.

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Children at a very young age are very capable of different types of math. Their thought processes need to be trusted

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Children at a very young age are very capable of different types of math. Their thought processes need to be trusted

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"Experiences solving multiplication and division in K and 1st grade can provide a foundation for understanding multiplication, division, and base-ten concepts in later grades."

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"Experiences solving multiplication and division in K and 1st grade can provide a foundation for understanding multiplication, division, and base-ten concepts in later grades."

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Students need experiences in grouping objects and partitive division to become adept at the idea of multiplication in higher grades. This exposure and grappling in lower grades provides the tools they need to better understand in upper grades.

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Exposing young children to multiplication and division problems will deepen their understanding of addition and subtraction.

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Students need to comfortable and flexible in understanding that tens may need to be broken apart.  "If children do no understand that 42 can be represented with 3 tens and 12 ones as well as with 4 tens and 2 ones, they will have difficulty..solving a partitive division problem."

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Students need to comfortable and flexible in understanding that tens may need to be broken apart.  "If children do no understand that 42 can be represented with 3 tens and 12 ones as well as with 4 tens and 2 ones, they will have difficulty..solving a partitive division problem."

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Young children can in fact solve multiplication and division problems by using direct modeling. This is sometimes even easier for them than addition and subtraction at first. I want to think more about how and when I will introduce my students to these types of problems within the scope of the year.

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provide opportunities fo young children to skip count

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I will expose student to measurement division and partitive division. Understanding that when we are doing measurement division we will count the number go groups. When we are doing partitive division, we are counting the objects in each group.

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I will expose student to measurement division and partitive division. Understanding that when we are doing measurement division we will count the number go groups. When we are doing partitive division, we are counting the objects in each group.

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Children do not have to wait to be introduced to multiplication and division. Children in kindergarten can share equally. As they grow, their understanding will continue to develop. Even though these may not be mathematical standards for the grade level, introducing these concepts early will help students build their comprehension of mathematics.

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Children do not have to wait to be introduced to multiplication and division. Children in kindergarten can share equally. As they grow, their understanding will continue to develop. Even though these may not be mathematical standards for the grade level, introducing these concepts early will help students build their comprehension of mathematics.

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“... children must recognize that they can count groups of objects as well as individual objects” I still have students who will draw/count individually, instead of trying to use 10s or a bigger number. These students need more practice recognizing groups of 10 (place value) for problems with multi-digit numbers. Counting 1 to 1 and struggling to count on is leading to many errors and a lack of fluency.