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I learned that mathematical modeling is a great way to ultimately show students how to make real-world connections

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Having students graph relationships from the real world helps build connections to algebra.

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After learning the general principles of equivalence, variables can be introduced to represent unknown quantities. These should be introduced with other aids to help the learning process like pictures.

KH

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Patterns help students visualize and solve algebra problems.

j.b

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Elementary students often think that seeing an equal sign means that it is true and that they are done, however, having a equal sign does not always mean the statement is true.

-K.N.

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Using models and pictures can help students visualize the unknown quantities.

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Using visuals or objects in place of numbers allows students to think or further their thinking process.

-TE

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It is important for students to use visuals to represent equivalence. It can help students understand quantities known and unknown.
RG

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use different representations like variables and different foundations of algebra.

TT

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I learned that equivalence does not always equal a sum. The use of objects can help students understand that there can be different unknown values.

CC

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The = should be taught as equivalent to help with the foundations of algebra. These skills are more relevant for students as they go past schooling.
SO

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Using pictures to show students different ways of looking at a problem can be very helpful.

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Variables represent an unknown quantity. Using pictures can help students visualize and represent these unknown quantities.

EL

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variables can be used to represent a unique or unknown quantity or a quantity that varies

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Using pictures to represent variables for the unknown in word problems may help young students understand better.
Also having the sum on either the left or right side of the equal sign helps check for student understanding.

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Students can use variables or pictures as a way to represent unknown numbers or unknown solutions to various math problems.

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using pictures to represent is important for visual learners

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When you are doing work on the whiteboard be careful not to write a run-on number sentence. Sometimes this can cause confusion about what the equal sign really means.
GS

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we can use the place value chart to help TT

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break the habit of run on sentences, it is confusing and not accurate all the time

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using patterns helps elementary students by being able to solve problems with using less steps in different ways. This will become more helpful when they get to algebra in highschool.
- KO

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When looking at patterns it is important for the student to understand not only the what but also the why and be able to explain their reasonings. We can use many forms to represent this such as graphs, pictures, models, etc.
RG

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Patters are the sequence of repeating objections, shapes or numbers. Patterns overall have rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.

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Students can justify their answer when discussing patterns by explaining their models/ pictures. And what happens at every step.
SO

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Patterns can be useful when teaching algebra because they help students show their thinking on why different equations represent the formulas and solutions that they do.

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Pictures and tables can be helpful in showing patterns

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Patterns can be shown in different ways such as using models, tables, words, symbols, graphs, etc.)

-K.N.

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Helping students see and become aware of patterns can help them when doing algebra.

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Using multiples different model and explains will help students most

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Generalizing patterns can look different for different students; it could be an equation or it can be iterating and describing the process that they used in their own words.

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It is helpful to draw tables and drawings to visually see what the pattern looks like. Equations can also be useful when determining an amount that is not given.

CC

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Being able to show the pattern and explain in multiple different ways (graph, pictures, words, equations)

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I learned that the skills and patterns that we teach students now will help them when they go on to higher grades and learn algebra.

EL

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When teaching algebra using a physical representation will better show a pattern. Students will be able to actually see what they are trying to solve.
GS

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We can explore the concept of base 10 values by finding patterns in our equations. Having manipulatives also helps the students visualize the pattern. Coming up with a reason would also help the student find the correct answer.

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using patterns is helpful because it allows students to use what they already know to try and find the answer.

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Learning place value can help students make sense of addition subtraction and multiplication. Very important to learn for operations.

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Base 10 helps students understand the meaning of place value by including visuals.

-K.N.

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Generalizing can be helpful for students when learning new math concepts because it allows them to see the same math concepts in different formats or contexts without staying with the standard set-up students might typically see it in.

KH

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The importance to understand the value of a number to understand the base 10, and any patterns. Also noting that the biggest number in the ones is a 9 then moving into another ten or a new ten.
RG

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Base 10 can help young students understand the patterns of fractions and odd and even numbers.

CC

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Algorithms can open up for opportunities for generalization. Set of problems relating to each other in a mathematical way, like 12x1/2 and 12x 1/4, are a good way for students to describe patterns and learn the operation.
-SO

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We can explore the concept of place value by using a Place Value Chart and searching for patterns.

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Base 10 can help students to understand place value by interpreting how many 100s,10s,or 1s are in each place of the number.

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Base 10 can make fractions easier to understand.

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Looking for patterns in different place values is helpful. Also it is important to use odd and even number patterns to predict what answers might be.

EL

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Noticing patterns can be helpful, such as 1/2 of 12 is 6; 1/4 of 12 is 3, and the smaller the fraction gets, also creates a pattern within the asnwer too

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the concept of odd vs even and incorporating open or closed sets

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When doing base 10 you can find fractions of a number that are related by halving the number, while doubling the denominator of a fraction.
GS

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We can explore place value relationships by using a Place Value Chart and searching for patterns.