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Proportional reasoning: using ratios and equivalency to solve for unknown variables.

Half of the American adults are not considered proportionate thinkers, making this a concept that is hard for some grasp (Van de Walle 357).

Proportionate reasoning goes beyond just setting fractions equal to each other, and is more a method of reasoning about manipulative situations, and encourages students to use a unifying thinking to draw conclusions and make connections between concepts using higher thinking.
Proportional reasoning is the explanation as to why two objects or compared or equivalent based on a scale.

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Rate
SCALING UP OR DOWN
SCALE FACTORS
RATIO TABLES
GRAPHS
EQUATIONS

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Proportional thinking is developed through activities involving comparing and determining the equivalence of ratios and solving proportions.

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A number that relates two quantities or measures within a given situation in a multiplicative relationship.

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A way to represent a ration and in fact represents an infinite number of ratios.

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A ratio that compares the number of outcomes in an event to the total possible outcomes.

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Refers to thinking of the ratio as one unit. For example, if kiwis are 4 for $1, then you can think of them as a unit, and then think about other multiples that would also be true, 8 for $2, 16 for $4, and so on.

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two quantities (a ratio) vary together. For example, five mangos cost $2; as the number of mangos varies, so does the cost.

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A ratio of two measures in the same setting.

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A ratio of two corresponding measures in different situations.

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Many students struggle with pacing the correct values in correct places.

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Misunderstanding between equivalent and equal.

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Inability to construct fraction models with making/ representing, naming, comparing, and renaming mixed fractions and decimal fractions greater than 1.

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A limited understanding of written ratios such as 4:1 , always being a constant relationship.

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According to Van De Walle, proportional reasoning is the cornerstone in understanding: algebra, fractions, percents, geometry, and probability.

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Proportional reasoning plays such an important role in many concepts that is crucial that students understand it's weighted importance. Plus! How great does it feel when your students get to use math in real life

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Students should be able to compare situations and determine if relationship is additive, multiplicative, or constant. Determining what kind of relationship is present is essential to indentifying whether the situation is proportional or non proportional.

Additive Relationship:
Two quantities can be expressed as related to each other through addition. y=x+a
Annie and Jannie were walking to school, each walking at the same rate. Jannie started first, and when Jannie has walked 6 blocks, Anne has walked 2 blocks. How far will Anne be when Jannie is at 12 blocks?

Constant Relationship:
Relationship between a variable and a product of another, they are directly proportional.
Lisa and Frank are planting corn on the same farm. Frank plants 4 rows and Lisa plants 6 rows. If Lisa's corn is ready to pick in 8 weeks, how many weeks will it take for Lisa's corn to be ready?

Multiplicative reasoning:
3 bags of sweets with 8 sweets in each bag. How many sweets all together?

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When reading this chapter I noticed how important it is for students to know what proportional reasoning is because it plays an important role in many concepts and you can always relate to the real world. When teaching proportional reasoning you should always include as many activities as you can to make it more engaging. In order for students to understand all math concepts they need to have a good understanding in proportional reasoning.

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Personally, this chapter related to me because it is one of the first standards to cover when teaching 6th grade, and even 7th grade. Proportions and ratios are used so often, even when students may not realize it. Another great thing about the chapter of proportional reasoning is that the activities can be extremely hands-on. Manipulatives and visual aids can easily be represented when discussing ratios. Students will use the concept of ratios all throughout their lives, so making it as relevant as possible will be most beneficial. Finally, when teaching this chapter, it's important to use the correct phrasing, because the terms can easily misinterpreted, so covering misinterpretations and misconceptions is vital for student understanding.

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When looking over this chapter i found it very interesting. I do believe it is important to teach this to students. while growing up this subject was difficult for me. I believe it is because there were not many manipulates for me to utilize. I love that there are many different ways to teach this subject such as hands on activities, games, and videos, etc. I enjoy leaning new and different ways to teach a subject and ways that cater to all of the different types of learning.

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While reading through the chapter and learning about proportional reasoning, this was very fun for me. I was very interested in this topic and can see how fun this can be for students. The misconceptions that students might have, I had myself. There are many different resources that can be used for this topic as well. Games, lesson plans, activities and others are available through the internet. Along with this, I also think that this information is very important for students. This is used in real life, in many different situations and can ultimately be important in their future.

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6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.A.1 Understand the concept of a ratio as comparing two quantities multiplicatively or joining/composing the two quantities in a way that preserves a multiplicative relationship. Use ratio language to describe a ratio relationship between two quantities. For example, "There were 2/3 as many men as women at the concert.”

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Using construction paper, students will use proportional reasoning. 

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Using construction paper, students will use proportional reasoning. 

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An architect decides to build a colorful new home using red and blue bricks. A blue strip of paper represents blue bricks. A red strip of paper represents red brick. For every 4 blue bricks placed, the architect places 6 red bricks. When the architect build one side of the building, he places 16 blue bricks, so how many red bricks did he place?