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Summary Post! Thanks for a great semester! :)

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Summary Post! Thanks for a great semester! :)

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Week 14: Multiplication/Division with Fractions 

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Week 14: Multiplication/Division with Fractions 

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Would you rather? Low floor, high ceiling, real world connections, using math to make sense of our world, thinking outside the box, building community within the classroom, and instructional routines.

Repeated addition and area models support development of concepts and algorithms for multiplication of fractions.
Partition and measurement models lead to two different thought processes for division of fractions.

When we are working on multiplication and division of fractions with students, it is important that we are working on identifying what of the whole and coming up with our answers based around the whole. As we are teaching fractions and using the operations with fractions, we are working to ensure that we are finding ways and strategies that work for the students to better understand and solve (using a ruler, a grid, etc.) that may assist them in understanding the parts of fractions and how to multiply and divide them between the two.

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When it comes to working with fractions with our students, it is essential that we are working on getting the students to be able to visualize and understand what the fractions represent out of a whole.

The meaning of each operation with fractions are the same as the meaning for the operations with whole numbers.

*Fraction Splat! Activity

Unit fraction: any fraction that has a 1 in the numerator-- used to build other fractions.

*It is important that we are working on using the proper vocabulary for the students to know how to identify. It is not an improper fraction, but rather a fraction that is greater than 1.

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Esti-mysteries: reasoning skills
*Rounding doesn't work

With measurement and geometry within the classroom, it is important that the teachers and the students are working on comparing attributes of items or situation with units that have the same attributes. Estimation can be used when students are familiar with the objects and their understanding of the information that is given to them about the problems.
*In my field placement classroom, I was able to see how the students used geometric figures and the sizes of the figures to determine the area of objects. With this, the teacher would provide them with shapes and the lengths and had them solve to figure out what the area of the shape is. They even went as far as to work on finding the area of shapes when they are missing some of the information on the figure.

*Area and volume formulas provide a method of measuring these attributes by using measures of length. Area, perimeter, and volume are related.

**Make sure students have reference points for their understanding of measurements!

When it comes to understanding and knowing what makes shapes different in characteristics, can be determined by the geometric properties to which the shapes can be classified into a hierarchy of categories.

*Activity: Shape Sorts

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Fractions are equal parts, same area, not the same shape.

When working on teaching fractions to students, it is important that we are using squares or rectangles to cut into pieces rather than circles all the time in order for the students to see equal parts in more scenarios than just about food. When students are working on comparing fractions, they need to work on the same size denominators, or same numerators, or more than/less than benchmarks, or the closeness/relation to the benchmarks.

*Partitioning-- taking one whole and breaking it into equal parts.
*Iterating-- taking one size parts and repeating it over and over.

**If you don't know the size of the whole, you can't determine size of the parts.

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Statistics work on formulating questions, collecting data, analyzing data, and interpreting results. When students are working on understanding and identifying data and graphs, it is important that the graphs are clear and relevant with the information that they are working on understanding. The choice of graphical representation can affect how the students understand the information. With statistics, students can get a sense of the data based upon what the graphs and statistical data represent for them.

Histogram data-- numbers are continuous within the graphs (something such as height).

Statistics is a different field of study from mathematics.
*The choice of graphical representation can affect how well the data are understood.
*Graphs and statistics can provide a sense of the shape of the data, including how spread out or how clustered they are.

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Samebutdifferentmath.com
When it comes to creating a problem to use within the classroom, it is important that we are ensuring that there is the option for all students to join in the discussion and can give their thoughts and feelings through sharing as well as having means to do so. When we are creating these low floor, high ceiling problems, we are opening up the discussions for everyone, giving them the options to join in and talk through because they can give simple answers that may not even relate to the math concept at hand; however, they are still joining in the conversation and are participating in doing so.

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Conjecture: a statement made based on what you know/did (based on evidence).

When using base ten blocks, the one can also be called a unit, the ten can also be called a long, and the hundred can also be called a flat-- this is done to show that the blocks can represent anything other than 1, 10, and 100.

Relational understanding: knowing what to do and why that works.

There are strands to mathematical proficiency: conceptual understanding, procedural understanding, productive disposition, adaptive reasoning, and strategic competence.

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wodb.com
When it comes to creating math problems/activities an activity such as determining which doesn't belong, works on problem-solving, sorting, low floor-high ceiling, reasoning/evidence, argument, math practices, as well as allowing for more than one answer.
*An example of this within my field placement was during their math warm-up: the teacher had multiple shapes with different sizes of squares within the shapes and would ask the students which shape doesn't belong and why; thus, allowing for the students to problem solve and work on answering and providing what they think to be the answer to the question.

Area is always the same; however, as the dimensions of one side (length/width) increase, the perimeter increases. The closer to a square, the smaller the perimeter.

Area: multiplication, inside something else, space, 2-D, formula is lXw.
Perimeter: addition, outside, all sides added together, measuring around a space, formula is 2l+2w.

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Subitizing: the ability to recognize the quantity of a small number of dots through instant recognition or the combination of known arrangement of dots.

Understanding "how many" without counting will help children: count on from a known patterned set, combine numbers from sets, and develop mathematical fluency.

The equal sign can be seen as either operational or relational. With determining the equal sign to being operational, the students see the equal sign to be something they have to do with the numbers, whereas the relational aspect and understanding of the equal sign are ways for the students to determine how to balance each side of the equation.

Working with students on early numeracy patterns and mathematical understandings, work on helping and assisting the students with working on number recognition, equation recognition, as well as finding patterns within the numbers and pictures.

(*Game: Tiny Polka Dot)

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Multiplicative-- additive reasoning
Game: Doubles Bingo! In the game, students used a deck of cards and whenever a number was drawn, the students doubled it to find the answer. (Potential Diagnostic Interview activity)

*Doubles Bingo Activity with Students
*Field Experience work time

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Week 5: Adding & Subtracting Two-Digit Whole Numbers

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Week 5: Adding & Subtracting Two-Digit Whole Numbers

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Instructional routines are: set plans, time guides, guidelines, consistent, structure, instructional/habit, instinct, recurring, knowing what to expect, no surprises, reliable, less stress.

When working on and teaching addition and subtraction within the classroom, it is important that we are working n purposeful problems, starting with smaller numbers and using a strings of problems that are related. It is important to come up with and develop a strategy for the students to use when solving, as well as working through specific problems with the students.
*In my field placement classroom, when the third graders were working on higher digit addition, the teacher presented multiple strategies for the students to use when solving the problems in order for them to better understand how they need to go about solving.

*When incorporating a 3 act task into a math lesson, ensure that it is done in whole group:
task 1 is to be engaging and perplexing (notice & wonder, estimates)
task 2 is to have information and solutions (questions, information needed to solve)
and task 3 has a solution discussion and reveals the solution (sharing the solution).

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When it comes to working through basic facts within the classroom, it is important that we are working on developing fact fluency for the students. With developing the fact fluencies for students, we are working on ensuring that we are teaching the accurate use of strategies, accuracy, different strategies and changing up for different students, as well as working on speed and pace to ensure we are helping students to work on their mastery of the skills.

There are multiple meaningful activities for basic facts, that include: solving number stories, quick looks, discuss/writing about strategy use, and playing basic fact games with a focus on reasoning strategies. Within the activities, there should be accountable talk from students.
*Accountable talk: students should be talking within the activities, and talking through their strategies.

**Games/activities should tie back to learning!!

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Would you rather activities are open-ended, have no right answer, and are quick for students to discuss.

Place value is important for students understanding and abilities to correctly identify numbers and accurately define and write numbers using the place value of the digits. With place value, students work on identifying numbers in sets of tens, and the positions of the digits within each number. There are 5 levels of place-value understanding for all: single numeral, position names, face value, transition to place-value, and full understanding.
*In my field placement classroom, a few of the students were struggling with place value, and they were typically working between the position names and the face value of the digits. With these students, they tended to write numbers with all the zeros in them rather than the proper way (EX: 345 they would write it as 30045).

*Decomposing and composing multi-digit numbers in flexible ways is a necessary foundation for computational estimation and exact computation.

Book: How Many Jelly Beans?

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a     +    b =          c
(initial) (change) (result)

Result: 8+4=[]              12-4=[]
Change: 8+[]=12          12-[]=8
Initial: []+4=12              []-4=8

With addition and subtraction, we need to work on building conceptual knowledge for the students. Ways in which we can do this is by direct modeling, counting by ones, use of base-ten models, invented strategies, supported by written recording, mental methods whenever appropriate, and standard algorithms.
Working with the students within addition and subtraction allows for them to work on and identify different types of missing parts within the equations.