Russell McNeil

About Me

Name: Russell McNeil

Site: Monterey Highlands

Grade(s): 5th

Technology ability: Proficient

A little about me:

This is my 5th year teaching, but my first in AUSD. Currently, I am teaching 5th grade at Monterey Highlands Elementary and I am excited to be a part of the team. At my last site I was the Teacher Tech Lead, as well at the SBAC site coordinator, and a member of the iTeach Team.

Favorite Apps and Sites:

1)Google Drive/Docs/Slides/Forms/ Classroom

2) Brainpop

3) Kahoot

4) Quizlet

5) Go Noodle

6) Plickers

7) Read Theory

8) Newsela

9) Wordly Wise

Technology I Recommend

An excellent App / Website to assist teachers is called Plickers. This is a low tech/ high tech solution for gathering understanding. All you need is a computer, projector, a smart phone, and copy paper.

After you teach a lesson, getting immediate feedback can help you plan accordingly, however every minute is valuable. To save time create 1-2 questions in Plickers online and project them to the class. Each student will have a QR code-esk image. Depending on how the student holds their sheet, they are responding A,B,C, or D. No image looks the same as another and cuts down on cheating. Students will turn their sheet in your direction and you can scan responses using your smart phone or tablet. This data is collected, crunched and is able to be exported as an excel file. You see immediately what percent understood the lesson, who needs intervention, and most importantly your success in teaching the lesson. Plickers isn't great for long tests, but it is an excellent tool to measure along the way.

Lesson

Dividing by a Unit Fraction

Technology used: Plickers

Subject: Math

Common Core Standard(s):

What standard(s) and/or cluster(s) am I targeting in this lesson?

5.NF.B.3 - Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.B.7 - Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

MP.1 - Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

MP.2 - Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP.3 - Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MP.4 - Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

MP.6 - Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

MP.7 - Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Lesson Details

Number of days/class periods for lesson: 1

Coherence

How does this work connect to previous or future work in the grade and what will I do to make that connection?

Previously, students had been successful multiplying unit fractions and whole numbers. This lesson builds on that knowledge and introduces the relationship between dividing and multiplying fractions.

Learning Goal

What is the learning goal for students in this lesson?

Students will divide a unit fraction by a whole number. To achieve this, students will invert the divisors into the reciprocal and invert the problem, making it a multiplication problem.

Rigor

Which aspect(s) of rigor do the targeted standards require?

Conceptual understanding

Procedural skill and fluency

Mathematical Explanations

What explanations, representations, and/or examples will I share to make the mathematics of this lesson clear?

We will begin by copying a sample problem into our notes and working it out in 3-4 simple steps. I will label and make note of new vocabulary. To help illustrate this process we will use page 93 in the student workbook to view a bar model. As an alternative to this model, I will play my dividing fraction rap to help engage auditory learners.

Grade-Level Problems

What grade-level problem(s) will I ask the whole class to solve? Attach a document or write below.

1/3 ÷ 5

1/3 x 1/5

1/2 ÷ 3

1/2 x 1/3

1/3÷ 4

1/3 x 1/4

1/5÷ 2

1/5 x 1/2

1/6 ÷ 4

1/6 x 1/4

Checks for Understanding

What strategies and opportunities will I use to check for understanding throughout the lesson?

1) Chin and Spin, an informal visual assessment.

2) Plickers, a low tech / high tech way to assess and get data in real time.

3) Exit ticket.

Discussion Questions

What questions will I ask to allow students to share their thinking and when will this happen in this lesson?

Questions will be asked throughout the lesson. Some questions will require chin and spin and others will have students turning and talking.

Questions:

What do you do to a whole number when it is multiplied by a fraction?

Why do we put it over 1? What does it represent?

Which part is the divisor?

What is the reciprocal of _______?

After we flip the divisor, what do we do?

What kind of problem is a single fraction, multiplication or division

Technology Insight & Tips

I used www.achievethecore.com to write up this lesson and I used www.plickers.com to support the quick assessment portion of the lesson. This lesson had 28 out of 30 students responding correctly. I was able to identify the students that needed intervention and had them work with clock partners to clarify the lesson. Knowing that my lesson was successful allows me to adjust my planning schedule and not worry about anyone falling through the cracks. The most important take away for me was the time I saved, by not having to "trade and grade".