2. The Learning Menu

The header of the grade level website has many helpful pages for educators, family members, and students including the Learning Menus page.

Today students will have the chance to practice using the Learning Menu.  Grade five teachers host a learning menu page on the class website. Students will get a computer, log in, go to the class website, and then follow the menu tasks. Students will work on the menu activities in class and are invited to work on the menu at home as well if they'd like.

This is an example of what the Learning Menu looks like.

The advantage of a learning menu is that it fosters independence which gives the teacher more time to work on targeted learning events with individuals and small groups. As the year continues, the learning menus become more sophisticated including greater choice and differentiation.

Teaching Coordinate Grids and Graph Literacy

One good resource for graph literacy and teaching coordinate grids is Concord Consortium's Smart Graph,  I will explore this more and write on how I use it later.

Teaching and Learning: Numerical Expression

It's great to start the school year with a challenging, engaging math lesson. Children love to come to school at the start of the year and learn something new. This sets the stage for a vigorous, engaging year ahead.

Teaching numerical expression lends itself to engagement and provides students with a terrific skill to use as they learn, practice, and apply mathematical operations with numbers simple and complex.

Introduction: What Do These Expressions Equal?
Evaluate one or more of the expressions below in any order by hand or with a calculator. Giving students the chance to use a calculator takes away the pressure to remember facts and to calculate correctly. This frees up all students to reach for higher level learning in this lesson. 

8 + 6 X 5 - 1/2 + (8-3)

99 - 1 + 2 X 3

Let students play with it. Some will finish quickly, others will take a bit of time, and some may not know where to begin. Give the students about 10 minutes, then ask for children to come up to the board to explain their thinking about each expression.

Teach Order of Operations

Show Flocabulary's PEMDAS movie. While some mathematicians are not in favor of PEMDAS, I still think it's a good tool for early learning with regard to Order of Operations. As students work becomes more advanced, they quickly understand where PEMDAS doesn't exactly fit, hence I still believe it's a good starting point. 

Also introduce this graphic shared by a former student:

Study and Practice
Net talk with students about what they can do to remember, study, and apply the Order of Operations. List their ideas. Then let them work with classmates to do all or some of the following activities plus any good ideas they've come up with that you want to add to the list:

• Create a mnemonic, poem, picture, or mini poster that will help you remember the Order of Operations.
• Watch the PEMDAS rap over again, then make up one of your own.
• Make up your own expressions and evaluate them. Check with the teacher.
• Write 5 different expressions and 5 different equations that equal 50 (remember expressions do not have equal signs while equations do). Use at least two different operations in each expression. Make sure you use every operation at least once. Use parentheses, brackets, and/or braces in at least two expressions.
• Use exponents in at least two expressions. 

More Practice

Study the chart below. Then determine where you might add parentheses, brackets, and/or braces to simplify the challenging expression and puzzle below. Then solve the puzzle and expression.

ASSESS

After a day or two of practice and some Khan Academy review and study related to the topic too, it's a good time to assess students' skills. This is one assessment that provides the teacher with a good understanding of what students learned and still need to know.

Related Grade Five Standards

Teaching and Learning: Coordinate Grids at Fifth Grade

Students truly enjoy learning and applying all information related to coordinate grids.

I like to introduce some of the fifth grade coordinate grid concepts and skills early in the year so that we can apply those skills to most units throughout the year. Plus it's the kind of skill that's highly accessible to most math learners making it a positive start-of-the-year unit, one where all students are able to work together with confidence and engagement.

Lesson Introduction: Whet Their Appetite, Make it Meaningful
We'll take a look at the aerial photo of the playground. It's easy to find an aerial view photo of your school playground and this immediately makes the lesson interesting to students.

Say, can anyone locate the "back swing set." Hands will raise quickly. Students describe where it is. They say things such as "in the back," "next to the trees," and "far from the building."  I write their words down, and underline the location words such as next to, far from, and in the back.

After that I'll explain that mathematicians aren't satisfied with vague descriptors like next to, far from, and in the the back since they typically want to be as specific, precise, and exact as possible. Math brings order and organization to our world, and that helps us to see accurate patterns, determine relationships, present facts and figures in meaningful, explicit ways, and solve problems.

I'll then explain that one way to order or organize a map is to overlay the map with a coordinate grid. Then I'll show the coordinate grid map overlay and explain how using the grid provides us a more accurate, specific, and exact way to discuss a map.

Learning Experience

Pass out the grid map to all and we'll identify the vocabulary.

Link for Handout

Complete the worksheet. Then graph a few significant coordinates or ordered pairs on the school map. After that practice making a picture(s) with ordered pairs. This is one free resource for practice pages. A quick Internet search will identify many more.

Finally, at the end of the lesson, review the vocabulary with this catchy Flocabulary rap.

Provide Opportunities for Review and Study for Homework
Encourage students to sing the Flocabulary rap for homework. Also ask them to practice drawing a number of pictures using ordered pairs and practice the concepts using Khan Academy.

Enrichment

• Have students create their own treasure hunt maps with coordinate pair clues to find the treasures in real time or on a digital or hard copy map.
• Have students create the coordinates for a wonderful ordered pair picture. Make sure they test the picture, then make copies of the ordered pair path for the class to use as they create the picture.
• Have students write real world problems like the ones they've completed on Khan Academy and then solve those problems using coordinate grids. 

Coordinate Grid Learning Standards:

CCSS Standards Language Used in This Lesson and Others

• 5.G.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate)
• 5.G.A.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

CCSS Standard Included in Khan Academy Review and Later Lessons

• 5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.