2nd Grade Unit 2: Applying Place Value to Patterns and Data

Unit Driving Question

How do patterns and graphs explain real-world situations?

Essential Questions

1. What are the ways we recognize patterns in our world?

2. Why are patterns meaningful?

3. Why is it important to organize information?

Big Ideas

1. Patterns can be used to describe our world.

2. Patterns can repeat, grow, and shrink.

3. Patterns can be used to solve problems and predict what comes next.

4. Graphs represent and help us make sense of our world.

Technology Resources

The following apps, websites, and smartboard lessons  can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation.

Addition Fluency Practice with logic Students have to chooses addends to make a target number.

Base Ten Recognition Students can practice identifying base ten blocks, matching it to the standard form.

Addition Fluency Practice Students create determine the missing addend.

The Jellybean Tree Students collect data, create a pie graph and a bar graph, then use the graphs to problem solve.

Virtual Base Ten Blocks

Create a Graph  Virtual tool to create line graphs, bar graphs and pie graphs.

Virtual Number Line

Launch Task

1 Lesson

• No Three in a Line Puzzle - This is a patterns puzzle instructional video for teachers from Math Pickle. Use the 4x4 grid in small groups, or use the 6x6 grid for differentiation or for early finishers. 

Big Ideas for Development Lessons

3-4 Weeks (approximately 1 week per big idea)

Big Idea 1: Patterns can be used to describe our world.

Collaborative Engagement 

1. Patterning - Students work in groups to document patterns in their classroom or around their school by taking pictures with a camera or drawing pictures of patterns they notice in the world around them. Afterward, lead a discussion about what they observed about patterns. Print out their pictures and make a picture collage to display during the unit. (adapted from Create Dream Explore)

Key Resources 

1. Unifix Cubes- This Math Pickle video of a pattern activity uses Unifix cubes. There are several different patterns used as examples in the video. The teacher watches the video in order to plan two or three activities for the students (rather than simply playing the video for the students). 
   
1. Sample activity from the beginning of the video:
1. Teacher guides students to make ABCD patterns for each fingertip. Before extending the pattern by linking them all together, let the students place the patterns like towers next to each other on the table.What do you notice? Why did this happen?
2. Instruct students to snap Unifix cubes into groups of five rather than four and place next to each other on the table. What do you notice? Why did this happen?
3. Let the students link them all together again and snap the cubes into groups of a different number with each group having equal numbers of cubes (Note there are only certain multiples that work, but let students to explore this problem, solving the problem by trying a different multiple, growing or shrinking the pattern. Allow students to find a solution on their own). What do you notice? Why did this happen?
2. Read a book about patterns and discuss what makes a pattern.
1. Suggested books:
1. Pattern by Henry Pluckrose
2. I See a Pattern Here by Bruce Goldstone
3. Teddy Bear Patterns by Barbara McGrath
4. Animal Patterns by Nathan Olson
5. Pattern Fish by Trudy Harris
6. Sort It Out! by Barbara Mariconda
2. Suggested facilitated questions:
1. What patterns do you notice in the picture or text?
2. What do you think would come next in the pattern?
3. What patterns do you notice in the world around you?
4. What do you think the pattern means?
5. Can you think of a pattern that has a specific meaning or purpose? (ex. camouflage, quilt blocks, Native American weaving)
6. Name a pattern you have noticed in real-life that is similar to/different from one in the book.

Big Idea Formative Assessment

1. 
1. What patterns do you notice in the picture ?
2. What do you think would come next in the pattern (going outward or inward)?
3. What do you think the pattern means?
4. Can you think of a specific purpose for this pattern?

Evidence of Understanding

• recognize patterns in real-world situations

• describe patterns in real-world situations 

Big Idea 2: Patterns can repeat, grow, and shrink.

Collaborative Engagement 

1. Stickers - Students complete a shapes pattern (from Balanced Mathematics Assessment, Harvard University Graduate School of Education, Cambridge MA). After completing the task as is, students will cut out sticker shapes and make a new repeating, growing, or shrinking pattern. Make additional sticker shapes as needed. 

Key Resources

1. Number Icicles - These overlapping number patterns puzzles that grow and shrink are from Math Pickle. Play the video for students to view up until the 2:50 mark.  Next, have students working in small groups to complete the puzzle sheet that is on the website. Students who complete the easy puzzle quickly may want to try a harder puzzle as well. After completing the puzzle, have students create their own icicle puzzle. Groups can exchange puzzles in order to solve one another’s puzzles. 
   
2. What’s Next and Why? (from Teaching Student-Centered Mathematics Grades K-3, Van de Walle and Lovin, 2006,  p. 285, Activity 10.8)
1. Show students five or six numbers from a number pattern. The task for students is to extend the pattern for several more numbers and to explain the rule for generating the pattern. The difficulty of the task depends on the number pattern and the familiarity of students with searching for patterns.
2. Sample patterns:
1. 1, 2, 2, 3, 3, 3, … each digit repeats according to its value
2. 5, 1, 5, 2, 5, 3, … the counting sequence interspersed with 5s
3. 2, 4, 6, 8, 10, … even numbers–skip counting by 2
4. 1, 2, 4, 5, 7, 8, 10, … two counts, then skip one
5. 1, 2, 4, 8, 16, … double the previous number
6. 2, 5, 11, 23, …  double the previous number and add 1
7. 1, 2, 4, 7, 11, 16, … successively increase the skip count
3. Most of the preceding examples also have variations you can try. Make up your own or challenge students to make up their own number rules. 

Big Idea Formative Assessment

1. Patterns - Students create and describe patterns made from shapes. Students will work with manipulatives to create a repeating pattern and a growing or shrinking pattern. Then, students will draw their pattern and write a description of their pattern. (from New Zealand Minister of Education)

Evidence of Understanding

• identify repeating, growing, and shrinking patterns

• complete repeating, growing, and shrinking patterns

• describe patterns

• represent patterns

• create patterns

• extend patterns 

Big Idea 3: Patterns can be used to solve problems and predict what comes next.

Collaborative Engagement

1. “Predict Down the Line” (from Elementary and Middle School Mathematics: Teaching Developmentally, Van De Walle, Karp, and Bay-Williams, p. 309, Activity 14.5) 
1. Provide students with a pattern to extend (e.g., ABC pattern made with Unifix cubes).
2. Before students begin to extend the pattern, have them predict exactly what elements will be in, say, the twelfth position. (Notice that in the ABC pattern the third, sixth, ninth, and twelfth terms are the C element because they are multiples of 3.)
3. After students predict, have them complete the pattern to check. Ask them how they knew.
4. You can differentiate this lesson by starting with a more basic AB pattern or by having different groups of students work on different types of patterns based on their readiness.
5. Students should be required to provide a reason for their prediction in writing supported with visuals. 

Key Resources 

1. Pennies Pattern
1. Display picture of pennies or set up a display as seen in the picture. Students may work in groups and use classroom pennies, manipulatives, or drawings to help solve the problems.
2. What pattern(s) do you notice?
3. What would the next column look like?
4. Is this a repeating, growing, or shrinking pattern? (While students will probably notice the growing pattern, many will notice the repeating pattern of the numbers.)
5. How many columns would it take to get to 700 pennies?
2. Number Transformer Challenge - Students analyze growing shapes patterns and predict what will occur next (from YouCubed at Stanford University).
3. Table Talk Two - Students fill in a hundreds chart and an addition table while using number patterns (Balanced Mathematics Assessment, Harvard University Graduate School of Education, Cambridge MA).

Big Idea Formative Assessment

1. Wall Design - Students complete and describe repeating patterns (from Balanced Mathematics Assessment, Harvard University Graduate School of Education, Cambridge MA).

Evidence of Understanding

• extend patterns

• use numbers to describe patterns

• make conjectures using patterns 

Big Idea 4: Graphs represent and help us make sense of our world.

Collaborative Engagement

1. Color Cubes - This activity is a 3-act sorting and graphing task from Catherine Castillo.

Key Resources 

1. We Scream for Ice Cream - Students analyze data on a pictograph (from Balanced Mathematics Assessment, Harvard University Graduate School of Education, Cambridge MA). Keep student data sheets for future task extension.
   
2. People in my House - Students collect, organize, and interpret data based on how many people live in their houses.
3. Subject to Interpretation - Students will organize data given to create a picture graph. (from GA Department of Education)
4. We Scream for Ice Cream Extension: (use data from the previous task)
1. Ask students: Is this pictograph the best way to represent this data?
2. In groups, have students try creating a bar graph using the same data using a 10X4 grid.
3. Ask students: Does this bar graph represent the data better? Why or why not?
5. Donuts Sold - Students will analyze a table and corresponding pictograph and bar graph. 

Big Idea Formative Assessment

1. Pizza Topping- Students are asked to a bar graph from a set of data and interpret the data. (from NC Department of Instruction)

Evidence of Understanding

• collect, sort, and categorize data

• identify parts of a graph

• title

• label

• number

• scale

• create graphs (pictographs and bar graphs) to describe data

• make sense and draw meanings from graphs

• solve simple problems based on a graph

• make predictions and draw conclusions based on a graph

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)

Patterns

1. Patch Tool - Students create their own patch of patterns and shapes using an interactive tool. (NCTM Illuminations)

Graphs

1. Ask students to answer a survey question on a sticky note (i.e. Which sport do you like best: football, basketball, soccer, or gymnastics?) Have students record answers on sticky notes. Collect and sort sticky notes into groups. Have students organize the data on an empty bar graph.

• Bar Graph Template