All Things Second Grade Math!
Unit 7-Data Analysis
This unit bundles student expectations that address organizing and representing data using bar graphs and pictographs with intervals of one or more, drawing conclusions,
making predictions, and writing and solving addition and subtraction problems using information in graphs. According to the Texas Education Agency, mathematical process
standards including application, problem-solving, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.
Prior to this unit, in Grade 1, students collected, sorted, organized, and represented data using picture and bar-type graphs, drew conclusions, generated questions, and answered questions from the data.
During this unit, students transition from bar-type graphs to bar graphs and from picture graphs to pictographs. A bar graph is a graphical representation to organize data
that uses solid bars that do not touch each other to show the frequency (number of times) that each category occurs. Each bar represents a category and each bar within
the bar graph is independent from the other bars. Students determine the total frequency of each category, the length of each bar, by associating the end of each bar to the scale marked interval of the axis. Frequency values may be interval values on the axis or in-between interval values on the axis. A pictograph is a graphical representation to organize data that uses a picture or symbol, where each picture or symbol represents one or more than one unit of data, to show the frequency (number of times) that each
category occurs. In a pictograph, the value of each picture or symbol is defined by the pictograph key. Students use skip counting or repeated addition to determine the frequency, the total value of all pictures (or symbols), including partial pictures (or partial symbols), within each category. Both vertical and horizontal orientations of bar graphs and pictographs with up to four categories and intervals of one or more are experienced during this unit. Students summarize the existing data, or the inferential data, in bar graphs and pictographs to draw conclusions and make predictions. Students also generate and solve one-step word problems based on the information in bar graphs
and pictographs with intervals of one.
Something to think about...
"A lack of fact fluency can be crippling for emerging mathematicians. Students who don’t understand number relationships struggle to use mathematics to solve problems, because they are using all of their mental energy on basic facts. A strategy based approach for learning facts leads to automaticity while at the same time it helps students understand how numbers are related. But instruction needs to go hand-in-hand with practice to build speed and fluency." -Donna Boucher
Have a GRAPH Talk
Due to unit and state testing, we often rush students to the abstract form of understanding before they are ready. Students have to learn by doing and that means using manipulatives 50% of daily instructional time. And smart boards, apps and the book are not manipulatives...they are tools! Now, I am not saying you cannot use these great resources, I am just reminding you that a manipulative is something the kids are handling and learning from. Think of \knowledge in these stages
Using-This is the time when there is no algorithm-just the materials (counters, beans, cubes) Looks like-lots of questioning that leads to student discovery. Kids are talking and “playing”.
Modeling-In this stage, the students have the materials and the teacher is modeling the procedure while using manipulatives. The students are still not writing the procedures/algorithm. Instead they are seeing patterns and predicting.
Materials & Procedures-Here students are copying procedures you are modeling and beginning to try problems on their own. They still have materials and you are watching to see who is using them for necessity vs. comfort or out of habit.
No Materials-This is where students understand the concept and can generalize their problem solving. They may not get to this during the unit-remember mastery may not come until the end of the year. “But on a test…?”-If you have truly covered the concept concretely, students will know they can draw a picture to solve. That is why it is important to transition from concrete to pictorial throughout the unit! In one lesson I may fluctuate between concrete materials and pictorial representations. Another day I may try to go from pictorial to abstract and back to concrete in small groups.
THIS APPLIES FOR GRAPHING AS WELL! STUDENTS SHOULD BE COLLECTING THE DATA AND CREATING GRAPHS.