Mathematical Emphasis
Investigation 1—Introduction to Data Analysis
- Making quick sketches of the data to use as working tools during the analysis process
- Describing the shape of the data, moving from noticing individual features of the data to describing the overall shape of the distribution
- Defining the way data will be collected
- Summarizing what is typical of a set of data
Investigation 2—Landmarks in the Data
- Inventing ways to compare and represent two sets of data by describing the shape of the data and what’s typical of the data
- Finding the median in a set of data arranged in numerical order (e.g., when students line up in order by height)
- Finding the median in a set of data grouped by frequency (e.g., on a line plot or other graph)
- Using the median to describe a set of data and to compare one data set to another
Investigation 3—A Data Project: Investigating Sleep
- Undertaking a complete data analysis project, from defining a question to publishing results
- Carrying out all the stages of a data analysis investigation
- Choosing and refining a research question
- Viewing the data in several different ways, using quick sketches and other representations to organize and display the data
Tips For Helping At Home
Questions To Ask:
- What is the problem about? Tell me in your own words.
- What did you do in class to get started?
- Can you solve a simpler version of the problem?
- What have you already tried? What steps did you take?
- Did you show all of your work?
- Does the answer make sense?
- How do you know your answer is correct?
Helping At Home
- Your child may ask you questions as part of his or her data collection in this unit. Give your full attention to these questions and help your child record your answers since they will be the basis of work in class.
- You will find many opportunities to examine data around your home. Which color or make of car is the most common on your street? Do more households in your neighborhood have a dog or a cat? After a while, collecting and thinking about data can become a habit you and your child share.
Vocabulary Terms
- Data
- A collection of information
- Line Plot
- A number line with data individually represented above corresponding numbers
- Median
- A measure of central tendency, the exact middle of the data when all the data are put in order
- Outlier
- A piece of data that has an unusual value
- Range
- Value of the difference between the lowest and highest piece of numerical data
- Representation
- A graph, picture or chart showing the data that was collected
- Shape of Data
- The outline or shape that data makes on a line plot or graph
- Statistics
- The study of data
- Typical
- Average, central for a data set
Mathematics Vocabulary Web site
Mathematics Strategy—Finding and Using the Median
The median is an important landmark in a set of data. It is an average or a measure of center that helps summarize how the data are distributed. The median is the midpoint of the data set. If all the pieces of data are lined up in order and one person counts from one end while another person counts from the other end, the value where they meet is the median value.
Below is a line plot showing the number of blue candies in a bag.
To find the median, take all the values from the line plot and stretch them out in order and locate the middle value:
When there are two middle values, the median is half way between the two.
Source: Investigations in Number, Data, and Space: The Shape of Data. Dale Seymour, 1998. (Pages 42 and 43)
Mathematics Activity—Practicing Multiplication Combinations for Automaticity
A unit like “The Shape of Data” provides an excellent time for families to practice and review information learned earlier in the year. Children need multiple and continued exposure to concepts and procedures before mathematics is learned at a mastery level. Practice activities help a child become efficient, accurate, and flexible in mathematics.
Play mathematics games at home that build and reinforce knowledge of multiplication and division combinations. Games could include “Multiples BINGO”, “Multiplication Pairs”, and Arrays games sent home from school this fall.
Practice multiplication facts with flashcards in different ways.
Which are easy? Which are hard?
- Give your child multiplication cards. Have them sort the cards into two piles: “Facts I Know” and “Facts I am Working On.” Cards are put into the known pile if they are at a recall level (students know the answer and can tell you in less than 3 seconds).
- Have your child choose one or two problems from the “working on” pile and analyze the problem. Come up with a hint to help remember that fact. Hints should be facts they already know that can help them remember the correct answer.
- After practicing with that hint for a week, have your child go through the pile again and see if more are remembered.
Learning Difficult Facts
Choose one multiplication fact that is not known and focus on it for a week. Every day have your child figure out a different way to remember the answer (7x6 could be remembered as 6x6+7 if a child knows 6x6. Another way would be 7x5+7 since most children know their 5’s). After a week of focus, have your child go through the whole pack of combinations again.
Adapted From Source: Investigations in Number, Data, and Space: Mathematical Thinking at Grade 3. Dale Seymour, 1998. (Page 27)
Use triangle flashcards to practice multiplication and division combinations.
Three corner flashcards help students develop number sense, recognize patterns, build fact strategies, boost problem solving skills, and relate division to multiplication.
- For multiplication, cover the top number (largest of the three numbers) and multiply the bottom two corners or numbers. The answer is the top numeral.
- For division, cover one of the bottom corners. Divide the top number by the uncovered bottom number. The covered numeral is the answer.
Get to Flashcards, Part 1 (for printing)
Get to Flashcards, Part 2 (for printing)