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Number Lines

Number Lines. goo.gl/px1eB. Taajah Witherspoon Mountain Brook Schools Learning Conference July 21, 2013. Use an index card to Define a number line Write the grade level that you teach . Lines are a tool. Doritou & Gray (2006). Yea! Number .

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Number Lines

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  1. Number Lines goo.gl/px1eB Taajah Witherspoon Mountain Brook Schools Learning Conference July 21, 2013

  2. Use an index card to Define a number line • Write the grade level that you teach

  3. Lines are a tool Doritou & Gray (2006) Yea! Number • none indicated the benefit had a formality based upon the repetition of a unit interval and the partition of the interval. Instead perceptual features dominated the definitions

  4. 74 participants Only 1, described as ……… “A line that contains all rational and irrational numbers. It is an infinite line.”

  5. “The use of number lines increases students’ ability to use numbers flexibly, estimate, and visualize numbers and therefore increase number sense.” Wright, 2001

  6. TPS: How can number lines be used in the classroom? • Number sequencing • Greater than and less than • Estimation and Rounding • Measuring length • Elapsed Time • Strategy for various operation (+, -, x, ÷) • Integers • Etc.

  7. Number Line Progression • Counters i.e. separate unifix cubes • Unifix cubes length model (tens) • Beaded necklace (counting) • Structured number line (model strategies) • Dual sided number line • Empty number line • Double number line • Fraction / percentage bar

  8. Number Path Kindergarten to First Grade • Take up space • Unifix cubes • Beads (concrete number line) • 1-20 • Discrete items

  9. Number Path vs Number Lines Number line - Measurement model rather than a counting model

  10. Connecting Models

  11. End of 1st Beginning of 2nd • Structured Number line 1-10 then 1-20 • Missing number(s) • Double-sided number line • Where is number 13 on the line? End of 2nd Grade • Open number line O.G.A.P.

  12. Prerequisite Knowledge to Empty Number Line • Counting by tens (N+10) • Jumping across or bridging tens • Place Value strategy More Sophisticated Strategies • Sequential strategies • Compensation strategy (Bobis, 2007)

  13. Empty Number Line 80’s Powerful model for reasoning Recording and Sharing students’ thinking strategies Students should only record relevant numbers

  14. Subtraction Strategies BSU Subtraction Progression

  15. Procedural Fluency

  16. “Take Away” 13 -7 “0 – 8 = 2”

  17. The Number Line has the ability to integrate “all the number systems of Pre-k to grade 8.” NRC, 2001 • Model for distance • Links geometric and arithmetic • Equivalency • Ordering

  18. Half or One-half • Over half - overgeneralized (Wong, 2008)

  19. Grade Level Specifics • K – unifix cubes as counters • 1st – connected unifix cubes linear model • 1st / 2nd – Bead necklace • 2nd – model strategies on structured number line • 3rd – open number line • 3rd – 5th model rational numbers on number line • 6th – model ratios • 7th – model +, -, x, ÷ integers • 8th – locate irrational numbers on number line

  20. Number Line and the CCSS Grade 2 • Represent whole numbers as lengths from 0 on a number line diagram …0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. Make a Line Plot with whole numbers

  21. Number Line and CCSS (Grade 3) Use multiplication and division within 100 to solve word problems… Three equal jumps forward from 0 on the number line to 12 or three equal jumps backwards from 12 to 0. Understand a fraction as a number

  22. In which order would you present the following number lines? http://caccssm.cmpso.org/

  23. 4th Grade and the CCSS • Compare two fractions with different numerators and different denominators… • Explain why a fraction is equivalent • Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Find the sum and difference.

  24. 5th Grade & CCSS (Number Line) – Coordinate Plane, (+) and (-) fractions Round 14.235 to the nearest tenth Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

  25. Number Line and CCSS 6th Grade Use ratio and rate reasoning to solve real-world …. problems, e.g., by reasoning about … double number line diagrams… (If 6 is 30% what is that value?) Understand ordering and absolute value of rational numbers. Represent account balance of -6 , write |–6| = 6 to describe the size of the debt in dollars. http://caccssm.cmpso.org/

  26. 7th - Apply and extend …..understandings ….to add and subtract rational numbers; on …number line diagram. • You have $4 and you need to pay a friend $3. What will you have after paying your friend? 4 + (-3) = 1 or (-3) + 4 = 1 8th- Use rational approximations …..to compare the size of irrational numbers, locate them approximately on a number line diagram….(e.g., π2). • Compare √2 and √3 by estimating their values, plotting them on a number line….

  27. Which Standards of Mathematical Practices are met with the use of the Number Line

  28. How will the number line impact your instruction?

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