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goo.gl/px1eB Taajah Witherspoon Mountain Brook Schools Learning Conference July 21, 2013 Use an index card to Define a number line Write teach the grade level that you Yea! Number Lines are a tool none indicated the benefit had a formality based upon the repetition of a unit interval and the partition of the interval. perceptual features dominated the definitions Instead Only 1, described as ……… “A line that contains all rational and irrational numbers. It is an infinite line.” “The use of number lines increases students’ ability to use numbers flexibly, estimate, and visualize numbers and therefore increase number sense.” Wright, 2001 Number sequencing Greater than and less than Estimation and Rounding Measuring length Elapsed Time Strategy for various operation (+, -, x, ÷) Integers Etc. 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 Kindergarten to First Grade Take up space Unifix cubes Beads (concrete number line) 1-20 Discrete items Grade Number K-1 Paths Number 2-8 Line Model Physical Count / Finite Each cube can be counted Model / Length Count Infinite length units Position is on the number of cubes/ space is the number Specific point Number line - Measurement model rather than a counting model 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. Counting by tens (N+10) Jumping across or bridging tens Place Value strategy More Sophisticated Strategies Sequential strategies Compensation strategy (Bobis, 2007) Powerful model for reasoning Recording and Sharing students’ thinking strategies Students should only record relevant numbers Transitional Early – Transitional Early BSU Subtraction Progression Traditional Algorithm Partial Difference Adding Up Compensation 13 -7 “0 – 8 = 2” Model for distance Links geometric and arithmetic Equivalency Ordering Hundreds Chart or Arithmetic Block Visualization Number Line Cognitive involvement (partitioning or labeling) Over half - overgeneralized (Wong, 2008) Pick any 2 of the following problems. Model with the Number Line On January 1 in Minnesota the low temperature was -4 degrees F and the high temperature was 6 degrees F. How much did the temperature increase? Use number line to solve 17 + ______ = 52 The distance between 50 and me is 27. What number(s) can I be? Solve (–n x –n) with the number line. Can you name a number smaller than nothing? 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 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 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 In which order would you present the following number lines? http://caccssm.cmpso.org/ 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. 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). 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/ 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…. How will the number line impact your instruction?