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M4.A.1.2 Compare quantities and magnitudes of numbers.

ASSESSMENT ANCHOR M4.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M4.A.1.2 Compare quantities and magnitudes of numbers. . M4.A.1.2 Eligible Content.

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M4.A.1.2 Compare quantities and magnitudes of numbers.

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  1. ASSESSMENT ANCHOR M4.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M4.A.1.2 Compare quantities and magnitudes of numbers.

  2. M4.A.1.2 Eligible Content • M4.A.1.2.1 Locate/identify fractions or decimals on a number line (decimals and fractions through the tenths – do not mix fractions and decimals). • M4.A.1.2.2 Compare and/or order whole numbers through 6 digits and amounts of money to $100 (limit sets for ordering, to no more than 4 numbers).

  3. M4.A.1.2.1 Locate/identify fractions or decimals on a number line (decimals and fractions through the tenths – do not mix fractions and decimals).

  4. PSSA Sample Item

  5. Representation of Decimals on a Number Line • To represent a decimal on a number line, divide each segment of the number line into ten equal parts. E.g.  To represent 8.4 on a number line, divide the segment between 8 and 9 into ten equal parts. • The arrow is four parts to the right of 8 where it points at 8.4.

  6. "Decimal" comes from the Latin root decem, which means ten.  To understand decimal numbers you need to understand how ten forms the basis of our number system. • Let's first explore decimals on the number line.  Draw little lines between 0 and 1 so that it is divided into ten tiny parts - tenths! • Now let's zoom in between 0 and 1.  See how the number line between 0 and 1 is divided into ten increments or parts.  Each of these ten parts is a tenth. • The first digit after the decimal point tells how many tenth parts or tenthsare in the number. • 0.4 means four tenths - the same as • 1.2 is the same as 1 4 10 2 10

  7. How to Find a Fraction on a Number line

  8. A number line and a ruler are very much alike. 0 2 1

  9. On a ruler, each inch is considered one whole inch Nine whole inches One Inch Two Inches Three Inches

  10. The marks in between the whole inches are fractions of an inch ½ Inch 2 ¾ Inches 7 ¼ inches

  11. Number lines are read the same way. • The Numbers are read as whole numbers. • The marks in between are read as fractions. 1 0 2

  12. There are three steps to reading fractions on a number line Step One-Count the spaces in between the zero and the one on the number line. That is your denominator. 2 0 1 4

  13. Step Two- Count the sticks, starting at the first stick after zero. Stop at the point you are naming.This is the Numerator. 0 1 3 4

  14. There is only a step three if the fraction is past a whole number. If the fraction is past a whole number, steps one and two are the same except that you count the spaces and marks in between the whole numbers closest to the fraction. 0 2 1

  15. Mixed number fractions Step One-Count the spaces in between the whole numbers where the fraction is placed. That is your denominator. 0 2 1 4

  16. Mixed number fractions Step Two- Count the sticks, starting at the first stick after the whole number. Stop at the point you are naming. This is the Numerator. 2 0 2 1 4

  17. Mixed number fractions Step Three- Write the whole number as a whole number beside the fraction. 2 1 0 2 1 4

  18. Practice Finding Decimals and Fractions on a Number Line

  19. Which decimal on this number line corresponds to the fraction 1/2? 

  20. Put these decimals in the proper place on the number line

  21. What number is at the arrow? • Answer.  The unit has been cut five times -- into six equal pieces. •   That number is 5 6

  22. Write the decimal number that the arrow points at in the following diagrams: 24.3

  23. M4.A.1.2.2 Compare and/or order whole numbers through 6 digits and amounts of money to $100 (limit sets for ordering, to no more than 4 numbers).

  24. PSSA Sample Item

  25. Comparing and Ordering Whole Numbers Example 1: Compare 76 and 67 Write: Say: 67 < 76 67 is less than 76 76 > 67 76 is greater than 67 Remember, the mouth of the symbol (> or <) always opens to the greater number.

  26. Example 2: Blanca Peak is 14,345 feet above sea level. Crestone Peak is 14,294 feet above sea level. Which peak is taller?

  27. Caution!!!!! Be sure to line up digits with the same place value when comparing or computing. Example: You score 108,464 points. Your friend scores 97,996. The higher score wins. Who wins? Lined Up IncorrectlyLined Up Correctly (at the ones place) 108,464 108,464 97,996 97,996 Note: When one whole number has more digits than the other, it is greater. Write: 108,464 > 97,996 or 97,996 < 108,464

  28. Let’s Try!Compare using <,>, or =. • 534 __ 509 • 45,943 __ 45,494 • 109,015 __ 109,005 • 845,182 __ 846,182

  29. Order the following numbers from greatest to least.61,565; 71,649; 75,367 75,367 ; 71,649; 61,565 (greatest to least)

  30. Let’s Try!! • Order from least to greatest… • 756,833; 756,820; 756,338 • 756,338; 756,820; 756,833 • Order from greatest to least… • 90,654; 87,223; 87,954; 90,556 • 90,654; 90,556; 87,954; 87,223

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