CAA Blueprints for Mathematics - CAASPP (CA Dept of …



California Alternate Assessments

Blueprint for Mathematics

Table of Contents

Grade Three 5

Operations & Algebraic Thinking 5

Operations & Algebraic Thinking 5

Operations & Algebraic Thinking 5

Number & Operations in Base Ten 5

Number & Operations in Base Ten 5

Number & Operations— Fractions 6

Number & Operations— Fractions 6

Measurement & Data 6

Measurement & Data 6

Geometry 6

Grade Four 7

Operations & Algebraic Thinking 7

Operations & Algebraic Thinking 7

Operations & Algebraic Thinking 7

Number & Operations in Base Ten 8

Number & Operations— Fractions 8

Number & Operations— Fractions 8

Number & Operations— Fractions 9

Measurement & Data 9

Measurement & Data 10

Geometry 10

Grade Five 11

Operations & Algebraic Thinking 11

Number & Operations in Base Ten 11

Number & Operations in Base Ten 11

Number & Operations in Base Ten 12

Number & Operations in Base Ten 12

Number & Operations— Fractions 12

Number & Operations— Fractions 13

Measurement & Data 13

Measurement & Data 13

Geometry 14

Grade Six 15

Ratios & Proportional Relationships 15

Ratios & Proportional Relationships 15

The Number System 16

The Number System 17

September 2015 © 2015 California Department of Education Page 2

The Number System 17

Expressions & Equations 17

Expressions & Equations 17

Expressions & Equations 18

Geometry 18

Statistics & Probability 18

Grade Seven 19

Ratios & Proportional Relationships 19

Ratios & Proportional Relationships 19

Ratios & Proportional Relationships 19

Ratios & Proportional Relationships 19

The Number System 20

The Number System 20

Expressions & Equations 20

Geometry 20

Geometry 20

Statistics & Probability 21

Grade Eight 22

The Number System 22

Expressions & Equations 22

Expressions & Equations 22

Functions 23

Functions 23

Geometry 23

Geometry 24

Geometry 24

Statistics & Probability 24

Statistics & Probability 25

Grade Eleven 26

Number and Quantity: The Real Number System 26

Number and Quantity: Quantities 26

Algebra: Creating Equations 26

Algebra: Creating Equations 26

Algebra: Creating Equations 26

Functions: Interpreting Functions 27

Functions: Interpreting Functions 27

Geometry: Similarity, Right Triangles, & Trigonometry 27

Statistics & Probability: Interpreting Categorical & Quantitative Data 27

Statistics & Probability: Interpreting Categorical & Quantitative Data 28

Acronyms and Initialisms Used in the California Alternate Assessments Blueprint

|CAA |California Alternate Assessment |

|ETS |Educational Testing Service |

|NCSC |National Center and State Collaborative |

|Grade Three |Note: Each test will contain from 25 to 27 operational items. |

|Domain |NCSC Percentage |CAA Percentage |Common Core State Standard |Core Content Connector |Essential Understanding |

|Operations & Algebraic |30% |30% |3.OA.A.1 Interpret products of whole numbers, e.g., |3.NO.2d3 Solve multiplication |Create an array of sets (e.g., 3 rows of 2). |

|Thinking | | |interpret 5 × 7 as the total number of objects in 5 |problems with neither number | |

| | | |groups of 7 objects each. For example, describe a |greater than 5. | |

| | | |context in which a total number of objects can be | | |

| | | |expressed as 5 × 7. | | |

|Operations & Algebraic | | |3.OA.D.8 Solve two-step word problems using the four |3.NO.2e1 Solve or solve and check |Combine (+), decompose (-), and multiply (x) |

|Thinking | | |operations. Represent these problems using equations |one or two-step word problems |with concrete objects; use counting to get the |

| | | |with a letter standing for the unknown quantity. Assess|requiring addition, subtraction or|answers. Match the action of combining with |

| | | |the reasonableness of answers using mental computation |multiplication with answers up to |vocabulary (i.e., in all; altogether) or the |

| | | |and estimation strategies including rounding. |100. |action of decomposing with vocabulary (i.e., |

| | | | | |have left; take away) in a word problem. |

|Operations & Algebraic | | |3.OA.D.9 Identify arithmetic patterns (including |3.PRF.2d1 Identify multiplication |Concrete understanding of a pattern as a set |

|Thinking | | |patterns in the addition table or multiplication |patterns in a real world setting. |that repeats regularly or grows according to a |

| | | |table), and explain them using properties of | |rule; Ability to identify a pattern that grows |

| | | |operations. For example, observe that 4 times a number | |(able to show a pattern) (shapes, symbols, |

| | | |is always even, and explain why 4 times a number can be| |objects). |

| | | |decomposed into two equal addends. | | |

|Number & Operations in |20% |35% |3.NBT.A.1 Use place value understanding to round whole |3.NO.1j3 Use place value to round |Identify ones or tens in bundled sets – |

|Base Ten | | |numbers to the nearest 10 or 100. |to the nearest 10 or 100. |Similar/different with concrete representations |

| | | | | |(i.e., is this set of manipulatives (8 ones) |

| | | | | |closer to this set (a ten) or this set (a |

| | | | | |one)?). |

|Number & Operations in | | |3.NBT.A.2 Fluently add and subtract within 1000 using |3.NO.2c1 Solve multi-step addition|Combine (+) or decompose (-) with concrete |

|Base Ten | | |strategies and algorithms based on place value, |and subtraction problems up to |objects; use counting to get the answers. |

| | | |properties of operations, and/or the relationship |100. | |

| | | |between addition and subtraction. | | |

|Number & Operations— |20% | |3.NF.A.1 Understand a fraction 1/b as the quantity |3.NO.1l3 Identify the fraction |Identify part and whole when item is divided. |

|Fractions | | |formed by 1 part when a whole is partitioned into b |that matches the representation |Count the number of the parts selected (3 of the|

| | | |equal parts; understand a fraction a/b as the quantity |(rectangles and circles; halves, |4 parts; have fraction present but not required |

| | | |formed by a parts of size 1/b. |fourths, and thirds, eighths). |to read ¾). |

|Number & Operations— | | |3.NF.A.3d Compare two fractions with the same numerator|3.SE.1g1 Use =, to compare|Concrete representation of a fractional part of |

|Fractions | | |or the same denominator by reasoning about their size. |two fractions with the same |a whole as greater than, less than, equal to |

| | | |Recognize that comparisons are valid only when the two |numerator or denominator. |another. |

| | | |fractions refer to the same whole. Record the results | | |

| | | |of comparisons with the symbols >, =, or 10. | |

| | | |statements of multiplicative comparisons as | | |

| | | |multiplication equations. | | |

|Operations & Algebraic | | |4.OA.A.2 Multiply or divide to solve word |4.PRF.1e3 Solve multiplicative comparisons |Identify visual multiplicative comparisons |

|Thinking | | |problems involving multiplicative |with an unknown using up to 2-digit numbers |(e.g., which shows two times as many tiles |

| | | |comparison, e.g., by using drawings and |with information presented in a graph or |as this set?). |

| | | |equations with a symbol for the unknown |word problem (e.g., an orange hat cost $3. A| |

| | | |number to represent the problem, |purple hat cost 2 times as much. How much | |

| | | |distinguishing multiplicative comparison |does the purple hat cost? [3 x 2 = p]). | |

| | | |from additive comparison. | | |

|Operations & Algebraic | | |4.OA.A.3 Solve multistep word problems posed|4.NO.2e2 Solve or solve and check one or two|Select the representation of manipulatives |

|Thinking | | |with whole numbers and having whole-number |step word problems requiring addition, |on a graphic organizer to show |

| | | |answers using the four operations, including|subtraction, or multiplication with answers |addition/multiplication equation; Match to |

| | | |problems in which remainders must be |up to 100. |same for representations of equations with |

| | | |interpreted. Represent these problems using | |equations provided (may be different |

| | | |equations with a letter standing for the | |objects but same configuration). |

| | | |unknown quantity. Assess the reasonableness | | |

| | | |of answers using mental computation and | | |

| | | |estimation strategies including rounding. | | |

|Number & Operations in |10% |40% |4.NBT.A.3 Use place value understanding to |4.NO.1j5 Use place value to round to any |Identify ones, tens, hundreds in bundled |

|Base Ten | | |round multi-digit whole numbers to any |place (i.e., ones, tens, hundreds, |sets – Similar/different with concrete |

| | | |place. |thousands). |representations (i.e., is this set of |

| | | | | |manipulatives (8 tens) closer to this set |

| | | | | |(a hundred) or this set (a ten)?). |

|Number & Operations— |30% | |4.NF.A.1 Explain why a fraction a/b is |4.NO.1m1 Determine equivalent fractions. |Equivalency: what is and what is not |

|Fractions | | |equivalent to a fraction (n × a)/(n × b) by | |equivalent; this may begin with |

| | | |using visual fraction models, with attention| |numbers/sets of objects: e.g., 3=3 or two |

| | | |to how the number and size of the parts | |fraction representations that are identical|

| | | |differ even though the two fractions | |(two pies showing 2/3). |

| | | |themselves are the same size. Use this | | |

| | | |principle to recognize and generate | | |

| | | |equivalent fractions. | | |

|Number & Operations— | | |4.NF.A.2 Compare two fractions with |4.NO.1n2 Compare up to 2 given fractions |Differentiate between parts and a whole. |

|Fractions | | |different numerators and different |that have different denominators. | |

| | | |denominators, e.g., by creating common | | |

| | | |denominators or numerators, or by comparing | | |

| | | |to a benchmark fraction such as 1/2. | | |

| | | |Recognize that comparisons are valid only | | |

| | | |when the two fractions refer to the same | | |

| | | |whole. Record the results of comparisons | | |

| | | |with symbols >, =, or , =, or ................
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