Arizona 4th Grade End-of-Year Universal Math Screener

 4th Grade EOG End-of-Grade 4 Universal Math Screener based on the Arizona Mathematics Standards. This tool is designed to assess mastery across the five domains taught in 4th grade and to identify students’ readiness for 5th grade math.

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📊 Arizona 4th Grade End-of-Year Universal Math Screener

Domains Assessed:

1. Operations and Algebraic Thinking (OA)

2. Number and Operations in Base Ten (NBT)

3. Number and Operations—Fractions (NF)

4. Measurement and Data (MD)

5. Geometry (G)

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🧠 General Instructions:

• Total Questions: 40

• Time: 60–75 minutes

• Format: Multiple choice, short answer, and constructed response

• Tools: Paper/pencil, basic ruler, optional hundreds chart and base ten blocks

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🟩 1. Operations and Algebraic Thinking (OA)

Standards: 4.OA.A, 4.OA.B, 4.OA.C

Concepts Covered:

• Interpreting multiplication equations

• Solving multistep word problems using four operations

• Finding patterns and rules in number sequences

Sample Questions:

1. Solve: $4 \times ? = 36$

2. A bakery sells 3 types of cupcakes. Each type has 12 cupcakes. If each box can hold 6 cupcakes, how many boxes are needed to package all the cupcakes?

3. What is the next number in this pattern: 3, 6, 12, 24, ___?

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🟨 2. Number and Operations in Base Ten (NBT)

Standards: 4.NBT.A, 4.NBT.B

Concepts Covered:

• Understanding place value to 1,000,000

• Comparing and rounding multi-digit numbers

• Fluently adding, subtracting, and multiplying multi-digit numbers

• Dividing with remainders

Sample Questions: 4. Write 543,210 in expanded form.
5. Round 867,392 to the nearest ten thousand.
6. Solve: $7,653 + 3,248$
7. Multiply: $3 \times 426$
8. Divide: $984 \div 6$

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🟦 3. Number and Operations—Fractions (NF)

Standards: 4.NF.A, 4.NF.B, 4.NF.C

Concepts Covered:

• Equivalent fractions and comparing fractions

• Adding/subtracting fractions with like denominators

• Multiplying a fraction by a whole number

• Converting fractions to decimals (tenths and hundredths)

• Understanding decimal notation for fractions

Sample Questions: 9. Are $\frac{2}{3}$ and $\frac{4}{6}$ equivalent? Explain.
10. $\frac{5}{8} + \frac{2}{8} = ?$
11. Multiply: $3 \times \frac{1}{4}$
12. Convert $\frac{7}{10}$ to a decimal.
13. Order from least to greatest: $\frac{1}{2}, \frac{3}{4}, \frac{2}{5}$

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🟧 4. Measurement and Data (MD)

Standards: 4.MD.A, 4.MD.B, 4.MD.C

Concepts Covered:

• Solving problems involving measurement and conversion

• Using and interpreting line plots

• Understanding angles and measuring with a protractor

• Area and perimeter of rectangles

Sample Questions: 14. Convert 3 feet into inches.
15. Measure an angle with a protractor (include image).
16. A rectangle has a length of 6 in and width of 3 in. Find the perimeter and area.
17. A class chart shows the number of pets each student has: Use the data to complete a line plot.
18. If a pencil is 7.25 inches long, how long is it in centimeters?

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🟪 5. Geometry (G)

Standards: 4.G.A

Concepts Covered:

• Classifying geometric figures based on lines and angles

• Recognizing right, acute, obtuse angles

• Identifying lines of symmetry

Sample Questions: 19. Classify the following shape: quadrilateral with 2 pairs of parallel sides and 4 right angles.
20. Draw a shape with one line of symmetry.
21. Identify all the angles in a triangle as right, acute, or obtuse.
22. Which shapes have at least one pair of perpendicular lines?
23. Which of these shapes is a rhombus? (include image options)

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✅ Constructed Response/Performance Task (Choose 2 of 3)

24. Multi-step Problem Solving (all 4 operations):
    A farmer has 5 fields. Each field grows 238 tomato plants. How many plants in total? If each box holds 12 tomatoes and each plant produces 3 tomatoes, how many boxes are needed?

25. Fraction Problem with Visual Representation:
    Use fraction bars or number lines to compare $\frac{3}{4}$ and $\frac{5}{8}$. Which is greater? Justify your answer.

26. Measurement Application:
    A classroom is 24 feet long and 18 feet wide. What is the area in square feet? If 1 tile covers 2 sq ft, how many tiles are needed?

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📈 Scoring Rubric:

• Multiple Choice/Short Answer: 1 point each

• Constructed Response: 4 points each (accuracy, explanation, math vocabulary, visual if required)

• Total Possible Points: 50

• Performance Bands:

  • 45–50: Ready for 5th Grade Math

  • 35–44: Approaching Proficiency

  • 25–34: Partial Understanding

  • Below 25: Intensive Support Needed

Using Montessori Materials to Support 4th Grade Arizona Math Standards

1. Operations and Algebraic Thinking (OA)

Golden Beads & Stamp Game Application

Multiplication Equations (4.OA.A)

• Concrete: Use golden bead materials to physically build multiplication problems. For example, to solve 4 × ? = 36, students can lay out 4 rows and add golden beads until they reach 36, discovering they need 9 beads per row.
• Representational: Transfer to the stamp game where colored tiles represent different place values, making the abstract concept more visible.
• Abstract: Move to algorithm writing once conceptual understanding is solid.

Multistep Word Problems (4.OA.B)

• For the bakery problem (3 types × 12 cupcakes ÷ 6 per box):
  1. Concrete: Use bead bars to represent the 3 groups of 12 cupcakes
  2. Representational: Use stamp game to show division by 6
  3. Abstract: Write and solve the equation 36 ÷ 6 = 6 boxes

Number Patterns (4.OA.C)

• Use bead chains to physically represent growing number patterns
• The pattern 3, 6, 12, 24 doubles each time - students can build this using bead bars, then predict the next value (48)

2. Number and Operations in Base Ten (NBT)

Golden Bead & Place Value Application

Place Value to 1,000,000 (4.NBT.A)

• Concrete: Extension of golden bead decimal system with thousand cubes, hundred squares, ten bars, and unit beads
• For expanded form of 543,210:
  1. Represent with appropriate quantity of each place value material
  2. Physically separate materials to show 500,000 + 40,000 + 3,000 + 200 + 10

Operations with Multi-digit Numbers (4.NBT.B)

• Addition/Subtraction:

  • For 7,653 + 3,248, use golden beads to physically combine quantities, exchanging 10 units for 1 ten, etc.
  • Transfer to stamp game for more symbolic representation

• Multiplication:

  • For 3 × 426, use bead frames to show 3 groups of 426
  • Show regrouping with physical exchanges

• Division:

  • For 984 ÷ 6, use division board with skittles and beads
  • Physically distribute 984 (represented by beads) into 6 equal groups

3. Number and Operations—Fractions (NF)

Fraction Materials Application

Equivalent Fractions (4.NF.A)

• Concrete: Use fraction circles/insets to physically show that 2/3 and 4/6 take up the same amount of space
• Colored bead bars help visualize equivalent fractions (laying 2/3 beside 4/6)

Adding/Subtracting Fractions (4.NF.B)

• For 5/8 + 2/8:
  • Use fraction insets to physically combine the parts
  • Show that 5 eighths plus 2 eighths makes 7 eighths

Multiplying Fractions by Whole Numbers (4.NF.B)

• For 3 × 1/4:
  • Use fraction circles to show 1/4 three times
  • Demonstrate that this equals 3/4

Decimal Connections (4.NF.C)

• Use decimal board to show connection between fractions and decimals
• For converting 7/10 to 0.7, use decimal material to show equivalence

4. Measurement and Data (MD)

Practical Applications

Measurement Conversions (4.MD.A)

• Use Montessori measurement materials to physically show conversions
• For 3 feet to inches, use measurement chains/sticks to count 36 inches

Angles (4.MD.C)

• Use geometric cabinet materials to explore angles
• Metal insets help develop understanding of right, acute, obtuse angles

Area and Perimeter (4.MD.C)

• For rectangle problems:
  • Use Montessori area material to physically build rectangles
  • Count units around perimeter (18 inches)
  • Count square units for area (18 square inches)

5. Geometry (G)

Geometric Figures (4.G.A)

• Geometric cabinet provides hands-on experience with shapes
• Geometric solids allow exploration of 3D shapes
• For symmetry exploration, use mirror material with geometric shapes

Addressing Students with Numeracy Gaps

For students with number sense deficits:

1. Subitizing Development:

   • Start with number rods and spindle boxes to develop basic number sense
   • Use teen and ten boards to build understanding of place value
   • Practice quick recognition of quantities with golden bead materials

2. Progressive Sequence:

   • Begin with sensorial materials (pink tower, brown stair) before moving to mathematical concepts
   • Use number cards with golden beads to connect quantity to symbol
   • Move very gradually from concrete to abstract

3. Individualized Pacing:

   • Create stations where students work at their own level
   • Allow repeated practice with manipulatives until mastery
   • Provide recording sheets to document observations with materials

Sample Lesson Plan: Multi-digit Multiplication

Topic: 3 × 426 (from NBT standards)

Materials: Golden beads, place value cards, stamp game, pencil and paper

Progression:

1. Concrete (Golden Beads):

   • Build 426 with golden beads (4 hundreds squares, 2 tens bars, 6 unit beads)
   • Repeat to show 3 groups of 426
   • Combine all beads by place value
   • Exchange as needed (18 units = 1 ten + 8 units, etc.)
   • Count final result: 1,278

2. Representational (Stamp Game):

   • Set up 3 rows of 426 using colored stamps
   • Combine stamps by color/place value
   • Exchange as needed
   • Record result: 1,278

3. Abstract (Algorithm):

   • Write multiplication in vertical format
   • Connect each step to previous manipulative work
   • Emphasize place value during exchanges

Implementation Strategy

1. Assessment First: Use Montessori observation techniques to identify specific gaps in understanding

2. Small Group Rotation: Create stations with different manipulatives targeting specific standards

3. Connection to Singapore Math: Use manipulatives to build conceptual understanding before introducing Singapore Math bar modeling

4. Documentation: Have students keep math journals showing progression from concrete to abstract

By using these Montessori materials systematically, students will develop both procedural fluency and conceptual understanding, addressing the gaps in their mathematical foundation while meeting grade-level standards.

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Arizona 4th Grade Mathematics End-of-Year Comprehensive Screener

Purpose

This universal screener assesses 4th grade students' mastery of the Arizona Mathematics Standards across all five domains, providing data on student readiness for 5th grade mathematics.

Administration Guidelines

• Time: 60-90 minutes (may be divided into multiple sessions)
• Materials: Test booklet, answer sheet, pencil, ruler, scratch paper
• Accommodations: Provide as needed according to student IEPs or 504 plans
• Scoring: Each question is worth 1 point unless otherwise noted

Domain 1: Operations and Algebraic Thinking

Section A: Use the four operations with whole numbers to solve problems

1. Julia has 243 stickers. She wants to give each of her 9 friends an equal number of stickers. How many stickers will each friend receive?

2. Mario is arranging 156 chairs into equal rows of 12 chairs each. How many complete rows can he make?

3. A carpenter has a board that is 96 inches long. She needs to cut it into pieces that are 8 inches long. How many pieces will she have after cutting the board?

4. The school cafeteria served 1,256 meals last week. If they served the same number of meals each day for 4 days, how many meals did they serve each day?

5. Mrs. Chen bought 8 packages of notebooks. Each package contained 6 notebooks. She distributed all the notebooks equally among her 4 children. How many notebooks did each child receive?

Section B: Generate and analyze patterns

6. Look at this pattern: 5, 8, 11, 14, 17, ... What is the next number in the pattern?

7. Sophia created a pattern with tiles: Pattern 1: 3 tiles Pattern 2: 7 tiles Pattern 3: 11 tiles Pattern 4: 15 tiles How many tiles would be in Pattern 7?

8. Identify the rule for this pattern: 80, 72, 64, 56, ... What will be the next two numbers in the pattern?

9. Tyler created a pattern where he adds 5 and then subtracts 2. If he starts with 3, what are the first 5 numbers in his pattern?

10. Create a number pattern starting with 4 that increases by 6 each time. Write the first six numbers in your pattern.

Domain 2: Number and Operations in Base Ten

Section A: Generalize place value understanding for multi-digit whole numbers

11. Write the number 38,427 in expanded form.

12. Write the number two hundred six thousand, five hundred eighty-nine in standard form.

13. Round 67,385 to the nearest thousand.

14. What is the value of the digit 7 in the number 374,621?

15. Compare the numbers 45,328 and 45,283 using <, >, or =.

Section B: Use place value understanding and properties of operations to perform multi-digit arithmetic

16. Calculate: 5,384 + 2,956

17. Calculate: 8,000 - 3,647

18. Calculate: 625 × 14

19. Calculate: 1,656 ÷ 6

20. Calculate: 2,016 ÷ 24

21. Ms. Garcia's class collected 3,487 bottle caps in March and 2,958 bottle caps in April. How many bottle caps did they collect altogether?

22. The library has 9,253 books. If 2,675 books are checked out, how many books remain in the library?

Domain 3: Number and Operations—Fractions

Section A: Extend understanding of fraction equivalence and ordering

23. Circle the fraction that is equivalent to 3/4: a) 9/12 b) 6/9 c) 4/5 d) 5/8

24. Order these fractions from least to greatest: 2/3, 5/6, 1/2, 7/12

25. Compare the fractions 5/8 and 7/12 using <, >, or =.

26. Which fraction is equivalent to 6/8? a) 3/4 b) 4/6 c) 3/5 d) 9/10

Section B: Build fractions from unit fractions by applying and extending previous understanding of operations

27. Calculate: 2/5 + 1/5

28. Calculate: 7/8 - 3/8

29. Calculate: 3/4 + 2/8

30. Calculate: 5/6 - 1/3

31. Calculate: 3 × 2/5

32. What is 4 × 3/8?

33. Maria has 3/4 of a pizza. She eats 1/4 of the pizza. What fraction of the pizza does she have left?

Section C: Understand decimal notation for fractions, and compare decimal fractions

34. Write 7/10 as a decimal.

35. Write 23/100 as a decimal.

36. Write 0.85 as a fraction in lowest terms.

37. Compare 0.6 and 0.60 using <, >, or =.

38. Order these decimals from least to greatest: 0.8, 0.08, 0.85, 0.58

Domain 4: Measurement and Data

Section A: Solve problems involving measurement and conversion of measurements

39. Convert 5 kilometers to meters.

40. Convert 3,500 grams to kilograms.

41. Convert 6 liters to milliliters.

42. Mike ran a race in 6 minutes and 45 seconds. Jamal ran the same race in 405 seconds. Who finished first?

43. A recipe calls for 3/4 cup of flour. If you want to make 3 batches of the recipe, how much flour will you need?

Section B: Represent and interpret data

44. The table shows how many books each student read during summer vacation:

Student	Books Read
Alex	12
Bella	8
Carlos	15
Dina	9

Create a line plot to display this data.

45. The line plot shows the heights (in inches) of plants in a garden: X X X X X X X X X X X X X X X X 5 6 7 8 9

How many plants are there in total?

46. Using the line plot in question 45, what is the most common plant height?

Section C: Geometric measurement: understanding concepts of angle and measuring angles

47. An angle that measures exactly 90° is called a ____________ angle.

48. Estimate the measure of this angle: [Simple drawing of an acute angle approximately 30°]

49. If an angle measures 180°, it is called a ____________ angle.

50. A complete rotation measures how many degrees?

51. The measure of angle ABC is 45°. The measure of angle CBD is 65°. What is the measure of angle ABD?

Domain 5: Geometry

Section A: Draw and identify lines and angles, and classify shapes by properties of their lines and angles

52. Draw a line segment that is 3 inches long.

53. Draw an angle that measures approximately 45°.

54. Circle the figure that has exactly one pair of parallel sides: a) square b) triangle c) trapezoid d) rhombus

55. Identify the figure that has 4 sides of equal length and 4 right angles.

56. Classify this triangle as acute, right, or obtuse: [Simple drawing of a triangle with one angle greater than 90°]

57. A quadrilateral has 4 sides of equal length but no right angles. What is this shape called?

58. Circle all the figures that have at least one line of symmetry: a) equilateral triangle b) rectangle c) rhombus d) scalene triangle

59. Draw a line of symmetry on this figure: [Simple drawing of an isosceles triangle]

60. Identify the figure with these properties: 4 sides, opposite sides are parallel, all angles are right angles.

Answer Key

1. 27 stickers
2. 13 rows
3. 12 pieces
4. 314 meals per day
5. 12 notebooks per child
6. 20
7. 27 tiles
8. 48, 40 (subtract 8 each time)
9. 3, 8, 6, 11, 9
10. 4, 10, 16, 22, 28, 34
11. 30,000 + 8,000 + 400 + 20 + 7
12. 206,589
13. 67,000
14. 70,000
16. 8,340
17. 4,353
18. 8,750
19. 276
20. 84
21. 6,445 bottle caps
22. 6,578 books
23. a) 9/12
24. 1/2, 7/12, 2/3, 5/6
26. a) 3/4
27. 3/5
28. 4/8 or 1/2
29. 1 whole or 8/8
30. 1/2
31. 6/5 or 1 1/5
32. 1 1/2 or 3/2
33. 2/4 or 1/2
34. 0.7
35. 0.23
36. 17/20
37. =
38. 0.08, 0.58, 0.8, 0.85
39. 5,000 meters
40. 3.5 kilograms
41. 6,000 milliliters
42. Jamal (405 seconds = 6 minutes and 45 seconds, so they tied)
43. 2 1/4 cups
44. [Line plot with x-axis 8-15, marks at appropriate heights]
45. 20 plants
46. 7 inches
47. right
48. 30°
49. straight
50. 360°
51. 110°
52. [3-inch line segment]
53. [45° angle]
54. c) trapezoid
55. square
56. obtuse
57. rhombus
58. a, b, c
59. [Vertical line from top vertex to base midpoint]
60. rectangle

Scoring Guide

• Advanced: 54-60 points (90-100%)
• Proficient: 42-53 points (70-89%)
• Approaching: 30-41 points (50-69%)
• Below: 0-29 points (0-49%)

Domain Proficiency Analysis

Calculate points earned in each domain:

• Operations and Algebraic Thinking (Questions 1-10): __/10
• Number and Operations in Base Ten (Questions 11-22): __/12
• Number and Operations—Fractions (Questions 23-38): __/16
• Measurement and Data (Questions 39-51): __/13
• Geometry (Questions 52-60): __/9

Recommendations for Instruction

Based on domain scores:

• 90-100% in domain: Ready for 5th grade instruction in this domain
• 70-89% in domain: Ready with minor review needed
• 50-69% in domain: Targeted intervention recommended before 5th grade instruction
• Below 50% in domain: Intensive intervention required before 5th grade instruction