Summit Math Toolkit Reference Sheet
4th Grade Math Support
Summit Math Toolkit
Use this reference sheet during your assessment!
Tool 1: Place Value Chart (Whole Numbers & Decimals)
Millions to Hundredths
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
.
Tenths
Hundredths
1,000,000
100,000
10,000
1,000
100
10
1
.
0.1
0.01
Moving left makes a digit 10 times bigger. Moving right makes it 10 times smaller (1/10 of the value).
Tool 2: Fraction Bars (Comparing & Equivalents)
Equivalence Tool
1
1 Whole
1/2
1/2
1/2
1/3
1/3
1/3
1/3
1/4
1/4
1/4
1/4
1/4
1/6
1/6
1/6
1/6
1/6
1/6
1/6
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
Equivalent fractions represent the same total length! (For example, look how 1/2 lines up exactly with 2/4 and 4/8).
Tool 3: Key Vocabulary & Word Problem Cue Cards
Operation Clues
Addition & Subtraction
SUM / TOTAL: Combine groups together (+).
DIFFERENCE / COMPARE: Find how they differ (-).
Multiplication & Division
PRODUCT / TIMES AS MANY: Equal groups together (×).
QUOTIENT / SHARE EQUALLY: Split into groups (÷).
Area & Perimeter
PERIMETER: Distance around outside. Add all sides.
AREA: Space inside. Multiply Length × Width.
Fractions & Decimals
NUMERATOR: Top number. Parts being counted.
DENOMINATOR: Bottom number. Total equal pieces.
Keep this sheet handy on your desk during the assessment! Summit Math Milestone
Summit Math Assessment Worksheet
Student Assessment
Summit Math Milestone
Name
Date
Part 1: Multi-Digit Arithmetic & Place Value
Q1. In the number 54,230, the digit 5 is in the ten-thousands place. In the number 5,230, the digit 5 is in the thousands place. How many times larger is the value of the 5 in 54,230 compared to the 5 in 5,230?
A 2 times larger
B 10 times larger
C 100 times larger
D 1,000 times larger
Q2. Complete the missing forms of the number 308,415.
Standard Form
Expanded Form
Word Form
308,415
Q3. Solve the division problem below. Show your work step-by-step.
Divide: 827 ÷ 6 Final Quotient & Remainder: ___________________
SHOW YOUR WORK HERE
Q4. Multiply the numbers below. Show all partial products.
Multiply: 43 × 26 Final Product: ___________________
SHOW YOUR WORK HERE
Summit Math Milestone • Grade 4 Assessment Page 1 of 3
Student Assessment
Summit Math Milestone
Section B
Part 2: Fractions & Decimals
Q5. Compare the two fractions shown below. Choose the correct comparison symbol.
3/8
< > =
5/8
A 3/8 > 5/8
B 3/8 < 5/8
C 3/8 = 5/8
Q6. Solve the fraction addition and subtraction equations below.
Part A: Addition
3/10 + 4/10 = ______
Part B: Subtraction
7/8 - 2/8 = ______
Q7. Which decimal value represents the same amount as the fraction 45/100?
A 4.5
B 0.45
C 0.045
D 45.0
Q8. Compare the two decimals below using <, >, or =. Show or explain your reasoning using a model, place value, or equivalent fractions.
Decimal Comparison: 0.6 ________ 0.58
SHOW YOUR WORK OR EXPLAIN HERE
Summit Math Milestone • Grade 4 Assessment Page 2 of 3
Student Assessment
Summit Math Milestone
Section C
Part 3: Area, Perimeter & Scaffolded Real-World Problems
Q9. Farmer Brown is building a rectangular fence for his sheep. The length of the fence is 12 meters and the width is .
Summit Math Answer Key
Teacher Resources
Summit Math Answer Key
Grading Guide & Rubric Included
Part 1 Solutions: Arithmetic & Place Value (Q1 - Q4)
Q1. Value of 5 in 54,230 vs 5,230 [1 Point]
Correct Answer: B (10 times larger)
Explanation: The 5 in 54,230 represents 50,000. The 5 in 5,230 represents 5,000. Since \(5,000 \times 10 = 50,000\), it is exactly 10 times larger.
Q2. Number Representations (308,415) [2 Points]
Expanded Form (1pt): \(300,000 + 8,000 + 400 + 10 + 5\)
Word Form (1pt): Three hundred eight thousand, four hundred fifteen.
Q3. Division (827 ÷ 6) [2 Points]
Correct Answer: 137 R 5 (or \(137\frac{5}{6}\))
Steps: 1. Divide \(8 \div 6 = 1\), remainder 2. Bring down 2.
2. Divide \(22 \div 6 = 3\), remainder 4. Bring down 7.
3. Divide \(47 \div 6 = 7\), remainder 5.
Award 1 point for correct process with calculation error, 2 points for fully correct answer.
Q4. Multiplication (43 × 26) [2 Points]
Correct Answer: 1,118
Steps: Multiply units: \(43 \times 6 = 258\). Multiply tens: \(43 \times 20 = 860\).
Add partial products: \(258 + 860 = 1,118\).
Award 1 point for correct process with calculation error, 2 points for fully correct answer.
Part 2 Solutions: Fractions & Decimals (Q5 - Q6)
Q5. Fraction Comparison [1 Point]
Correct Answer: B (3/8 < 5/8)
Explanation: Denominators are identical, so compare the numerators: \(3 < 5\). The model visually reinforces that 5 colored parts out of 8 is greater than 3 colored parts.
Q6. Fraction Addition & Subtraction [2 Points]
Part A: Addition (1pt) = 7/10 (Keep denominator, add numerators: \(3 + 4 = 7\))
Part B: Subtraction (1pt) = 5/8 (Keep denominator, subtract numerators: \(7 - 2 = 5\))
Summit Math Milestone • Teacher Answer Key Page 1 of 2
Teacher Resources
Summit Math Milestone Key
Section B & C Solutions
Part 2 Continued: Fractions & Decimals (Q7 - Q8)
Q7. Fraction to Decimal (45/100) [1 Point]
Correct Answer: B (0.45)
Explanation: "45 hundredths" is written as 0.45. Options A (4.5) and D (45.0) are whole-number scale values, and C (0.045) is 45 thousandths.
Q8. Decimal Comparison (0.6 vs 0.58) [2 Points]
Correct Answer: 0.6 > 0.58
Students should write that 0.6 is equivalent to 0.60 (60 hundredths). Comparing 60 hundredths to 58 hundredths shows that 60 hundredths is greater (\(0.60 > 0.58\)).
