A comprehensive curriculum mapping, planning, and assessment suite for 4th Grade Bridges Math, fully aligned with Common Core and California State Standards (CCSS-M / CA Common Core). Includes a year-long scope and sequence, weekly and daily planning templates, and an assessment tracker.
Directions: Record students' scores or achievement levels (EM, DV, PR, AD) for each of the core Bridges Unit Assessments below. Use the final columns to track the crucial diagnostic benchmark scores across the school term.
Student Name
U1
U2
U3
U4
Base
U5
U6
U7
Final
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Roster Key: Mark grades or mastery standards (EM, DV, PR, AD) to dynamically track interventions and workshop group setups.
Pacing Guidelines: Aim to complete assessments within 2 days of completing each corresponding Bridges Unit.
Unit 2 Teacher Setup: Cut and organize ratio tables matching mats. Introduce daily metric estimation checks inside the October Number Corner routine to scaffold ratio scaling calculations.
Unit 3 Teacher Setup: Prepare fraction cards and overhead decimal transparent grids. Connect the daily decimal cards within Number Corner to establish a base-ten understanding before the summative test.
D4: Session 4 - Filling multi-unit ratio scaling tables
D5: Session 5 - Metric Conversions Quiz Check
WEEK 4: Problem Solving CCSS: 4.OA.3
D1: Session 1 - Balancing standard algorithms scales
D2: Session 2 - Real-world measurement word stories
D3: Session 3 - Checking estimations of complex sums
D4: Session 4 - Practice test and review workbook
D5: Session 5 - Unit 4 Formal Post-Assessment
Unit 4 Teacher Setup: Prepare place-value charts and meter scales. Work Place "Summit Climbers" must be introduced early on Day 5 of Week 1 to sustain computational automaticity.
Unit 5 Teacher Setup: Organize geometric pattern blocks and hand-held mirrors. The Daily Number Corner Calendar Collector tracking angles will reinforce measuring precision prior to Week 4 checks.
Unit 6 Teacher Setup: Prepare ruler rules and fractional plot charts. Students must play "Double Conquest" starting in Week 1 to master double-digit partial product structures.
Unit 7 Teacher Setup: Prepare coordinate pattern grids and ledger sheets. Daily Calendar coordinate graphing will establish coordinate pair skills prior to the final module.
Unit 8 Teacher Setup: Collect grid paper card stocks and glue sticks. Daily Number Corner solid metrics challenges will support the 3D construction phase during Week 4.
2. Investigation: Let students explore making all possible rectangles for 24 tiles. Instruct: "Draw your arrays in your grid journals and label the dimensions (e.g. 3 x 8, 4 x 6). Write down the factor list of 24 on your board."
3. Reflection: "What makes 24 a composite number instead of prime? Correct, it has more than two factors."
U2, W1, D3: Partial Products Area Models 4.NBT.5
Objectives & Materials:
Solve 12 x 15 using area models. Connect to partial products.
Prep: Colored markers, grid boards.
Instructional Script:
1. Launch: Write "12 x 15" on the board. Say: "We don't want to add 15 twelve times. How can we partition 12 and 15 into tens and ones to make this easier?"
2. Investigation: Sketch a rectangle. Partition sides into (10+2) and (10+5). Script: "Calculate the area of each quadrant. We have 10x10=100, 10x5=50, 2x10=20, and 2x5=10. What is our sum? 100+50+20+10 = 180."
3. Reflection: "How do these four quadrant values connect to partial products? They represent the segments of the area model."
U3, W2, D1: Comparing Fractions via 1/2 Benchmark 4.NF.2
Focus & Prep:
Compare 3/8 and 4/6 using half as a baseline scale. Prep: Fraction strip sets.
Launch: "If you have eaten 3/8 of a pizza, have you eaten more or less than half? Why? Yes, because half of 8 is 4."
Investigation: Have students place 3/8 strip and 4/6 strip against a 1/2 strip block. Ask: "Since 3/8 is less than 1/2, and 4/6 is greater than 1/2, what comparison statement can we write? Right, 3/8 < 4/6."
U4, W2, D3: Subtraction Algorithms over Zeroes 4.NBT.4
Focus & Prep:
Borrow over zero column digits. Prep: Place-value block mats, markers.
Launch: Write "4,005 - 1,428" vertically. "How can we borrow from the tens if it's a zero? How does the thousands place help?"
Investigation: Model decomposition step-by-step: borrow 1 thousand (leaves 3), make 10 hundreds, borrow 1 hundred (leaves 9) to make 10 tens, borrow 1 ten (leaves 9) to make 15 ones. Calculate: 15-8=7, 9-2=7, 9-4=5, 3-1=2. Sum is 2,577.
U5, W1, D3: Aligning Protractors Bases 4.MD.6
Focus & Prep:
Measure adjacent angle intersections with protractors. Prep: Plastic protractors.
Launch: "Why are there two numbers on the protractor scale? How do we know whether to read 50 degrees or 130 degrees?"
Investigation: "First, classify the angle. Is it acute? If yes, it MUST be less than 90, so read the smaller scale. Align the origin hole with the vertex ray."
Calculate 136 ÷ 4 using partial quotients. Prep: Whiteboards, ratio grids.
Launch: "Think about factors of 4. What are some easy multiples we can subtract from 136? Can we subtract 4 x 10? What about 4 x 30?"
Investigation: Write vertical column. Subtract 4 x 30 = 120 (leaves 16). Ask: "What's left? 16. How many 4s are in 16? 4. Write 4. Add partial quotients: 30 + 4 = 34."
U7, W3, D2: Fraction Whole-Number Scaling 4.NF.4b
Focus & Prep:
Calculate 4 x 2/3 as integer scaling multiples. Prep: Number lines worksheets.
Launch: "If we have 4 bags of apples and each weighs 2/3 of a pound, how can we calculate the total weight without standard equations?"
Investigation: Model 4 hops of 2/3 along a fraction number line: 2/3, 4/3, 6/3, 8/3. Show that 8/3 is equivalent to 2 whole integers and 2/3.
U8, W2, D1: Area of Safety Buffers 4.MD.3
Focus & Prep:
Map dimensions of a swing zone safety buffer. Prep: Blueprint grid boards.
Launch: "If a swing set is 10 x 6 feet, we can't place a sandbox right next to it. We need a 6-foot safety buffer all around. How does that change our area?"
Investigation: Draw new dimensions on blueprints: add 6 ft to all sides. (Width is 10+12=22, Length is 6+12=18). Solve for Area: 22 x 18 = 396 sq. feet.
Problem 2: Is 4 a factor of 18? Explain why or why not.
Bridges Curriculum Navigator • Session Plans Page 1 of 5
Unit 1 • Week 1 • Session 2 • Comprehensive Lesson Plan
Session 2: Arrays & Dimensions
Core Target: 4.OA.4 • Math Practices: SMP.4 (Model with mathematics), SMP.6 (Attend to precision)
Day 2
Teacher Background & Model focus Visualizing multiplication as a physical area grid is the core foundation for multi-digit multiplication. When drawing rectangular dimensions, enforce consistent orientation rules (rows × columns) to build spatial consistency.
1. Detailed Session Launch (10 Minutes)
Distribute square colored tiles to pairs. Project a 1-inch square grid on the front whiteboard.
Detailed Teacher Script: "We have 12 square blocks. Arrange them so they make a perfect rectangle. Make sure there are no gaps or sticking-out blocks. How many rows do you have? How many columns? Some pairs made 2 rows of 6. Let's sketch that. This rectangle's dimensions are 2 by 6. Its area is 12. What other dimensions can we make?"
Sketch the arrays on the projected grid: 1 × 12 (long bar), 2 × 6, 3 × 4. Write: "The side dimensions represent the factor pairs."
Instruct students to open their grid paper notebooks. They will discover and color all possible rectangular area configurations for **16** and **18**.
Investigation Guidelines & Board Math:
Problem 1: Draw Area 16. Say: "Let's draw. Row count 1 × column count 16. Color it yellow. Next, row count 2. How many columns? 8. Color it orange. Next, row count 3. Can we make a perfect rectangle of 16 with 3 rows? No, \( 3 \times 5 = 15 \) and \( 3 \times 6 = 18 \). Skip 3. Row count 4? Yes, 4 columns. Color it red. Label side lengths."
Problem 2: Analyze Squares. Ask: "What makes the 4 × 4 array special?" (It forms a perfect square). Explain that 16 is a **square number** because it can form a square array with identical integer side dimensions.
3. Differentiation & Active Work Places (13 Minutes)
Intervention (Tier 2) Limit target product to 8 and 12. Guide student fingers to trace rows and write down multiplication labels.
On-Level Focus Draw and color all array configurations for 20 and 24. Record all dimensions in journals.
Extension Tasks Determine how many different arrays can be made for 36. Label the side lengths of the square layout.
Session 2: Daily Student Practice Problems
Problem 1: Sketch two different rectangular arrays for the product 10 on grid paper.
Problem 2: If an array has an area of 14, and one side length is 2, what is the other side?
Bridges Curriculum Navigator • Session Plans Page 2 of 5
Unit 1 • Week 1 • Session 3 • Comprehensive Lesson Plan
Session 3: Finding Factor Pairs
Core Target: 4.OA.4 • Math Practices: SMP.5 (Use appropriate tools strategically), SMP.7 (Look for structure)
Day 3
Teacher Background & Method Focus To ensure students find *every* factor of a number without random guessing, introduce the "Systematic Division Test." By constructing T-Charts starting at 1 and testing each consecutive number, students build an elegant mathematical testing algorithm.
1. Detailed Session Launch (10 Minutes)
Write a large 24 on the front board. Ask the students: "How do we know we found *every* factor and didn't miss one?"
Detailed Teacher Script: "We start at 1. We check 1, then 2, then 3, then 4, and so on. Let's draw a vertical T-Chart with 24 at the top. Let's test: Does 1 divide 24? Yes, 24 times. Write 1 on the left, 24 on the right. Does 2 divide 24? Yes, 2 is even, so 12 times. Write 2 and 12. Does 3 divide 24? Yes, \( 3 \times 8 = 24 \). Write 3 and 8. What about 4? Yes, \( 4 \times 6 = 24 \). Write 4 and 6. Does 5 divide 24? No! Draw a small dot next to 5."
"Next is 6. But wait! 6 is already on our right side! Once we reach a number already written, we stop! We are done."
Instruct students to draw T-Charts on their dry-erase lapboards for **30** and **36**.
Step-by-Step T-Chart Checking Protocol:
Problem 1: Test 30. Ask: "Is 30 even? Yes, so 2 divides it (\( 2 \times 15 \)). Does 3 divide it? Yes (\( 3 \times 10 \)). Does 4? No, mark a dot next to 4. Does 5? Yes, ends in 0, so \( 5 \times 6 \). Next is 6, which is already listed. Stop! Our factors are 1, 2, 3, 5, 6, 10, 15, 30."
Problem 2: Error Analysis. Write a fake T-Chart for 18 showing: (1x18, 3x6). Ask: "What did I miss?" (2x9). Teach them to inspect their T-Charts to ensure no gaps exist in their numbers checklist.
3. Differentiation & Active Work Places (13 Minutes)
Intervention (Tier 2) Limit numbers to under 15. Check numbers one-by-one by counting out cubes into equal cups.
On-Level Focus Create T-Charts for products 25, 27, and 32 in math journals. Identify factors in order.
Extension Tasks Build T-Charts for complex composite products 48 and 64. Identify which has an odd number of factors.
Session 3: Daily Student Practice Problems
Problem 1: Complete this systematic T-Chart for the number 21:
1 × _____ • 3 × _____
Problem 2: Find all factor pairs for the number 25 using a T-chart.
Bridges Curriculum Navigator • Session Plans Page 3 of 5
Unit 1 • Week 1 • Session 4 • Comprehensive Lesson Plan
Teacher Background & Conceptual Focus A prime number represents a quantity that can only be organized into a single line array (1 × n). Enforce the definition of prime: **exactly two distinct factors** (1 and itself). This clears up the common misconception that 1 is prime (it only has 1 factor).
1. Detailed Session Launch (10 Minutes)
Give Student A exactly 7 plastic block tiles and Student B exactly 8 tiles.
Detailed Teacher Script: "Arrange your blocks into a perfect solid rectangle. Student B made a 2 × 4 block array and a 1 × 8 array. Student A, what about you? Can you make anything besides a single long 1 × 7 row? No! 7 is unique. Its only factors are 1 and 7. Since it has exactly two factors, 7 is a Prime Number. 8 has more than two factors (1, 2, 4, 8), making it a Composite Number."
2. Problems & Investigations: Classification and Proofs (30 Minutes)
Have students work in pairs with number tokens from 1 to 20. They will construct T-Charts to classify each.
Guided Sort and Discussion Prompts:
Step 1: Check 11 and 15. Have student pairs build T-Charts. "Factors of 11: 1, 11 (Prime). Factors of 15: 1, 3, 5, 15 (Composite)." Ask: "Both end in odd digits. Does being odd mean a number is always prime?" (No, 15 is odd but composite).
Step 2: Check 2. T-chart of 2 shows only 1 and 2. Ask: "Is 2 prime? Yes! It is the only even prime number because every other even number is divisible by 2."
3. Differentiation & Active Work Places (13 Minutes)
Intervention (Tier 2) Use a multiplication matrix. Color-code products that do *not* appear inside the internal body columns (besides row 1); these are prime.
On-Level Focus Sort number cards 1-25. Record factor count lists for prime selections.
Extension Tasks Investigate the number 2. Prove why 2 is the *only* even prime number in mathematics.
Session 4: Daily Student Practice Problems
Problem 1: Circle the prime numbers in this list:
5, • 9, • 13, • 15, • 19
Problem 2: Explain why 12 is a composite number. How many factors does it have?
Bridges Curriculum Navigator • Session Plans Page 4 of 5
Unit 1 • Week 1 • Session 5 • Comprehensive Lesson Plan
Session 5: Factor Rainbow Maps
Core Target: 4.OA.4 • Math Practices: SMP.4 (Model with math), SMP.6 (Attend to precision)
Day 5
Teacher Background & Graphic Organization The "Factor Rainbow" is a spatial self-check tool. When students list factors in ascending order, linking the outer pairs with arches should form a symmetric nest of arcs.
1. Launch & Group Investigation (15 Minutes)
Write the factor list of 20 on the board: **1, 2, 4, 5, 10, 20**. Script: "We connect the outer limits: 1 to 20. Then 2 to 10. Then 4 to 5. These links form a perfect rainbow arc structure!"
