HavenHub Math • Edition 2 • Workbook

Unit 4: The Bridge

"I am the way, the truth, and the life." — John 14:6

The Navigator's Vocabulary Bank

Decompose: To break a number into two smaller parts. We decompose 5 into 2 and 3 to help an 8 become a 10!

Safe Harbor: The number TEN. It is the solid place we land before we jump to the final answer.

Bridge: A mental path that uses the Ten as a midpoint.

Near Double: Two numbers that are almost twins ($6$ and $7$). We use $6+6$ to solve them.

Compensation: Pretending a number is easy (like 10), then fixing it at the end.

Vault: The "Reserve Ten" we use for subtraction.

Navigator: A student who uses logic instead of fingers!

Lesson 4.1: The Stepping Stones (Making Ten)

Scribe's Hint: When you see a "Hungry" number like 8 or 7, look at his neighbor. Ask for a "Portion" to make a Ten. Once you stand on the Ten, the answer is just a small step away!

Part 1: Redeeming the Number
Break the second number to help the first number become a strong TEN.

1. $8 + 4 \implies (8 + 2) + $ ____ $=$ ____
2. $7 + 5 \implies (7 + 3) + $ ____ $=$ ____
3. $9 + 6 \implies (9 + 1) + $ ____ $=$ ____
4. $8 + 7 \implies (8 + 2) + $ ____ $=$ ____
5. $7 + 6 \implies (7 + 3) + $ ____ $=$ ____

Part 2: The Mental Bridge
Build the bridge in your mind. Write the Ten first, then the total.

6. $8 + 3 \implies 10 + $ ____ $=$ ____
7. $9 + 5 \implies 10 + $ ____ $=$ ____
8. $7 + 4 \implies 10 + $ ____ $=$ ____
9. $8 + 5 \implies 10 + $ ____ $=$ ____
10. Deep Thinking: If you add $8 + 2$, do you have a leftover part? (Yes/No)

Verification Node: The Short Bridge

Scenario: A student adds $8 + 5$. He takes 1 from the five to make the eight a nine. Then he adds the four leftover. ($9 + 4 = 13$).

The Rupture: Did he use the Bridge of Ten? Is a Nine as safe to stand on as a Ten? Explain why we always aim for the Ten.

Verdict:

Signet Challenge: Show a parent how to solve $8 + 6$ by moving two counters. Draw the "Jump" here.

Lesson 4.2: Twins + 1 (Near Doubles)

Scribe's Hint: Symmetry is speed! If you see two numbers that are neighbors (like 6 and 7), don't count them. Just double the smaller twin and add 1 for the "hat" friend!

Part 1: The Tag-Along Friend
Use the Double to solve the Near Double.

1. If $5 + 5 = 10$, then $5 + 6 =$ ____
2. If $6 + 6 = 12$, then $6 + 7 =$ ____
3. If $7 + 7 = 14$, then $7 + 8 =$ ____
4. If $8 + 8 = 16$, then $8 + 9 =$ ____
5. If $4 + 4 = 8$, then $4 + 5 =$ ____

Part 2: Finding the Foundation
Which Double helps you solve these? Write the Double fact first.

6. $9 + 8 \implies $ (____ + ____) $+ 1 =$ ____
7. $6 + 5 \implies $ (____ + ____) $+ 1 =$ ____
8. $3 + 4 \implies $ (____ + ____) $+ 1 =$ ____
9. $7 + 6 \implies $ (____ + ____) $+ 1 =$ ____
10. Advanced Logic: Can you solve $6 + 7$ by doubling the BIG twin? (____ + ____) $- 1 =$ ____

Verification Node: The Pattern of Twins

Truth: Near Doubles are always ODD numbers. Why? Because an even number (the double) plus 1 always makes an odd number!

Task: List three Near Double sums. Are they all odd?

Signet Challenge: Find two things in your house that are twins (like two shoes). Add a third thing. Show your mentor the "Double + 1" logic.

Lesson 4.3: Almost a Ten (Adding 9)

Scribe's Hint: The 9 is a "Greedy" number! He wants to be a Ten. Let him borrow 1 from his neighbor to become a Ten, then subtract 1 from the total to stay honest. Jump 10, back 1!

Part 1: The Jump and Step
Pretend the 9 is a 10, then correct the balance.

1. $9 + 4 \implies (10 + 4) - 1 =$ ____
2. $9 + 7 \implies (10 + 7) - 1 =$ ____
3. $9 + 2 \implies (10 + 2) - 1 =$ ____
4. $9 + 8 \implies (10 + 8) - 1 =$ ____
5. $9 + 5 \implies (10 + 5) - 1 =$ ____

Part 2: Fast Navigation
Solve these using the 9-trick in your mind. No writing the steps!

6. $9 + 3 =$ ____
7. $9 + 6 =$ ____
8. $9 + 1 =$ ____ (Wait, is this easier a different way?)
9. $9 + 9 =$ ____ (Twin Trick or 9-Trick?)
10. Mental Sovereignty: What is $99 + 5$? (Jump forward to 100, back 1!)

Verification Node: The Honesty Check

Truth: When we pretend 9 is 10, we are "borrowing" 1 from the Royal Bank of Math.

Task: If you add $9 + 6$ and get 16, what did you forget to do? Why is 16 a "false witness"?

Signet Challenge: Time yourself! How many seconds does it take to solve ten "+9" problems? Record your speed here:

Lesson 4.4: Taking from the Vault (Subtraction)

Scribe's Hint: When you have to pay a debt (subtract) and your "Pocket Ones" aren't enough, go to the Vault! Open the Ten-Bundle, pay the debt, and add what's left to your pocket ones.

Part 1: Breaking the Vault
Subtract from the 10 first, then add the leftovers.

1. $13 - 8 \implies (10 - 8) + 3 =$ ____
2. $15 - 7 \implies (10 - 7) + 5 =$ ____
3. $12 - 9 \implies (10 - 9) + 2 =$ ____
4. $11 - 6 \implies (10 - 6) + 1 =$ ____
5. $14 - 8 \implies (10 - 8) + 4 =$ ____

Part 2: The Scribe's Reserve
Choose the best path. Take from the Ten!

6. $16 - 7 =$ ____
7. $12 - 4 =$ ____
8. $15 - 9 =$ ____
9. $11 - 3 =$ ____
10. Mental Challenge: If you have 14 and take away 4, do you need to open the Vault? (Yes/No)

Verification Node: The Backwards Walk

Scenario: A student solves $13 - 8$ by counting back: "12, 11, 10, 9, 8, 7, 6, 5."

The Rupture: Why is this dangerous? What happens if the student skips a number in the dark? Explain why the Vault is safer.

Signet Challenge: Explain to a parent why $10 - 7$ is the first step to solving $13 - 7$. Use sticks to show the "Exchange."

Lesson 4.5: The Rhythm of Grace (Agility)

Scribe's Hint: You have grown your wings! The Bridge, the Twins, the Greedy Nine, and the Vault are your wings. Choose the best wing for each problem and fly across the numbers!

Part 1: The Navigator's Choice
Solve each problem and name the "Wing" (Strategy) you used.

1. $8 + 5 =$ ____ Strategy: ____
2. $6 + 7 =$ ____ Strategy: ____
3. $9 + 4 =$ ____ Strategy: ____
4. $12 - 8 =$ ____ Strategy: ____
5. $7 + 8 =$ ____ Strategy: ____

Part 2: The Harvest Tally
Solve these faster and faster. Trust the patterns!

6. $9 + 9 =$ ____
7. $15 - 6 =$ ____
8. $7 + 4 =$ ____
9. $8 + 9 =$ ____
10. $14 - 5 =$ ____
11. $13 - 6 =$ ____
12. $11 - 8 =$ ____
13. Final Flight: $9 + 8 + 1 =$ ____ (Hint: Can you make a Ten first?)

Verification Node: The God of Patterns

Scripture: "He telleth the number of the stars; he calleth them all by their names." (Psalm 147:4)

Truth: God uses patterns to keep the universe in order. When you use a strategy, you are aligning your mind with His creation.

Task: Draw a picture of a bridge crossing a river. Label the rocks with the numbers 8, 10, and 13.

Unit 4 Review: The Navigator's Final Course

"Faith is the substance of things hoped for, the evidence of things not seen."

Part 1: Identify the Best Path
Which strategy is best? (Bridge, Twins, 9-Trick, or Vault?)

1. $9 + 7$: ____
2. $8 + 5$: ____
3. $7 + 8$: ____
4. $14 - 6$: ____

Part 2: The Mental Jump
Solve these in your mind as fast as you can!

5. $9 + 2 =$ ____
6. $8 + 4 =$ ____
7. $6 + 5 =$ ____
8. $11 - 7 =$ ____
9. $9 + 9 =$ ____
10. Mental Jump: $8 + 8 =$ ____
11. Mental Jump: $7 + 7 =$ ____
12. The Big Finish: Explain to your mentor why the number 10 is the "Safe Harbor."

Parent Mentor Guide: The Heart of Unit 4

The Goal: This unit is about Efficiency. We want the student to move away from fingers and toward mental visualization. If they struggle, return to the physical Ten-Frame for a few days.

Key Strategies to Reinforce:

The Spiritual Bridge: Remind your child that Jesus is the Bridge who makes our way easy. Math is a way to practice finding the path that God has provided for us!

The Navigator's Final Vow

"I, ____________________________, a Navigator of the King's Abundance, promise to use the Bridge of Ten with excellence. I will trust the patterns, honor the portions, and walk across the numbers with peace and speed. Hallelujah!"

Student Navigator Signature

UNIT 4 COMPLETE!

You have reached the Safe Harbor.

GLORIA IN EXCELSIS DEO!

Certificate of Navigation

This certifies that

Has successfully crossed Unit 4: The Bridge

And has proven themselves to be a Master of Mental Strategies and Pattern Flow.

Mentor Signature

Date

Appendix: Extra Navigator Practice

Use your strategies to fill the table. No fingers allowed!

Problem Strategy Used Answer
$8 + 6$
$9 + 5$
$7 + 8$
$14 - 9$
$6 + 5$
$12 - 7$
$9 + 8$
$15 - 8$
$7 + 4$
$11 - 5$
$8 + 9$
$13 - 7$