Try it yourself first — the explanation is most useful after you’ve attempted it.
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Toolkit + CCSS Solution
Understand
Restated: Carlos was born on Saturday, November 9, 2002. Day $0$ of his life is that Saturday. On what day of the week will day $706$ of his life fall?
Givens: Day $0$ (birth day) is a Saturday; We want the day of the week on day $706$; Answer choices: (A) Monday, (B) Wednesday, (C) Friday, (D) Saturday, (E) Sunday
Unknowns: The day of the week $706$ days after a Saturday
Understand
Restated: Carlos was born on Saturday, November 9, 2002. Day $0$ of his life is that Saturday. On what day of the week will day $706$ of his life fall?
Givens: Day $0$ (birth day) is a Saturday; We want the day of the week on day $706$; Answer choices: (A) Monday, (B) Wednesday, (C) Friday, (D) Saturday, (E) Sunday
Plan
Primary tool: #5 Look for a Pattern
Secondary: #9 Solve an Easier Related Problem
The week is a length-$7$ repetition cycle, which is the signature trigger for Tool #5 (Look for a Pattern). Once we see the cycle, the only thing that controls the answer is the remainder when $706$ is divided by $7$ — everything else is a multiple of $7$ that just lands back on Saturday. Tool #9 (Solve an Easier Related Problem) supports this: we replace $706$ with the nearby multiple of $7$ that is easy to handle ($700 = 7 \times 100$), solve that toy version in one line, and then add the small leftover.
Execute — Answer: C
#5 Look for a Pattern 4.OA.C.5Step 1
Name the cycle.
The days of the week repeat in a loop of length $7$.
So adding any multiple of $7$ to a Saturday gives a Saturday again.
This means we only care about $706 \bmod 7$ — the remainder after taking out as many full weeks as possible.
$$706 = 7q + r, \quad 0 \le r < 7$$
💡 Spotting the length-$7$ cycle turns a big day count into a small leftover count.
#9 Solve an Easier Related Problem 4.OA.A.3Step 2
Solve an easier version first.
Use the nearest multiple of $7$ below $706$, which is $700 = 7 \times 100$.
Day $700$ is exactly $100$ full weeks after birth, so day $700$ is the same weekday as day $0$ — a Saturday.
💡 The remainder $6$ is all the information the cycle needs to pick the weekday.
[1]
#5 4.OA.C.5Name the cycle. The days of the week repeat in a loop of length $7$. So adding a
[2]
#9 4.OA.A.3Solve an easier version first. Use the nearest multiple of $7$ below $706$, whic
[3]
#5 4.OA.C.5Walk forward the leftover $6$ days from Saturday. After day $700$ (Saturday): da
[4]
#5 4.OA.A.3Read off the answer. Day $706$ is Friday, which matches choice (C).
Review
Reasonableness: Check by going the other direction: $707 = 7 \times 101$, so day $707$ is exactly $101$ full weeks after birth — another Saturday. One day before Saturday is Friday, so day $706$ is Friday. Same answer (C). Either anchor ($700$ or $707$) gives the same Friday, which is the sign that the cycle is being used correctly.
Alternative: Tool #2 (Make a Systematic List) on a very small scale: list the seven possibilities for $706 \bmod 7$. Compute $706 \div 7 = 100$ remainder $6$. So shift Saturday forward by $6$ days using the weekday list Sat, Sun, Mon, Tue, Wed, Thu, Fri — landing on Friday, choice (C).
CCSS standards used (min grade 4)
4.OA.C.5 Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern that were not explicit in the rule itself (Recognizing the weekday cycle of length $7$ and using the rule "adding $7$ returns to the same weekday" to reduce day $706$ to a short walk from day $700$.)
4.OA.A.3 Solve multistep word problems posed with whole numbers, including problems in which remainders must be interpreted (Dividing $706$ by $7$ and interpreting the remainder $6$ as the number of weekday steps forward from Saturday.)
⭐ Weekdays repeat every $7$ days, so for any "how many days later" question, divide by $7$ and use only the remainder. $706 \div 7$ leaves $6$, so jump $6$ days forward from Saturday and land on Friday — answer (C).
⭐ Weekdays repeat every $7$ days, so for any "how many days later" question, divide by $7$ and use only the remainder. $706 \div 7$ leaves $6$, so jump $6$ days forward from Saturday and land on Friday — answer (C).
