אני צריכה לוח זמנים קצת יותר גמיש, כי בימי שלישי אני לוקחת את הילדים לבית הספר.

Because the speaker is female.

In Hebrew, verbs in the present tense and words like צריך / צריכה agree with gender:

• אני צריך = I need / I am in need of (male speaker)
• אני צריכה = I need / I am in need of (female speaker)

Likewise:

• אני לוקח = I take (male speaker)
• אני לוקחת = I take (female speaker)

So this sentence is being said by a woman.

Not exactly in the same way as English need.

Hebrew often expresses need with the word צריך / צריכה / צריכים / צריכות, which behaves like an adjective meaning something like in need of / needing.

So:

• אני צריכה לוח זמנים... literally feels like I am needing a schedule...
• In natural English, we simply say I need a schedule...

This is a very common Hebrew pattern.

Literally, לוח זמנים is something like board of times or table of times, but in actual usage it means:

• schedule
• timetable
• sometimes calendar or agenda, depending on context

It is a fixed expression, so learners should memorize it as one unit:

• לוח = board / chart / table
• זמנים = times

Together: לוח זמנים = schedule

This is the normal Hebrew order for a little more flexible:

• קצת = a little / a bit
• יותר = more
• גמיש = flexible

So:

• קצת יותר גמיש = a bit more flexible

Hebrew usually places these words before the adjective they modify:

• יותר גדול = bigger / more big
• קצת יותר נוח = a bit more comfortable
• קצת יותר גמיש = a bit more flexible

Also note that גמיש is masculine singular here because it describes לוח זמנים, which is masculine singular.

Because גמיש describes לוח זמנים, not אני.

Agreement depends on the noun being described:

• לוח זמנים is masculine singular
• so the adjective must also be masculine singular: גמיש

If the noun were feminine, the adjective would change:

• תוכנית גמישה = a flexible plan

So the speaker’s gender affects צריכה and לוקחת, but גמיש agrees with לוח זמנים.

בימי שלישי means on Tuesdays or on Tuesday(s) regularly.

Here is the difference:

• ביום שלישי = on Tuesday (one specific Tuesday, or sometimes this Tuesday depending on context)
• בימי שלישי = on Tuesdays (habitually, every Tuesday / Tuesdays in general)

This is a very common pattern in Hebrew:

• בימי ראשון = on Sundays
• בימי שני = on Mondays
• בימי שלישי = on Tuesdays

Literally, בימי שלישי is something like on the days of Tuesday, but the natural meaning is on Tuesdays.

לוקחת is the present tense, feminine singular form of the verb לקחת (to take).

Here are some present-tense forms:

• לוקח = taking / take (masculine singular)
• לוקחת = taking / take (feminine singular)
• לוקחים = taking / take (masculine plural or mixed group)
• לוקחות = taking / take (feminine plural)

With אני, the present tense can often be translated in more than one way in English:

• אני לוקחת את הילדים לבית הספר
  = I take the children to school = I am taking the children to school
  The wider context decides which sounds best.

Here, because of בימי שלישי, the habitual meaning I take is the natural one.

את marks a definite direct object.

In this sentence:

• אני לוקחת = I take
• את הילדים = the children

Hebrew uses את before a direct object when that object is definite, for example:

• has ה־ (the)
• is a proper name
• has a possessive like my, your, etc.

Examples:

• אני רואה את הילד = I see the boy
• אני רואה את דני = I see Danny
• אני רואה את הילדים שלי = I see my children

But:

• אני רואה ילד = I see a boy
  No את, because the object is indefinite.

So את הילדים means the children as a definite object.

Literally, it means the children.

However, in context, Hebrew often uses the children where English might naturally say my children, especially when the relationship is obvious.

So this sentence could mean:

• I take the children to school
• and in real-life context, probably I take my children to school

If the speaker wanted to be fully explicit, they could say:

• אני לוקחת את הילדים שלי לבית הספר = I take my children to school

Because ל־ is very commonly used to mean to when showing destination.

So:

• לבית הספר = to school / to the school

Hebrew often prefers ל־ for movement toward a place:

• אני הולך לבית = I’m going home / to the house
• היא נוסעת לעבודה = She is traveling to work
• אני לוקחת את הילדים לבית הספר = I take the children to school

You can sometimes use אל for to / toward, but ל־ is often more natural in everyday Hebrew.

Because בית הספר is a construct chain (סמיכות), a very common Hebrew structure.

In a construct chain:

• the first noun changes form or stays in a special linked form
• definiteness is usually shown on the second noun

So:

• בית ספר = a school
• בית הספר = the school

Even though only הספר has ה־, the whole phrase becomes definite.

Then when you add ל־:

• ל + בית הספר = לבית הספר

This whole phrase means to the school, though in English we often simply say to school.

כי means because.

It introduces the reason:

• אני צריכה לוח זמנים קצת יותר גמיש = I need a slightly more flexible schedule
• כי... = because...
• בימי שלישי אני לוקחת את הילדים לבית הספר = on Tuesdays I take the children to school

So the second clause explains why the speaker needs a more flexible schedule.

In the present tense, Hebrew normally does not use a separate present form of to be.

So Hebrew says:

• אני עייפה = I am tired
• אני שמח = I am happy
• אני צריכה = I need / I am needing
• אני לוקחת = I take / I am taking

There is no present-tense word corresponding to English am / is / are in ordinary sentences like this.

That is completely normal in Hebrew.