Bibi alipenda kutuambia methali, lakini leo mwalimu alitufundisha nahau mpya.

Because ali- contains the markers for a singular human subject and past tense.

• a- = he/she
• -li- = past tense

So:

• a-li-penda = he/she liked
• a-li-tu-fundisha = he/she taught us

In this sentence, both bibi and mwalimu are singular people, so the verb uses the same subject pattern.

tu means us.

It is an object marker, and in Swahili object pronouns are often built directly into the verb.

• ku-tu-ambia = to tell us
• a-li-tu-fundisha = he/she taught us

So instead of using a separate word for us, Swahili often places it inside the verb.

Because after alipenda (liked), the next verb needs to be in the infinitive form, like English to tell.

• ku- = the infinitive marker, like English to
• ku-tu-ambia = to tell us

So:

• alipenda kutuambia = she liked to tell us

Without ku-, it would not be the normal infinitive form here.

It can be broken down like this:

• ku- = to
• tu- = us
• -ambia = tell / say to

So kutuambia literally means to-us-tell or more naturally to tell us.

This is very common in Swahili: several pieces of meaning are packed into one verb.

Because alitufundisha is the main finite verb of the second clause, not an infinitive.

Compare:

• alipenda kutuambia = she liked to tell us
  
  • kutuambia is an infinitive after liked
• mwalimu alitufundisha = the teacher taught us
  
  • this is a complete past-tense verb

So ku- appears on infinitives, but not on ordinary past-tense verbs like alitufundisha.

Yes, it is one word, but in Swahili many nouns do not change form between singular and plural.

Methali can mean:

• a proverb
• proverbs

The context tells you which one is meant. In this sentence, proverbs makes the most sense, because grandma is being described as someone who liked telling them in general.

In Swahili, adjectives usually come after the noun.

So:

• nahau mpya = new idiom
• literally: idiom new

This is normal Swahili word order.

Also, mpya agrees with the noun class of nahau, but in this class the form stays mpya.

Because Swahili does not use articles like English the, a, or an.

So:

• mwalimu can mean the teacher or a teacher
• nahau mpya can mean a new idiom or the new idiom, depending on context

English has to choose an article when translating, but Swahili usually leaves that idea to context.

Not always.

Bibi can mean:

• grandmother
• old woman
• sometimes a respectful way to refer to an older woman or lady

In this sentence, grandmother is the most natural interpretation.

Lakini means but, and leo means today.

Together they set up a contrast:

• Bibi alipenda kutuambia methali = Grandma liked to tell us proverbs
• lakini leo mwalimu alitufundisha nahau mpya = but today the teacher taught us a new idiom

So the sentence contrasts what grandma used to do with what the teacher did today.

Yes, Swahili often allows some flexibility with time words like leo.

For example, these are possible:

• Lakini leo mwalimu alitufundisha nahau mpya
• Lakini mwalimu alitufundisha nahau mpya leo

The version in your sentence puts leo earlier, which helps emphasize today as the contrast point.

They are related, but they are not the same.

• methali = proverb
  A fixed saying that expresses general wisdom, like Haste makes waste.

• nahau = idiom
  A fixed expression whose meaning is not fully literal, like kick the bucket in English.

So the sentence contrasts two kinds of figurative language: proverbs and idioms.

The overall order is quite similar to English:

• Bibi = subject
• alipenda = verb
• kutuambia = infinitive phrase
• methali = object

Then:

• lakini = but
• leo = today
• mwalimu = subject
• alitufundisha = verb
• nahau mpya = object + adjective

A very literal unpacking would be:

• Grandmother liked to-tell-us proverbs, but today teacher taught-us idiom new.

That shows how Swahili keeps object markers inside the verb and usually places adjectives after nouns.