atui hi ha, kodomotati wo yuugu no tikaku no hikage de yasumasemasu.

Because 暑い is an i-adjective, and when an i-adjective directly modifies a noun, it stays in its plain form:

• 暑い日 = a hot day / hot days
• 寒い朝 = a cold morning

The -く form is used for other grammar patterns, not for directly modifying a noun.

は marks 暑い日 as the topic: as for hot days or on hot days.

So:

• 暑い日は、... = On hot days, ... / As for hot days, ...

It sets the situation or condition under which the rest of the sentence happens.

Japanese nouns usually do not show singular vs. plural the way English does.

So 暑い日 can mean:

• a hot day
• hot days
• on hot days

The exact number is understood from context.

子供 means child / children.
たち is a common plural-like marker used especially for people.

So:

• 子供 = child / children
• 子供たち = children

However, たち is not exactly the same as English plural -s in every case. Japanese often leaves nouns unmarked, but たち makes it clearer that we are talking about a group.

This is because 休ませます is the causative form of 休む.

• 休む = to rest
• 休ませる / 休ませます = to make someone rest / let someone rest

In causative sentences, the person being made or allowed to do something is often marked with を, especially with intransitive verbs like 休む.

So:

• 子供たちを休ませます = make/let the children rest

Here, 子供たち is the one being caused or allowed to rest.

It can mean either, depending on context.

The causative form in Japanese often covers both:

• make someone do something
• let someone do something

In this sentence, because the action is kind and protective, the natural meaning is often closer to:

• let the children rest
• have the children rest

But grammatically, it is still the causative form.

遊具 means playground equipment or play equipment.

Examples include things like:

• swings
• slides
• climbing structures

So 遊具の近く means near the playground equipment.

近い is the adjective near.
近く here is a noun-like form meaning nearby area / vicinity / near.

So:

• 近い公園 = a nearby park
• 公園の近く = near the park

In this sentence:

• 遊具の近く = near the playground equipment

This 近く works very naturally with の.

This is a noun chain, and each の links one noun to the next.

Break it down like this:

• 遊具 = playground equipment
• 遊具の近く = the area near the playground equipment
• 日陰 = shade
• 遊具の近くの日陰 = the shade near the playground equipment

So the second の connects 近く and 日陰:

• the shade of the nearby area of the playground equipment
• more naturally: the shade near the playground equipment

Japanese often stacks nouns this way.

で marks the place where an action happens.

Here, the action is resting:

• 日陰で休ませます = have/let them rest in the shade

So で tells you the location of the action.

Compare:

• 公園で遊ぶ = play in the park
• 部屋で休む = rest in the room

Because this sentence focuses on where the resting happens, not where someone moves to.

• で = location of an action
• に = destination, existence, or specific point in time

So:

• 日陰で休む = rest in the shade
• 日陰に行く = go to the shade

If the sentence were about moving the children into the shade, に might appear with a movement verb. But here the main action is resting, so で is the natural choice.

Japanese often leaves out the subject when it is understood from context.

So this sentence does not explicitly say who is making or letting the children rest. It could be:

• a teacher
• a parent
• a caregiver
• a coach

The subject is omitted because Japanese frequently relies on context instead of stating it directly.

休ませます is the polite non-past form.

This makes the sentence polite and neutral, which is common in:

• explanations
• instructions
• written descriptions
• everyday polite speech

The plain form would be:

• 休ませる

So:

• 休ませます = polite
• 休ませる = plain

Yes.

• 日陰 specifically means shade, especially a place protected from the sun
• 影 more often means shadow

In a sentence about hot days and resting, 日陰 is the natural word because it refers to a cool shaded place.

So 日陰で休ませます strongly suggests protecting the children from the heat by having them rest in the shade.