der Haufe
heap
A disorderly collection or pile of things lying loosely on top of one another.
Auf dem Schreibtisch lag ein großer Haufe Papiere.
There was a large heap of papers on the desk.

heap / bunch
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heap
A disorderly collection or pile of things lying loosely on top of one another.
Auf dem Schreibtisch lag ein großer Haufe Papiere.
There was a large heap of papers on the desk.

'Der Haufe' belongs to the word family of 'häufen' (to pile up, to accumulate) and 'die Anhäufung' (accumulation). A 'Haufe' is the result when things or people accumulate.
Im Laufe der Woche häufte sich die schmutzige Wäsche im Korb.
Over the course of the week, the dirty laundry piled up in the basket.
The idiom 'etwas über den Haufen werfen' means to completely change or discard a plan, an idea, or an order. It is very common in everyday language.
Wegen des starken Regens mussten wir unsere Pläne für das Picknick über den Haufen werfen.
Because of the heavy rain, we had to throw our plans for the picnic out the window.
The word 'Haufe' usually describes a disorderly or chaotic collection. It often has a slightly negative or informal connotation, especially when used for people or messy things.
Auf seinem Schreibtisch türmte sich ein riesiger Haufe alter Zeitungen.
A huge heap of old newspapers was piling up on his desk.
In the meaning 'Kothaufen' (pile of feces), the word is very colloquial and is often considered crude or impolite. It is usually used in connection with animals, especially dogs.
Der Gärtner ärgerte sich über den Hunde-Haufen auf seinem Rasen.
The gardener was annoyed about the dog poop on his lawn.
amount / crowd
'die Menge' and 'der Haufe' can both refer to many things or people. 'die Menge' is neutral and fits when you want to emphasize the number or size. It can also mean a large group of people. 'der Haufe' sounds much more disorderly: things are lying all mixed up, or people are standing together without any clear order. Learners may confuse the words because both can express 'a lot'. As a guide: for numbers, quantities, and neutral groups, use 'die Menge'; for something disorderly or colloquial, 'der Haufe' is more suitable.

Neben dem Schreibtisch liegt ein Haufe alter Zeitungen.
There is a heap of old newspapers next to the desk.
Für die Suppe brauchen wir eine größere Menge Gemüse.
For the soup, we need a larger amount of vegetables.