One way of framing it is that, information is about data like sensory inputs, and knowledge is about salience and situating yourself and other mental objects in relation to the information.
Observing a cow, we have images which we process and abstract from (eg small vs far away, it's blue vs white but in shadow) - this is a far more complex business than we typically realise, with around 1/3 of the brain occupied with visual and spatial processing alone.
Then we have non-conscious integration, into appearances of solid objects, in spatial relation to us. This corresponds with Aristotle's common sense, and the faculty of Manovijnana called the ayatana of mental consciousness in Buddhist thought.
Then we abstract mental tokens (eg human vs manikin, stranger or specific person, and attributes like number of legs). These abstractions form reused groups of phenomena which are defined by language use. Non-language using animals like octopuses and bears can clearly do a lot of reasoning, but it seems non-linguistic animals can only use subitism to experience numbers, limited to recognising small numbers in immediate awareness; whereas language users can count and do math operations (like the parrot Alex, the most sophisticated animal math user yet known, far better than any ape). This corresponds to Aristotle's imaginative faculty, and the seventh in the Mahayana elaboration of sense-gates. The idea we need language for advanced abstraction and inference is captured in The Private Language Argument developed from Wittgenstein's work - see his points about whether we experience pain privately in his beetle-in-a-box argument. I'd also relate this to the idea conscious awareness is a mental Global Workspace where conscious integration of mental objects and events happens.
Then in Aristotle's picture is nous, active intellect. In Mahayana thought the final eighth consciousness corresponds with the memesphere or substrate-independent concepts, comparable to Plato's accessing logos through the faculty of reasoning. In this realm is the concept of being a self, and inferences derived from intersubjectivity in general, the source of advanced or elaborated systems of inference.
Aquinas recognised four internal senses: the common sense, imagination, vis cogitativa, and memory. Avicenna argued for five internal senses: the common sense, imagination, fantasy, vis aestimativa, and memory. Descartes and Hobbes recognised 'five wits', complementing the five external senses.
Aristotle's picture of a tripartite soul, pictured the vegetative soul as supervened over by the animal soul, and the animal as supervened on by the rational soul. In this picture the supervening layer can be a cause on the supervened layer, but in reverse causes are optional not necessary. This implies either the mental (subjectivity) is fundamental as in pansychism, as in idealism, or the 'mind only' Buddhist Yogacara philosophy. Or, that the mental is emergent from the physical, forming supervenient explanatory layers, where phenomena are grouped lumped or chunked with a mental shorthand that grants them causes in their own terms in a layer of similar groups (eg of human character and intentions, far more efficient a predictor than knowing a humans atomic states even if they could give more complete predictions).
Hostadter's Strange Loops picture relates human cognition to there being something important about the point where a layer of abstraction can include a self-model, because then feedback and self-reference can occur, and relationships between layers of explanation and situating, can be organised into tangled hierarchies that can loop back on themselves - solving the problem face by a Foundationalist picture of knowledge summarised in Munchausens Trilemma, with a Coherentist picture of an adapting and growing basis. Discussed in more detail here, and related to intersubjectivity (extended our minds by seeing each other's points of view): According to the major theories of concepts, where do meanings come from?
Vervaeke's picture that knowledge is about salience landscapes that give us cognitive grip is useful too I think. We arrange information in relation to ourselves, that situates us to information, and this helps enable the kinds of tasks we want to do. That relates to Wittgenstein's language games:
"In this sort of predicament, always ask yourself: How did we learn
the meaning of this word ("good", for instance)? From what sort of
examples? In what language-games? Then it will be easier for you to
see that the word must have a family of meanings."
-Wittgenstein, in Philosophical Investigations
I would relate mathematics specifically to abstraction from a shared experience of spatial geometry, so as getting it's apparent universality from necessarily shared experiences related to being in spacetime. Discussed here: The Unreasonable Ineffectiveness of Mathematics in most sciences I like the point that imaginary numbers represent rotations, which allows them to capture amplitude and phase. More on math as a ladder from specific to abstract here: What do we explictly refer to in mathematical expressios
So in summary, I would say we observe information, and abstract knowledge from that by relating or situating ourselves to it (science focuses on getting the best observations, and we can understand it's distinct contribution to knowledge-making from that). Situating ourselves, can involve creativity, like deciding what kind of person we want to be in relation to inferences about the future; or by how we assemble our ideas into an inferred meaning-cosmology; so knowledge-making can be creative. See Popper's points about how hypothesis generation in science cannot be automated, it must involve creativity - we get the best information, but then we situate ourselves eg geocentric or heliocentric model.
Consider also the relationship of knowledge to wisdom, discussed here: Wisdom and John Vervaeke's awakening from the meaning crises?