Final answer:
Olivia begins teaching grouping by tens and ones using d. concrete objects, then abstract symbols, and ends with mental representations, matching the learning process from tangible to mental internalization.
Step-by-step explanation:
When Olivia is teaching her students to group by ones and tens, she starts with d. concrete objects, then uses abstract symbols, and finally moves to mental representations.
This sequence follows educational and cognitive development theories that suggest children learn best through hands-on experiences, before moving to more symbolic representations and then to operations they can perform mentally.
Starting with concrete objects allows students to physically manipulate and see the grouping in a tangible form.
As they become more comfortable with the concept, they can move on to abstract symbols such as numbers and digits, which represent groups of ones and tens without the need for physical objects.
Lastly, mental representations involve students internalizing and visualizing the grouping in their mind, without the need for physical or visual aids.