Zozie's actual fraction calculations were solid once she knew what operation to use. She picked up multi step problems quickly when we broke them into smaller pieces first, and by the end of the session she was reading through a question and identifying the right operation on her own, without me prompting her.

She still hesitates at the start of a word problem, especially when the numbers aren't given in a straightforward order or when there's extra information in the question that isn't needed for the calculation.

Jasmine was comfortable with single digit addition and subtraction and completed the warm-up questions with confidence, which provided a good starting point for introducing two digit methods. She followed the step by step explanation of the column method well and was able to replicate the process in straightforward examples without carrying or borrowing. Her attitude throughout the session was positive and she was willing to ask questions when she was unsure, which helped the session run smoothly.

The concept of carrying in addition and borrowing in subtraction proved to be the main challenge of the session. Jasmine found it difficult to keep track of the carried digit and occasionally forgot to add it into the tens column. Borrowing in subtraction was particularly confusing, as understanding why the tens digit decreases by one requires a solid grasp of place value, which will need further reinforcement. While Jasmine could follow the procedure with guidance, applying it independently and consistently under slight time pressure was still a challenge by the end of the session. More practice across a variety of question types will be needed before the logic feels fully secure.

Zozie engaged reasonably well once the session was underway. She was able to understand the basic concept of what a fraction represents and could correctly identify the numerator and denominator. Comparing fractions with the same denominator came relatively naturally to her and she was able to work through these questions with growing confidence by the end of the session.

Zozie showed some initial reluctance when introduced to the topic, as she does with new mathematical concepts. She found it difficult to remember the terminology and needed reminders about the difference between numerator and denominator throughout the session. Comparing fractions with different denominators was introduced briefly but not yet consolidated, as more groundwork was needed first.

Zozie showed noticeable improvement in her willingness to engage compared to the first session. She grasped the idea of equivalent fractions well and was able to generate them correctly with some guidance. Addition of fractions with the same denominator was handled confidently, and she was beginning to apply the common denominator method to addition problems by the end of the session.

Finding the lowest common denominator remained a challenge, particularly when the numbers involved were larger. Zozie's recall of times tables was inconsistent, which slowed down the process of finding common denominators. She also found it difficult to remember the steps in the correct order without being prompted, suggesting the method needs further reinforcement before it becomes automatic.