In my prealgebra classes I have used my own curriculum for a number of years, but it seemed that I was always re-writing or re-sequencing. This year I decided to try out the Illustrative Mathematics curriculum for Grade 7, and let someone else make the decisions for me. So far I think I put myself in the right hands. These are good problem-based units, they stretch the students in ways that I realize I have been shying away from, and they develop multiple threads of skills at the same time. Sometimes that sequencing is obvious, sometimes more subtle.
The first decision I made for myself was in fact a mistake: I was concerned about time for some of my own topics and activities that I wanted to keep, and I thought I could do without Unit 1. Scale drawings and Proportional Relationships seemed like they would be covering similar ground, and scale drawings weren’t as critical a topic as proportions. But the two units together develop the two kinds of relationships you find in proportional relations:
The first decision I made for myself was in fact a mistake: I was concerned about time for some of my own topics and activities that I wanted to keep, and I thought I could do without Unit 1. Scale drawings and Proportional Relationships seemed like they would be covering similar ground, and scale drawings weren’t as critical a topic as proportions. But the two units together develop the two kinds of relationships you find in proportional relations:
Scale factors are the relationships between pairs of ratios and the constant of proportionality is the relationship across each equivalent ratio … which stays constant for each row of the table. Unit 1 develops the idea of scale factors and Unit 2 applies scale factors to tables and adds the constant of proportionality. So they really build nicely on each other.
Fraction skills are also a concern of mine (more on that later) and Unit 1 is an important part of that sequence as well. In Unit 1, the students multiply by unit fractions and are reminded of the equivalence of dividing by 4 and multiplying by ¼. They also find 3/5 of a number or 2.5 of a number, and are reminded of reciprocals. In both Unit 1 and 2 IM ventures into fractions gently, introducing a skill with whole numbers, then using numbers that the students can make sense of mentally or with relatively easy calculations. I have tried to do that myself in the past, but it is nice to have the details thought through for me, and so far it has worked well for my students.
I have been able to make things work this year with a little extra time and attention to scale factors, but I will be using Unit 1 next year.
Fraction skills are also a concern of mine (more on that later) and Unit 1 is an important part of that sequence as well. In Unit 1, the students multiply by unit fractions and are reminded of the equivalence of dividing by 4 and multiplying by ¼. They also find 3/5 of a number or 2.5 of a number, and are reminded of reciprocals. In both Unit 1 and 2 IM ventures into fractions gently, introducing a skill with whole numbers, then using numbers that the students can make sense of mentally or with relatively easy calculations. I have tried to do that myself in the past, but it is nice to have the details thought through for me, and so far it has worked well for my students.
I have been able to make things work this year with a little extra time and attention to scale factors, but I will be using Unit 1 next year.
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