Unit rate
Definition: A rate expressed for one unit of another quantity.
Example: Six notebooks cost $18, so the price is $3 per notebook.
Watch out: $18 for six notebooks is a rate, but it is not yet expressed per one notebook.
Describe prices precisely in math, then distinguish genetic information from observable traits in science.
I can calculate a unit rate, identify a constant of proportionality, and distinguish alleles, genotypes, and phenotypes so I can explain patterns accurately.
I know I am successful when I can explain all five terms, use them in new examples, and answer at least 3 of 4 exit questions correctly.
Definition: A rate expressed for one unit of another quantity.
Example: Six notebooks cost $18, so the price is $3 per notebook.
Watch out: $18 for six notebooks is a rate, but it is not yet expressed per one notebook.
Definition: The fixed value k in a proportional relationship y = kx; for x ≠ 0, k = y ÷ x.
Example: At $3 per notebook, cost y = 3x and k = 3 dollars per notebook.
Watch out: A $2 starting fee plus $3 per notebook gives y = 3x + 2, which is not proportional.
Definition: One of the different versions of a DNA sequence at a particular location; here, a version of a gene.
Example: In a simplified plant model, A and a label two alleles of one gene.
Watch out: A whole organism is not an allele.
Definition: The allele combination an organism has at a particular gene or location.
Example: Aa describes a genotype in a simplified two-allele model.
Watch out: Purple flower color describes a phenotype, not an allele combination.
Definition: An observable or measurable characteristic influenced by genetic makeup and sometimes the environment.
Example: Flower color or measured plant height can be phenotypes.
Watch out: The written allele combination Aa is a genotype, not a phenotype.
Two notebooks cost $6; four cost $12; six cost $18. Dividing cost by notebook count always gives 3. The unit rate is $3 per notebook, and the constant of proportionality is 3 dollars per notebook: y = 3x.
A and a are alleles of one gene. In this model, AA and Aa plants have purple flowers; aa plants have white flowers. AA, Aa, and aa are genotypes. Purple and white flower color are phenotypes.
Model limit: This is an invented single-gene teaching model, not a rule for all traits. Many traits depend on multiple genes and environmental conditions. An uppercase letter does not mean an allele is stronger or more common.
Choose an answer for each question. Check the explanations and retry.
Ten identical seed packets cost $25 with no extra fee. In the plant model above, one plant is AA and another is Aa. Explain the price per packet, write a proportional cost equation, and compare the plants’ genotypes and flower-color phenotypes.
Sentence frame: “The unit rate is ___, so y = ___. The genotypes are ___, but the flower-color phenotypes are ___.”
$25 ÷ 10 = $2.50 per packet, so y = 2.5x. AA and Aa are different genotypes with the same purple-flower phenotype in this model.
Complete all four questions. You can review feedback and retry. The summary appears after you submit; it does not submit a grade.
Allow about 15 minutes: 5 for vocabulary and models, 5 for practice and application, 5 for the exit check. Ask students to explain why a starting fee breaks proportionality and why two genotypes can share a phenotype.
Practice: 1 $3/notebook; 2 4 dollars/item; 3 allele; 4 Aa; 5 white flower color. Exit: 1 $3/notebook; 2 y = 5x; 3 allele combination; 4 different genotypes, same phenotype.
Math vocabulary supports CCSS Grade 7 Ratios and Proportional Relationships, 7.RP.A.2. Science definitions are grounded in the National Human Genome Research Institute glossary: allele, genotype, and phenotype.