Question

make groups that represent the same situation. some groups will be missing a representation.
a cake baking kit says:
28 tablespoons of
sugar is provided for 2
cakes. for each cake,
save 4 tablespoons of
sugar for frosting and
put the rest in the
batter.
rikus mom buys 4
cinnamon buns, one
per family member.
each person also gets
$2 to spend on a
beverage. the bill is
$28 total.

Explanation:

Step1: Analyze cake baking scenario

Total sugar: 28 tbsp. 2 cakes, each saves 4 tbsp frosting sugar. Let $x$ = sugar per cake batter. Total per cake: $x+4$. For 2 cakes: $2(x+4)=28$. The bar model with two $x+4$ blocks matches this equation.

Step2: Analyze Riku's bill scenario

4 family members. Each gets 1 bun ($x$) + $2$ beverage. Cost per person: $x+2$. 4 people: $4(x+2)=28$, which expands to $4x+8=28$, or matches the bar model with four $x+2$ blocks.

Step3: Match remaining elements

The bar model with four $x$ blocks plus a 2 does not fit, but the equation $4x+2=28$ is not a match for either scenario, while the four $x$ block bar does not align. Correct groupings:

1. Cake baking: $2(x+4)=28$ + bar model with two $x+4$ segments
2. Riku's bill: Bar model with four $x+2$ segments
3. Unmatched: Bar model with four $x$ segments + $4x+2=28$ (these do not fit either scenario)

Answer:

1. Cake Baking Group:

• Situation: A cake baking kit says: 28 tablespoons of sugar is provided for 2 cakes. For each cake, save 4 tablespoons of sugar for frosting and put the rest in the batter.
• Equation: $2(x + 4) = 28$
• Bar Model: The model with two segments labeled $x+4$ totaling 28

1. Riku's Bill Group:

• Situation: Riku's mom buys 4 cinnamon buns, one per family member. Each person also gets $2 to spend on a beverage. The bill is $28 total.
• Bar Model: The model with four segments labeled $x+2$ totaling 28

1. Unmatched Pair:

• Equation: $4x + 2 = 28$
• Bar Model: The model with four segments labeled $x$ plus a 2 totaling 28 (does not correspond to either scenario)