6th Grade
What Are Equivalent Ratios?
{
"voice_prompt": "",
"manuscript": {
"title": {
"text": "What Are Equivalent Ratios?",
"audio": "What are equivalent ratios?"
},
"description": {
"text": "Equivalent ratios are two or more ratios that show the same relationship between parts, even if the numbers are different.",
"audio": "Equivalent ratios are two or more ratios that show the same relationship between parts, even if the numbers are different."
},
"scenes": [
{
"text": "Knowing about equivalent ratios helps you scale things up or down while keeping the same relationship between amounts. This is super useful when you're baking, reading maps, or even in engineering!"
},
{
"text": "Let’s understand equivalent ratios by making some juice. Start by mixing 1 cup of syrup with 2 cups of water. This gives you a tasty drink with a ratio of 1 to 2. Which you can also write as the fraction one half. For every 1 cup of syrup, there are 2 cups of water.",
"latex": "\\text{Syrup: 1 cup, Water: 2 cups} \\quad \\text{Ratio: } \\frac{1}{2}"
},
{
"text": "Now try using 2 cups of syrup and 4 cups of water. Will the juice still taste the same? Yes! Because the ratio is still 1 to 2. You just made more of it.",
"latex": "\\text{Syrup: 2 cups, Water: 4 cups} \\quad \\text{Ratio: } \\frac{2}{4} = \\frac{1}{2}"
},
{
"text": "See how multiplying both the amount of syrup and water by 2 keeps the same ratio? The relationship stays the same — that’s what makes it an equivalent ratio.",
"latex": "\\frac{1}{2} \\times \\frac{2}{2} = \\frac{2}{4} = \\frac{1}{2}"
},
{
"text": "Let’s try tripling the recipe. 1 times 3 is 3, and 2 times 3 is 6. So now you have 3 cups of syrup and 6 cups of water — a 3 to 6 ratio. That’s also equivalent!",
"latex": "\\frac{1}{2} = \\frac{2}{4} = \\frac{3}{6}"
},
{
"text": "Let’s pause and picture the juice in measuring cups. Can you see how the balance between syrup and water stays the same in each one?",
"latex": "\\text{Visual: Measuring cups labeled 1:2, 2:4, and 3:6 showing equal proportions}"
}
],
"outro": {
"text": "Equivalent ratios are two or more ratios that show the same relationship between parts, even if the numbers are different.",
"audio": "Equivalent ratios are two or more ratios that show the same relationship between parts, even if the numbers are different."
}
}
}
en_6_nq_equiv_ratios.jsonOpen with Text Editor Share
Displaying en_6_nq_equiv_ratios.json.